Decision 2012, President Barack Obama re-elected to a second term. Elizabeth Warren wins a decisive U.S. Senate seat, becoming the first female U.S. senator for Massachusetts. BUTV News at Noon, concluding our election coverage special, Decision 2012. I'm DD Sun. And I'm Chris Costa. As you just heard, our lead at this hour, a Senate first from Massachusetts and a re-election win for President Obama after voters made their choices at the polls. GOP nominee Mitt Romney arrived to the polls this morning to cast his ballot in one of the tightest presidential races in U.S. history. Let's take a look at the final electoral college results from last night. President Obama won 26 states, earning himself 303 electoral votes. Governor Romney took 23 states, including Indiana and North Carolina, both of whom voted for Obama in 2008. Today is election day and polls are active. Several voters have showed up to cast the ballot. I voted for Barack Obama for the second term. What can we expect starting, I guess, day one, you know, the second term of Barack Obama? I think a much less tentative Barack Obama. The crowd exploded with cheers and applause last night. After it was announced, Elizabeth Warren would be headed to the U.S. Senate. The Massachusetts Senate seat is of importance on a national scale. For Decision 2012, I'm Yanni Carter. For me, it was an honor to carry your flag, even if for a little while. Scott Brown's Watch Party did not end as anticipated. Who will win the seat held by Barney Frank for over 30 years? Will it be Joe Kennedy, who got his start serving in the Peace Corps, graduated Harvard Law and was an assistant DA? New Hampshire's four electoral votes could be the determining factor in tonight's election. For Decision 2012, I'm Brittany Exum. Great moments, unfortunately. I blew it. In the end, too bad. As I say to people, I owe you all an apology. If I'd beaten Bush one, you'd never heard of Bush two. We wouldn't be in this mess. Regrets. Over the past dozen presidential elections, candidates from the state of Massachusetts certainly have some.


Okay, let's get started. Okay, we have a question from Lifestyle evangelism, so it depends on when the session was let me just check, you know, you would have got a schedule. Okay, John Paul So Okay, I hope that answers the question Okay Right. Okay. Let's let me just pray and get started. Okay Let's pray Father, we we thank you for this day. We thank you for this session Lord, I just want to thank you for each and every person who is connected and I just pray God Lord for their the season that they are in Lord and the Lord in their special journey with you in their walk with you father God I pray that This course will be a blessing to them. I pray God that you will lead us To discover my truth. Oh God that you've kept for us father God and Holy Spirit I we ask that you would reveal these so that we might Lord receive it and walk in it or God and We commit this time into your mighty hands and we pray that you would speak to us and you would write your word Upon our hearts as only you can We just want to thank you. We give you all the praise and all the glory in Jesus matchless name. We pray man, man Okay If you have your notes, you know the notes for the Holy Spirit class it's in the classwork section Which which is there in the Know if you've joined in if you've connected through the phone or through your Laptop, you'll notice it in the classwork section. You can download that. It's a PDF You can refer to that. So we're going to be looking at that and then going through those notes, right? so, let me just present I know just to give you an overview of what the course is about and Yeah, I hope you can see my screen. It's just coming up Right, okay, so Oops So Holy Spirit We will start by so this course is about the person And the ministry and the working of the Holy Spirit the person and the work of the Holy Spirit So we're going to be looking at several scriptures. So it'll help if you keep your Bible Handy, right? So we're going to be starting by looking at the Trinity And we're going to look at the person of the Holy Spirit the work of the Holy Spirit in the Old Testament and The work of the Holy Spirit in the New Testament the work of the Holy Spirit in the life of Jesus in the book of Acts in church history Towards a sinner in a believer's life sorry and And then we also go down to The gifts right the back the anointing of the Holy Spirit The baptism in the Holy Spirit the gifts of the Holy Spirit, so we're going to be looking at each of these You know, we're gonna have an Overview of each of these gifts how these gifts function and so on and then you want to look at Foundation for release of these gifts ministering in these gifts and and so on then we're going to look at anointing What is it? What does what is called the anointing and and and also the minister gives And how the anointing of Holy Spirit functions on specific these ministry gifts and so on and Yeah, and then we'll finish with the names of the Holy Spirit and symbols of the Holy Spirit So it's quite interesting quite exciting So this is how the grading is we will have four quizzes during the course of this semester and Typically, this will be at the end of every month so end of August September October and November and This will be great. It's so 25% of each of the scores will be taken and It'll be added to the final score, right and you know, this is the Table for the grades There's some recommended reading actually some of these are already there in your In our textbook, we'll be adding it to your textbook section Okay, so Yeah So that's that's just a overview of how what we're going to do and how we're gonna do the course. Okay Okay, so Lou Bega Class code for your I think you're talking about lifestyle evangelism So you basically you need to sign in first and then you will get the Class just like how you did for this course and then you can have to click on the link in order to get into so we'll Probably one of our students will help out. Do you all have the? What's that do? Are you all part of a what's that group has it not been not started yet? Okay? Okay, so Yeah, so we'll we'll we'll try and sort that out after the class Right, you can get in touch with the maybe in some of us here or you can try to Admin at public college apc public college dot org and we'll get that sorted. Okay, so let's let's move on Okay, first of all we need to understand You know something about about the way God is Is he said them done the the character the very nature of God the fact that he is a Triune God right what makes God God is the fact that he is Omni present which means he's present everywhere He is all-knowing or omniscient and he is also all powerful or omni omnipotent So that's what makes him God that's what makes God God and When we look at scripture, we see God being presented to us as a triune God That he is God the father the son and the Holy Spirit You know just like how we when you look at the Bible you see that the Bible doesn't really explain and and And say okay build up a case for God it just starts by saying you know Genesis 1 1 in the beginning God Okay, so in the beginning God this is it Okay, God is in other words God is that God created and this is how he created. That's how it starts So we see God being presented as a triune God that he's the father the son and the Holy Spirit So it's one God existing in three persons But in essence he is One God So it's not he's not three different gods Like some of the other world views are he's not three different gods, but he is one God one in essence but existing as three persons now as Much as we try to explain to the you know We can make it very simple and very simplistic ways people have tried to explain it and saying oh It's like water I he's in and steam and but you know everything falls short of really explaining right to the fullest extent the Trinity Because the thing is that as much as we try to explain and you know dive in and and see The possibilities of how he is and who he is as a as a triune God At the end of the day, you know the whole Aspect of God being a triune God is a mystery for us. Okay, because we are finite beings We are finite beings now. We cannot be omnipresent. We can't be present in you know Except in one place and we can't be present in multiple places at the same time. So for us the aspect of God being Omnipresent itself is Something that we cannot wrap our minds around. Yes or no Yeah, the fact that God is speaking to me right now and the fact that God could be speaking to you know 2024 of you at the same time having a parallel conversation Itself is something that I cannot wrap my mind around Right, so I just imagine the entire You know the body of Christ the global body of Christ that God is who he is to them helping them Revealing things to each and every person So that's who he is right. He is Omnipresent and he's all-knowing infinite wisdom and so on so At the end of the day, we know that this whole thing of God being a triune God is the mystery and we will have Eternity to find out Okay, we're gonna spend eternity finding out more and more about this triune God So I'm not going to go into explaining Trinity, but we're going to look at scripture and Several places in scripture where we see these this triune God where we see where scripture gives us the picture that hey You know and gives us a picture of the triune God, right? So we're going to look at several verses Okay, first off The word Trinity is not there in scripture Okay, so it's a theological construct in the in the sense that it's a word which people use or theologians used to explain this triune God So the word Trinity is not there.  Yes, it is definitely not there It's just a word to explain Like the character of the nature of God, right? Okay, so let's look at some scriptures Which give us the picture of the triune God? Okay When we look at creation itself If you have your notes, you can just follow in your notes and that'll be great When you look at creation itself Genesis chapter 1 the verses that we just read Genesis 1 verses 2 and 3 so it Talks about let me just put the verse here. Okay, it talks about The fact that earth was without form and void darkness was on the face of the deep and The spirit of God was hovering over the face of the waters spirit of God was hovering over the face of the waters Spirit of God, obviously the Holy Spirit and verse 3 says then and then God said let there be Light and there was right so it's referring to so two different words are used there to refer to You know the spirit of God and to refer to and God said, right? We see Let me just read out those words in the beginning God so we see Elohim as as the word which is used there to refer to The God the father Elohim created and then when we look at the word the spirit we see that Ruach which means breadth so Ruach Spirit of God was over The waters right so we we see this so in creation we see both the father Elohim and we see This Holy Spirit Moving on the face of the waters. Yeah, so we see a parallel of that in Hebrews one here, so let's let's go to Hebrews one and Let's look at a few verses here. Okay, Hebrews one says God who at various times and in various Ways spoke in time pass to the fathers by the prophets has in these last days spoken to us by his son Whom he is appointed heir of all things through whom also he made the worlds. Okay, so So in Genesis the verses that we read versus two and three we see the we see God being present there We see the Holy Spirit Brooding over the waters or hovering over the waters and here Hebrews referring to that account the writer of Hebrews says that you know that Through whom also he made the worlds that Referring to the Lord Jesus the son that God has spoken to us by his son and through the son He made the world who bring let's read verse three Hebrews one who being the The brightness of his glory and the express image of his person and upholding all things by the word of his power When he had by himself purged us and sat down at the right hand of the majesty on high and so on okay, and if you look at chapter two and And verse verses three and four Maybe verses two onwards for if the word spoken through angels proved steadfast and Every transgression and disobedience received a just reward. How shall we escape if we neglect so great a salvation? Which at the first began to be spoken by the Lord and was confirmed to us by those who heard him God also bearing witness both with signs and wonders With various miracles and gifts of the Holy Spirit according to his own Well, so we see the father being mentioned there We see because he's the one who has who at various times and spoke and various ways spoken times fast times past to To the fathers by the prophets That's what was one says and then we look at the world's being created by the son And then we when we look at chapter two and was us was for talks about how God Oh witness with signs and miracles and wonders By the Holy Spirit according to his own rules So we see you know the three persons of the triune God of the Godhead Being mentioned here right there right there when it comes to creation Okay, let's move on let's move on and look at another verse which these are you know different pictures that we see right there in In scripture which talks to about the triune God and it's important for us to Understand that acknowledge that if this is how God is presented right through Scripture father son and the Holy Spirit and just like how scripture assumes That you know in in the beginning God The same way the writer of scripture, you know, there's no there's no confusion Right in their minds This is how God existed and this is how God worked or exists and he works Right, so let's look at another scripture. We go to the gospel of Luke and here we read about the the birth and Some verses referring to that okay, so Luke chapter 1 and Let's look at verse 30 onwards. Okay, the angel said to her. So this is the angel which has come with the news of what's going to happen Angel Gabriel and said to her referring to Mary The angel said to her Do not be afraid Mary for you have found favor with God and behold you will conceive in your womb and Bring forth a son and she'll call his name Jesus He will be great and will be called the son of the highest and The Lord God will give him the throne of his father David and he will reign over the house of Jacob forever And of his kingdom there will be no end Then Mary said to the angel, how can this be since I do not know a man And the angel answered and said to her the Holy Spirit Will come upon you and the power of the highest will overshadow you Therefore also that holy one who is to be born Will be called the son of God Okay Verse 37 for with God nothing will be impossible so again we We see the God being mentioned that bring forth a son So the Lord Jesus being mentioned and how it's the power of the highest the Holy Spirit the work of the Holy Spirit and the power of the Holy Spirit which causes this conception and Which causes this miraculous work? Okay, so in the birth Referring this when we look at the scriptures referring to the birth of the Lord Jesus we see the picture of Trinity, okay Another scripture is in Matthew chapter 3 Okay, we're going to look at several verses and these Give us the picture of the Triune God So we're going to look at Matthew chapter 3 and this is you know, this is this is very dramatic and this is This is one of my favorite person. You just imagine the scene Matthew 3 and verse the whole Chapter is about John the Baptist coming and he's preaching repentance and he's He's baptizing people and very exciting, right? So he's talking about the Lord Jesus.  So can you just picture the scene? You know, just being there and Experiencing the whole, you know, this whole thing unfolding before eyes must have been very exciting must have been, you know full very dramatic and and and wonderful to see all that and Verse 16, okay, let's read from verse was 30 non words Then Jesus came from Galilee to John at the Jordan to be baptized by him Then John tried to prevent him saying I need to be baptized by you and are you coming to me? But Jesus answered and said to him permitted to be so now for thus it is fitting for us to fulfill all righteousness then he allowed him Look at verse 16 when he had been baptized Jesus came up immediately from the water and behold the heavens were opened to him and He saw the Spirit of God Descending like a dove and alighting upon him was 17 and suddenly a voice came from heaven Saying this is my beloved son in whom I am Well pleased, okay, Matthew 3 16 and 17 so so he comes out out of the water The heavens were opened Sees the Holy Spirit the Spirit of God descending upon him and alighting upon him like a dove and there's the voice Which is from heaven Obviously the voice of the father Because this is what he hears This is my beloved son in whom I am well pleased so the son is there There's a voice of the father and We see the Holy Spirit alighting upon the Sun like descending and alighting upon the Sun like a Wonderful picture of the triune God, you know different roles different functions, but one God One in essence and three in persons Okay, let's move on. Let's look at Another another scripture, which is right at the end of the Gospel of Matthew Matthew 28 and Let's look at verses 18 onwards. Jesus came and spoke to them saying all authority has been given to me in heaven and on earth Go therefore and make disciples of all the nations baptizing them in the name of the father and of the son and Of the Holy Spirit Teaching them to observe all things that I have commanded you and lo I and with you always even to the end of the age so the Lord Jesus In commissioning the disciples I'm commissioning his followers. He is sending them out. He's giving them a very important instruction He's saying go make disciples of all the nations all the people groups the ethnic go make disciples baptizing them in the name of the father the Sun and Holy Spirit So the Lord Jesus saying, you know, this is how you baptize them You baptize them and and we know that baptism is a symbol of the death burial and resurrection. It's symbolic We read about it in Roman chapter 6 as well.  It's refers to the internal change It's an external act that refers to the internal change and the Lord is saying this is how you will baptize If you baptize them in the name of the father Son and the Holy Spirit, you know, a beautiful picture again of the triune God Okay Is it exciting? Yeah, so, you know many times we we have in our minds right people ask, you know How can God be triune? How can maybe, you know, you're talking about three gods and it's not one God and so on but So in the in the mind or in the heart of the Lord Jesus the same thing, you know, he came to reveal the father He came to instruct us About God's heart, right? We see many parables the parable of the lost coin the lost son the lost sheep He came to show us the father's heart.  So you see that three are one and and the Lord Jesus very clearly Just declaring this is how you will baptize. Okay Let's look at another scripture in the plan of redemption Okay, so Humanity fallen humanity in God's plan of redeeming Fallen humanity redeeming people from sin. Okay, we we look at again the Trinity, let's look at Hebrews 9 okay, Hebrews chapter 9 and Verse 14 and Hebrews 9 and verse 14 Maybe I'll read from Verse 13 for if the blood of bulls and goats and the ashes of a high firm Sprinkling the unclean sanctifies for the purifying of the flesh. He's talking about the shadow talking about the time till the The you know till the cross How much more shall the blood of Christ who through the eternal Spirit Offered himself Without spot to God cleanse your conscience from dead works to serve the living God Okay, and goes on to say he's the mediator for this reason Let's read verse 14 again. How much more shall the blood of Christ who through the eternal Spirit? Offered himself without spot to God cleanse your conscience from dead works to serve the living God. So we see the Lord Jesus Christ being mentioned there his blood was shed and Talks about What made that possible through the eternal Spirit? He offered himself through the work of the Spirit He offered himself and the Holy Spirit was the power of God in resurrecting the Lord Jesus from the dead we read about that in the episodes as well and Through the Holy Spirit offered himself without spot to God again in the plan of redemption. We see The the the Trinity right we see the Triune God being mentioned at work there Each one doing different things right and we see that okay in the resurrection Okay, Romans chapter 8 and verse 11 Romans 8 and verse 11 Maybe some someone can read Romans 8 verse 11 and another person can read after that Romans 6 and verse 4 also Yeah anyone Romans I'll just Romans 8 11 Romans 8 11 But if the spirit of him who raised Jesus from the dead dwells in you He who raised Jesus Christ Jesus from the dead will also give life to your mortal bodies through his spirit Who dwells in you? Yeah, so if the spirit of him Who raised Jesus from the dead dwells in you he who raised Christ from the dead will also give life to your mortal bodies through his Spirit who dwells in you again. We see It's about talking about the resurrection and we see the father son and the Holy Spirit being mentioned here Okay, anyone Romans 6 and verse 4 We were therefore buried with him through baptism into death in Order that Jesus that just as Christ was raised from the dead through the glory of the father We too may live a new life Yeah, so here there's no reference to the Holy Spirit, but we see the the son and the father and when we read Romans 8 and verse 11 we see The spirit the father and Christ being mentioned there. So we see in the In the resurrection, right? The Triune God being mentioned there. Okay Okay, a few more few more scriptures and then we you know, we if there are any questions we'll take up Okay, so we see that the next one we see is in Acts chapter 7 now This refers to Stephen the first martyr for the sake of for the sake of his faith Acts chapter 7. Okay, so let's look at Acts chapter 7 and versus You know Acts chapter 7 we see that Stephen actually gives a wonderful sermon It gives a wonderful message starting from starting from Abraham and He goes on, you know, right through history and he talks about The Lord Jesus and and and the prophets whom they the fathers killed and so on now Verse 54 when they heard these things they were cut to the heart and they mashed at him with their teeth but he being full of the Holy Spirit gazed into heaven and saw the glory of God and Jesus standing at the right hand of God okay, and Said look I see the heavens opened and the son of man standing at the right hand of God so any any You know doubts or any questions or any clarifications Any any doubts about the deity of the Lord Jesus and also about the train God again, you know, we see more and more evidence here About the train God, right? Stephen himself was full of the Holy Spirit and then he sees heaven opened and then he sees the father and He sees the son standing at the right hand of the father. Okay, so we see We see that in Stephen's case where he was martyred and we see this mention. Okay, so in heaven Okay, revelation chapter 5 Revelation 5 and verse 6 Talks about the Lamb of God it talks about the spirits seven spirits or seven facets of the spirit of God and These two verses talk about that. Okay, let me read Revelation 5 verse 6 and I looked and behold in the midst of the throne and of the four living creatures So it's referring to the throne where God Sad and God says and in the midst of the elders to the lamb as though it had been Slain having seven horns and seven eyes, which are the seven spirits of God sent out into all the earth Okay, so so in the heavens also see the the picture of the train Okay, and several other scriptures that we can we can look at Which refer to the train God, you know, let's say if you look at John chapter 14 and verse 16 John 14 and verse 16 So this is John chapter 14 actually holds 14 15 and 16 It's a good place to go to Where we read about the Holy Spirit where Jesus actually teaches about the Holy Spirit and he says this is what The Holy Spirit will do, you know, he's going to do this. He's going to teach you. He's going to Remind you and so on so John chapter Chapter 14 15 and 16 a great place to study about the work of the Holy Spirit and the Lord Jesus himself teaching, right? so if you look at 14 and verse 15 He says if you love me keep my commandments and then verse 16 and I will pray the father and He will give you another Helper that he may abide with you forever So who is this he that he's referring to who's this help that he's referring to verse 17 The spirit of truth whom the world cannot receive because it neither sees and or knows him But you know him for he dwells with you and will be in you. I will not leave you often I will come to you. Okay, so Several other scriptures that are listed there in the notes. You can you can take a look at it But then so this is what we see, right? This is what we see. So scripture very Unapologetically very categorically Declaring the about the father the son of the Holy Spirit right and in the in the chapters to come you want to see how the Holy Spirit is God And how he is a person and so on so so any questions based on what we looked at just now any questions you can go ahead and you can either ask or you can put it on the chat and We'll try to look at that before we proceed further any questions Okay, so Here's another thing What I will also do at the end of the class is put up a Google sheet and put the link For that sheet in the classwork section Right below or right above the resource material section. So What you can do is whatever questions that you might have so each of you will have access To it. So whatever questions that you might have about the subject of the Holy Spirit Okay, now it could be about the questions that you always had Right, how can a person who has a Holy Spirit? How can he sin or how can a Holy Spirit in dwell a person who is sinful, you know Whatever questions that you might have had right through life. Okay, so you can just enter that just enter that enter type in the question there and and Hopefully by the end of this semester, we would have answered all those questions sufficiently Through the course through the classes the sessions and that we have we would have answered those questions And we'll look at we'll take a look at that sheet at the end of the class End of the semester and we'll see if there are any unanswered questions and we will try and address that as well. Okay, so Maybe the after 12 12 o'clock or maybe by 1 o'clock you can India time you can check that check your stream again or check the classwork section and this sheet will be there You can type in those questions. Okay? Here's a question. Can you kindly explain revelation 5 verse 6? Okay, the the the reason we go to revelation 5 6 was to just for us to know that the lamb of God Who is the Lord Jesus the lamb who took away the sin of the world? You know, he is then this is something that the John saw, right? the whole of revelation is based on the encounter that John had with the Lord Jesus, that's how it starts and And the message for the church or for the you know, what is to come The Lord Jesus asked him to write down. Right? So this is what he writes down. So revelation 5 He he continues to write about what he saw, right? And this is what he saw revelation 5 and 6 he looked and in the midst of the throne there were four living creatures and There were these so several people are mentioned there, right the living creatures the elders then you see the land and then Which having seven horns and seven eyes and seven spirits of God and you know always mentioned there so So this is what he Okay, this is what he saw, right? So So he's just explaining what he saw. Okay, I hope that helps now If you know if your question is Okay, what is what are those seven horns? What are those seven eyes and what are the seven spirits? If you I just want to request you to hold on a little You know just put it on pause We will address that, you know, we're going to be looking at how this Holy Spirit is the spirit of revelation wisdom and so on So we looking at the we'll be looking at Isaiah chapter 11 and where it talks about the seven characteristics or aspects of God and seven being number of completion Okay, so So we will be looking at that I hope that's fine Zalitoli, right? Yes. Yes, thank you. Okay And to be caught as a question. How does the Holy Spirit work in human beings? Amazing ways we cannot function as believers without the Holy Spirit, right? The Holy Spirit speaks to us He's the one who gives us the confidence that we are sons and daughters of God, you know, we might wake up one morning and feel that Hey, I feel so disconnected from God. I feel I feel all weird and I Feel I feel as if I'm not a believer. The Holy Spirit gives us the confirmation He gives us the confidence because that is what we read in Romans chapter 8. He actually Confirms to us that we are sons and daughters of the most high God It is cause of the Holy Spirit that we cry out above our father So that is just identity, you know, the identity that we have Holy Spirit gives to us all Enforces that Holy Spirit also teaches us the Lord Jesus says that he will he will teach you things to come He will guide you into all truth. The Holy Spirit kicks us of sin The Holy Spirit reveals scripture to us and so many other things, right? So he is the one who There he releases the gifts so we can minister effectively and so on so we're going to be looking at all that In the classes to come Okay, how is the Holy Spirit the the spirit of truth? okay, so John 14 17, okay, I'm just going to copy all these questions and You know, we'll put that in that sheet also, right? Just a minute, please Okay, okay, so Just a couple of questions, okay, how is Holy Spirit the spirit of truth of course one of the You know things that we see is that The Lord Jesus when he's talking about himself in you know in that same chapter He says that he's the way the truth and the life so one of the characteristics of God is that He's truth personified It's this very nature to If you want truth you look at God, right?  That's his nature So he will lead us into truth You know that gives us confidence that he will not lead us into error Which is the opposite of truth or he will not deceive us Lead us into deception, but he is the spirit of truth if you look at that worse He says he will dwell with you he will be with you and And and you will know him and he will be with you and so on and if you and we read through That was that chapter, sorry We see that Holy Spirit is the helper and he will teach you and he will cause you to remember He will he will remind you bring to remembrance all the things that the Lord Jesus has taught has spoken so this is the work of Holy Spirit, you know, he's a spirit of truth. So we know that he will not lead us into error He will teach us and where we when we know that he will teach us what is the truth He will not teach us something that is You know that is mixed with lies or something that is Okay So Josh, I hope that helps Another question is How can a sinning man still speak in tongues and move on the gifts and you know, Romans 11 29 We looked at the bus this morning in the mentoring session We see that the gifts and the calling are really walkable Okay, so if you look at the gift of tongue specifically It's given so that we will be Edified personally, you know 1 Corinthians 14 talks about he who speaks in a tongue edifies himself builds up himself There's a you know spiritual edification happening. There's something that is built in the inner man The gift of tongues also, you know, we speak the mysteries of God again 1 Corinthians 14 You know, we talks about how we speak the mysteries of God how they God has put this in place or release that for believers so that we can speak the mysteries of God that You know, so this a gift that he's given us so that we might be strong and overcome the things of the flesh Right, so that's a beautiful as if he's the gift of tongues is released to a person because he's reached a several You know a level of holiness. No, he is given to us and we might be struggling in different things But he's given to us that we might be edified Spirit of God comes and dwells us that we might be edified. He wants us to become like Jesus So that's a beautiful thing that we know struggling in several things, but the gift actually Is to bring us out of that To make us conform to the image of Jesus. He has come to do that He's come to teachers. He's come to feed us into truth and one of the ways he does that is by Release the gifts of tongues. We're going to study about the gift of learn for the gift of tongues as well So that's going to be exciting Okay Okay, I think Abu Bakr as the lifter his hand you have a question Abu Bakr. Okay, if you have a question you can put it in the chat I I'm okay. Another question. What is the familiar spirit and how does it come into a believer's life? Okay a familiar spirit is obviously a spirit it's it's a it's it's an evil spirit and We we see that I'll share the reference a little later but if I'm a spirit actually is familiar with our ways is familiar with you know the ways of You know, maybe our history and so on and and the work of the spirit is to actually Take us away from the destiny of God, right? Maybe create create some kind of Confusion so it's it's definitely opposite of the of what God wants or what the Holy Spirit wants for us So how does the Holy's how does the family spirit come into a life of the believer? Could be several ways. Maybe a person is deceived Maybe a sin Rebels against God. It could be several ways where we open up a doorway for the spirit to influence a person or you know, so it So we'll talk about you know more about the spiritual realm and the work of You know the work of the evil spirits and so on in another course But this is this is what I can share When does the Holy Spirit come in a believer Aradhana? So, you know, if you when you at the time Scripture says when we believe when we receive The Lord Jesus into our lives we are sealed by the Holy Spirit and he at that moment He comes and he indwells us He's the one who teaches us and shows us that we are children of the Messiah God So he indwells us. So if you have received the Lord Jesus as your Lord and Savior and and you are born again Then you can be sure that the Holy Spirit indwells you to teach you to to show you And also to confirm the things right that you are a child of God Right. Okay. How can a believer receive? Okay. That was your question. How about you? How can a believer receive the power of the Holy Spirit? Okay, so the power of the Holy Spirit? You know the Lord Jesus when he instructed his disciples, he Know they were already following the Lord. He told them to wait for wait in Jerusalem. He said that Wait in Jerusalem so that You know for you will have an encounter you will have an experience and we see that We see that in accept a one where We see that You accept a one and worse was five You have heard from me for June John truly baptized with water But you shall be baptized with the Holy Spirit not many days from now Okay, that accept a one was five Except a one was eight, but you shall receive power when the Holy Spirit has come upon you And you shall be witnesses to me in Jerusalem and in all Judea and Samaria and through the ends of the earth Okay, so so how does how can I believe I receive by simply by asking and receiving and And that's how it's as simple as that right? That's how we see The believers in the book of Acts they pray they were in prayer and they see first instance that we see the day of Pentecost they were all in prayer and Holy Spirit came upon them and they were in filled or filled with the Holy Spirit Okay, how did indwelling of the Holy Spirit differ from the baptism in the Holy Spirit? Okay? We're going to take a lot of time Looking at that. Okay that question Alessia. So Is there a difference? Let me just answer this. You know, is there a difference? Yes. Okay, and why is there a difference? Very quickly if you look at it One the indwelling is for our personal edification is for our personal growth. The Holy Spirit comes to help us Lead us out of sin into the truth The anointing or the baptism is for For for him to flow out of us It does not mean that you know, he will he will deal with stuff in our lives But it's to flow out of us like a river to touch lives to touch Touch others, you know, that's what we see right in Acts 1 8 You will receive power you will be witnesses and you will go and do these things you'll be witnesses in all these places So empowering us to be witnesses. So that's the Work or that's the reason objective of the baptism in the Holy Spirit. Okay Can I believe I have the Holy Spirit and the familiar spirit? Okay? Nicholson and once we receive the Holy Spirit, is it possible that you might leave because of sin? Okay? I think we are actually No progressing further Into what we are going to be looking at and it's 953. What we'll do is we'll take a break and Then we'll come back and we look at these questions as well. Okay, so you can Make a break a quick 10 minute break and then we'll come back. Thank you so much. Thank you, Pastor


If you hold on to bitterness, if you have the right to hold on to bitterness, Satan has the right to hold you in bondage. If you say, I have the right to be bitter, I have the right to be mad, of what they've done, of what, you know, they didn't do, I have a right.  If you have a right to be bitter, Satan has a right to keep you in bondage. You may have a right, you may have a reason, but you must lay that right down so that you can strip the devil from his right to keep you in bondage. Somebody say, man, you gotta lay the right down. When we get betrayed, when we get rejected at a young age, or maybe we have an absence of the father or mother in our life, or maybe we get abused. Or if you have in that household where your parents want you to really be like your neighbor's kid.  They don't mean to compare you, they just want to motivate you, because nothing else motivates you. And you live with that comparison and after a while, you know, it begins to hurt. You're not good enough and it begins to affect your life. And when you begin to develop that offense, when you begin to develop that bitterness, when you begin to allow that pain to come and settle in and you hold on to that. Instead of letting it go and saying, God, this hurts. God, this is not fair. God, what did I do to deserve this? But God, I refuse to be mad. I refuse to hold on to that. I refuse to hold on to that pain. I refuse to punish somebody. I refuse to live my life trying to make them pay. I refuse to live my life that I surrender it to you. Something happens.  He can hold you. You begin to move out and he begins to hold you and you snap out because he doesn't have a grip. He can't have a grip because the oil of the Holy Spirit is being released on you. The moment you release people. The moment you release people from the prison that they have caused, put themselves into because of what they've done to you or left undone to you. The Holy Spirit releases oil and Satan can no longer hold you. See, the problem many times that happens is that Satan holds us with sins, bondages, alcohol, pornography, cheating, lying. It could be a self-destructive behavior. It could be a reckless behavior. It could be other bondages that Satan holds us with. But the power for him is actually what we hold on to. And so what we do is we keep praying, Satan, get your hands off of me. And God is saying, get your hands off of stuff that belongs to him.   The person who drinks it dies when you and I take the poison of the devil.  It empowers Satan even more.


So, I am working as a data scientist currently in server security space and I am also a architect. So, actually ensure both the data science we build also works in production. So, to actually solve a real world problem. Talking about I guess real world, I guess all of us are working in data science field, somehow in enterprise solving the science problems. So, I guess everybody knows people come to us and say you are a, I think do solve this machine learning problem and give us some answers. So, they do come to us, but everybody knows we never get something called a label data. You don't get labels. Life is pretty hard for a data scientist. So, you have to turn to unsupervised techniques and when you use those techniques, it's most often they don't work straight forward. So, you have to then actually develop new things to make things work in real world. So, that's what the talk is about going beyond the normal basically. How do we solve the real world problems and figure out those unsupervised machine learning problems and finally get the thing working. So, I'll quickly go through the agenda. So, we have three main themes I want to cover. First, the motivation of data geometry. So, what do I mean by data geometry? How can we understand the geometry of a data? So, first I'll go through a analytical part. That's mostly theory. So, it would be short. Don't worry. I won't bore you much with theory. So, then would be the applied machine learning part. Where will we take a few examples, understand how does a manifold work, what are spaces and other stuff and work with examples. Last would be the technology part. How do the same things in big data? So, let me start with the motivation part. So, in big data I think the main concern is we have to discover interesting patterns and we have to uncover unknown knowledge from the data because we just thrown the data and just they come to us and say find some patterns, find something. So, typical ways doing clustering. Find some homogeneous groups like clusters basically. So, the homogeneity can be defined mathematically in terms of similarity or distance. So, I'll talk about them more detail later on. But if we summarize in short, if you have some notion of similarity like how to data objects are closer or farther, then we can actually use it to do two things. Create clusters which are more homogenous. As in collect or join those points which are very similar to each other based on some notion of similarity. Similarity could be anything, could be like some of their properties, could be they're referring to the same thing, anything. I'll just come to those in details in subsequent slides. Other part is basically separate apart the different clusters or the heterogeneity. So, these are the two main principles we want to basically obtain from a cluster analysis. So, talking about geometry. Where does the geometry comes in? And the data. So, I'll just pick a few points from the research people have done worldwide. So, one of the most important things people discovered is the curse of dimensionality. So, as you know, we live in a three-dimensional world. We see data as how do we see the world? Like in an occlusion space, we have the three dimensions and that's what basically we see and apply the senses. But in a high-dimensional data, the same intuition doesn't work. Why? Because in high dimensions, most of the mass is actually not real the mean. Like we have a typical Gaussian bell curve. We expect the majority stuff to be at the center, at the mean basically. But when you go to high dimensions, that doesn't come to be true. What happens? It's mostly around a shell around it. So, people classify this or account with an example. They say imagine an orange. So, it's a high-dimensional orange. These most center or the mass of the orange would be around the skin, not in the pulp. So, that's what a high-dimensional orange would look like. It may not be the typical one that we imagine. So, that's where our intuitions break down. And what we apply typically does not apply in high dimensions. But we also have another benefit from high-dimension, what I call as the blessing of non-uniformity. So, data which is non-uniform, normally clusters around in small, small notions. Like in the case of orange, around the skin, there would be patches of data. So, it would be around its local groups. So, that's a good part that you can capture. So, this would be some of the natural thing that data would be having. So, what's our job is to understand the natural shape or geometry of data in that domain. So, whatever the data is, let it be that way. We don't enforce it to be mapping to an equitably flat space or some other space. Let's discover the real geometry of data. So, that's the key idea. Let me give a small example to illustrate the point. It's a simple example. Everybody knows, I think we need to create clusters from this. We have two circles, the inner circle, outer circle. So, although it's a very typical intuitive problem for everybody, we can figure out which is the cluster. But if you have to solve it by a cluster, it's like a K-means. It's hard to draw a line between the two circles and separate them. So, it's not separable by any simple algorithm. If you try a classifier, try an SVM, mean SVM, they also don't work. But you have some complex algorithm that will make them apart. That's possible. But giving the idea, no simple algorithm can work. Coming from the context, if we look, focus on geometry or the metric space that we have, if we simply transform into different geometry, then maybe the job becomes easier. So, let's say we convert it to an R-theta space, the radius and the angle over here. So, now this is simple, just a linear line. And I can use a simple K-means algorithm to split it basically up. So, it's a trivial thing. So, the point is, geometries can tell us what's the inherent nature of data is. If you capture that, it's pretty easy. The job becomes easier. This was a simple case, but if you go to more complex cases, then the undoable things becomes doable. So, that's what's the main idea is. So, now I'll first start it with the main thing. Yeah. So, I'll tell you two parts. First, the theoretical part and then the applied machine learning part. Or you can use tools and other things to actually understand the geometry of the data. So, I'll quickly go through the analytical part and then we'll come to focus on the big data part. How do the same things in the big data space? So, first the analytical part. Talking about topological spaces. So, in the world of mathematics, this is the most generic notion that we have. So, in general, any space can be classified as a topological space. It's a topology, basically, that we understand. In simple words, it's a set of points. It's a notion of a set theory, basically. You have multiple sets in the data. So, those points have some neighborhoods. In this image, you have a yellow color, a blue color and a different color. So, these are defining neighborhoods for data. So, then there could be some set of axioms we can define that relate the points to the neighborhood. And then, if we just pick all these groups, let's say the intersections and the unions of these groups of data, they collectively can make a space. That's called a topological space. The most generic notion of a space that we can define. So, what we can study from these spaces? Connectedness. So, basically, how they're connected. So, that's where the clusters will come from. Then, the compactness. Basically, it's data dense. Is it two spars? Dimensionality. We talked about earlier. Continuity. Then, there is also possibility that in the real world, you can't define distances in many conditions. There could be holes in data. So, point A and B may not have a distance, basically. That's a real-world problem. But, in equal space, you have to have a distance. So, that's why your assumptions will fail over there. So, how do we tackle those cases where we break the continuity or we have holes? So, that's the generic idea. So, the first, we'll take one sub-example called the metric spaces. The topology was a bigger notion. We'll focus on a sub-area called metric space. So, metric space is basically just one more constraint added on the topological space where we also have a distance function that every point has to obey a distance. What does a distance mean? They are four properties to defining a distance. Like, a non-negativity, it has to be positive, definitely. Identity. If two points are equal, the distance has to be zero, basically. And then, distance xy should be same as distance yx. So, and the last is the most important one, the triangle inequality. So, you'll find lots of measures called similarities and dissimilarities. But, they may not be distances. So, because if we have points like x and y, so, xy plus yz could be greater than xz. But, that should concern that this should be smaller. Like, we have a triangle. If this is enforced, then we have a real distance, basically, that we can use in geometry and actually work upon finding clusters. So, we need to have all the four things to classify it as a proper distance. I'll take the most intuitive example we know, the Euclidean space. So, that's the formula we already know. We are learning from school, basically. x1 minus x2 square and square root of that. So, that's the most typical one. And supplied in majority of the clustering algorithms that we do, it's by default over there. But, yeah, it has drawbacks. Although, it's pretty intuitive. How we can imagine, like, the points are in different spaces. And then, they're basically mapping it to a coordinate space. It's easy to imagine. But, yeah, it has drawbacks. It may work well in many scenarios, but we need to ask the question, is the assumption of Euclidean metric valid? It's like, what if the geometry is not Euclidean? There is not a flat space. There is something else. But, we are just forcing it to that. And what if we are actually distorting the actual geometry? And we are maybe then adding some new notion of data, which is not present data, basically. So, adding new information. So, all these are nuances of an Euclidean space. That's been used by everybody by default with all the major algorithms. I'll take the most obvious example, the Earth that we know. So, on an Earth, I think everybody knows, let's say we create a triangle. On a curve, the sum of all angles of triangle would be more than 180. But, on a flat space, it would be 180. So, a curved space is the most obvious non-equivalent space that we know about, basically. So, if we, let's say, use the red dotted lines to find distances, we are actually distorting the real space. So, the points are, the distance on this is not really a straight-line distance. It's a curved distance. So, if we actually use those, that would be the real geometry of the data. So, to measure those, we call, measure something called a geodesic distance, basically. So, the lines over here, the curved line A, B and C, these are along the curves of the surface, of the sphere, basically. So, that's what we call a geodesic. It's measured over some of the great circles. So, great circles are basically the circles which are having the same origin as of the sphere. So, if we move along great circles, you will exactly have only one single path on the great circle, leaving aside the points which are basically exactly opposite. So, if you leave the opposite points for every other two set of points, there's exactly one great circle on that sphere. So, that's one way of looking at a geodesic. So, the concept gets more complex. I think we can only imagine a sphere by default. So, but things get more complicated. I'll show you just one example of a more complex geodesic. Sure. Yeah. So, the origin has to be same, basically. For a great circle, the origin of the circle and the origin of the sphere has to coincide. So, basically, the diameter has to be same of the circle in the sphere. That's a great circle. If I'm using along the great circle, then you'll always find exactly one great circle for two set of points which are not opposite. So, they do a unique distance. So, you'll have a unique thing and it will always give you a single answer. So, what's the question? But then you can have multiple distances, basically. You have multiple versions to have a generic version and to be basically there should be no issues. So, you have a defined concept, basically. So, define a great circle and that will have a unique distance. So, just to remove any ambiguity, basically. So, that's the idea. So, this was a simpler case. I'll just show you an case of a more complex geodesic. So, people must be hungry. This is not a doughnut. It's called a torus, basically. So, it's a complex thing. If you place an insect on top of that, it works in a straight line. Just look at the part of that. Just observe this, a small little animation. The insect is just walking in a straight line. Nothing else. But this is also a geodesic. The earlier one, earth or a spear was a simple thing. But, yeah, it completed it one round. So, just completing one round had a very complex path it took. But this is also a geodesic. So, things can get complex. And we need to figure out different geometries, how we can do those things. So, that's just an example, just to show it. Coming to the point, how can we relate distances with geometries, basically? So, the key idea, whenever we use a metric between two points, like Euclidean or geodesic, we actually define the geometry. So, by using a geodesic, we assume it to be a spear. By defining Euclidean, we assume it to be a plane. So, we actually impose that. So, a metric has basically one-to-one correspondence with the geometry. So, that's why we need to be thinking what kind of distance function we are using. So, every distance function is imposing a geometry on data, basically. You could be using your cosine distance, you could be using Euclidean, it could be anything else, it could be dice. Everything is imposing a geometry. So, that's where we need to understand is it the right geometry or is it we are enforcing or distorting the real one. So, now though, as you can understand, like even case of spear also, we could enforce multiple geometries between set of points, like a plane, a spear, anything. But, which is the right one? We don't know. So, as there are multiple infinite combinations of geometries possible, the problem is to choosing the right one. So, one useful measure for choosing the right geometry is called the Gaussian curvature. So, this can help us choose among multiple available geometries between the given data, which is the most appropriate one. So, I'll just quickly go through what does the Gaussian curvature mean basically. It's a number, a number given to every surface. So, I am showing three surface over here. So, the k value in the first one is actually negative. It's and if you see the, it's curved inside, just focus at the surface and it's flat for this and bulging out for this. So, k is positive over here and it is zero, it's flat. So, although I think people get sometimes confused, they say, how does it look flat? It's a cylinder, cylinder is not flat. But, look at the surface. The surface is flat actually. So, the surface over here is bending inwards. Here it's flat, it's bending outwards. So, that's basically telling us that these are different curvatures and even a plane and a cylinder will have a similar geometry. So, we can also convert a cylinder to a plane by just using like the radius and the angle, that gives you the same occlusion space. So, this is same as a flat plane. So, now if we just use these indexes and I just will show you how these different index can give you different distances. So, every curvature has a distance. So, the most typical one, the occlusion that we saw earlier, is for a flat surface. If the surface curve outside, then we have a dot product and a cos inverse basically. That's the spherical distance. Now, if we have a hyperboloid, it gets more complex. So, it's a cos hyperbolic inverse of the different dimensions. So, I think the formula is over here. I won't go through that. But that shows that as we go to more complex surfaces, the geometry gets more complex. The distance gets complex. Now, just imagine the torus that I showed back earlier. It had two curvatures. The outside curvatures were bulging out and the inner was bulging in basically. So, it has a positive curvature and negative curvature. So, we had to combine this. So, the distance would be more complex over there. So, complicity can increase. So, one way to solve this thing is to get back to a space that we know. So, that's where a concept called manifold comes in. Map that topological space to a local euclidean. So, it may be possible that the whole thing may be complex, but in parts may be flat. Like earth, you know, as always. Like before, I think a century back, we assume that to be flat. It was still doing pretty good. We were doing our distances and we were doing things fine, but it was not flat. Similarly, all complex surfaces, majority of them, could be mapped to locally flat surfaces. That's what we call a manifold construction. And we know of a very simple example, but we don't know it's a manifold. It's the earth. So, when we create atlas, that's a manifold. So, everybody is working on atlas on school days. So, that's actually a three-dimensional manifold on a two-dimensional space, basically. So, that's a simple example. Of how a manifold can be constructed. So, I'll slightly go into a little bit of how a manifold is constructed, just to give you an idea, because that would be useful. So, in general, if you have any curved space, it could be of any varying curvature. So, you can have functions. If we have a function that can map a curved point to a flat point, and you can do an inverse of that, and you always have a unique mapping, then the manifold exists basically. Only this criteria is enough for that. And these points are called charts, basically. Collection of these charts is an atlas, similar to what we did on the earth from the globe we got the atlas back. So, these, if the function exists, then we can have a manifold. There could be complex scenarios where we could be having multiple functions where the curvature is changing. So, it is part of both the curvatures. So, then there is a function called a tarnation function, which basically looks at the intersection of different functions, and you can then combine them and again get a manifold. So, a tarnation map, along with an atlas, is basically a complete set to create a manifold of any curved surfaces. So, that's the generic point. And now, coming to the main point, manifold can be learned in two different ways. One, call it topology. That looks at the global structure of the data. Second, call geometry. That looks at the local structure of the data. So, we need to choose what's our area of research. Do you want to look at the global structure or look at the local structure? I'll come with an example. But to the last slide of my theory, I'll just give mention a way. This is a technique called re-emanian geometry. So, this is a generic way of discovering the manifolds on any curved surfaces. This is projecting a sphere to a plane based on the tangents. So, for every point you can draw a tangent on that, and you can understand the curvature. So, it constructs something called a smooth manifold or a re-man manifold based on a re-man metric. The metric is very simple. Just a product of tangent space at a point varying at the surface. So, this basic idea, it's a complex mathematics thing. So, I'll just leave it as it is. But this is very powerful. This was even used by Einstein in general relativity to create the spacetime curvature. So, this is, I guess, the most generic form of defining geometry. And I'll just leave it as it is because this is an area of research and people can study them on their own and figure out how you can do theoretically. So, in short, this was a theoretical way of understanding the geometry of data. If we can buy some analogy or buy some theory, can understand which structure should I apply on the data and can test that. So, in this approach, the theory comes first. You imagine a space and then get the metric. So, that's one way. Now, let's come to the easier part. How are we going to do it in the applied machine learning? So, I'll pick some examples. Let's pick the first one. We need to find the clusters in this. So, I guess, no points for this. It's an easy one. The clusters are pretty simple. So, we have four clusters over here in the data and we can easily separate them. Now, let me slightly change the example. So, if I actually change the ODFC to this way, will it make a difference? Do you think, can K-means catch that? Yeah, it can catch that. So, because easily, it could be metrics that are invariant to any rotation reflection thing. If things work in basic space, it will also work after rotation reflection. That's an easy thing. Let's make it slightly more interesting. If you take a plane and slant it, will it still work? Do you think? Yeah, it will still work because it's, again, a flat plane. Yeah. Let's make it more interesting. It's still the same ODFC in the S form. It's the O, the D, the S and the C. Now, what do you think? Will it work? Yeah. So, how many of you think it will work, basically? So, can you raise your hands to people believe it will work with K-means? And people who believe it won't work with K-means. So, the first one, one, it does work with K-means because it is still, locally, it can be, a plane can be drawn. The coverage is small. The coverage is not good enough, basically. To, it can still be approximate by plane. So, it can still capture that, the points. So, they can be a plane drawn over here. They get the O out, the D out, this and the C out, basically. So, the clustering can still work easily. But now, let's make it more interesting. The same example. I've bent the S further down. Now, what do you think? Will this one work? Yeah. Okay. How many of you think it will work? Okay. So, this time, probably, I think, yeah, it won't work because the curvature now is too sharp, basically. So, look at this color. This color, light blue, now is being affected by all the four clusters. So, it's spread in all four of them. And, yeah. So, it can't figure out, basically. It says, basically, I've bent this further, basically. The same S. Actually, it's more like an hourglass, yeah. That's a better way to say. It's more like an hourglass. So, but the curvature is so high that they are close at the center, basically. Yeah, but it's actually not overlapping. So, that's a good question. So, to understand, does it overlapping or not overlapping? Yeah, it's not. So, that's the other way. Use a manifold. So, if you use a global manifold, then you can MDS. So, in case of this image, we can clearly see the position of this three-dimensional S on this. It's in clear S. No overlap and no nothing, basically, yeah. Now, if we look at this one. So, if we again create the same image, we got the clustering. Now, take up position of this on a two-dimensional world. So, now you can see they were not really overlapping. Yeah. So, they were too close, but there was actually physical separation. So, it's an issue with the clustering technique, basically. Not really with the data. Definitely, yeah. That's the idea. This is an example to show if you can visualize three-dimension, but yes, it can work with n-dimension and back to any low dimensions. So, and but I think that's a good point. Which dimension to take first? The higher or the lower? So, now I'll just reverse the same technique. So, let's say we had the same data and now we do the projection first. I'm not doing clustering. If I just go back over here, the clustering was on three-dimensional data. So, we were not able to find the good clustering in a three-dimensional world. So, now I'm doing the reverse of that. First, take up position. Now, do a clustering. We are still not the best case, but still better. We only have one polluted cluster. Yeah. The three are still fine. So, that gives an important principle that if we can map to a local Euclidean manifold, then probably clustering will work fine because yeah, it will work fine better, basically. So, if that's possible, yeah, get it to lower dimension space and cluster on the manifold as compared to original data. If they had some clusters and there was a manifold possible, you will get that. Yeah. Yeah. So, I think they're both pros and cons. So, yeah, that's a valid point that in some cases, you can make out that, is it viable, worth doing or not worth doing? But the general case is indimensional. I'll come to that case. That's also what I'm also proposing, that that's a better idea to do in general case. But how? So, there's one more thing. If you can see, we were able to find the structure at a global level. So, still there's lots of information. I can't see the ODAC. Can you see? There is no ODAC over here. We lost the ODAC, right? Yeah, we got the structure, but we got ODAC. So, there is another idea called a local manifold. So, now if we take a local manifold, let's see what do we got? I think that's awesome. We got the ODAC back just from this curve thing. Yeah. So, I think that's the power of a local manifold. This actually preserved the information that was more relevant. So, the information was much more than just the curvature S that we had. It also had some inherent data, the O, the D, the AC, and that's what a local manifold captured. So, let me tell you what the, let's compare both of them. The same S looks like this in a global manifold. Looks like that in local manifold. So, they are both looking at different areas and working in different fashions. So, what happened in both of these? So, this is what happened in a global manifold. So, it took all the pairs and basically found the distances for each pair. So, it was understanding at every possible distance that's possible, then took a prediction. So, that was a more complex thing. But in case of local manifold, if you can see, I don't know if the lines are visible, but only the lines between these points are highlighted over here basically. So, all the local distances are only being looked upon. So, it's looking at the neighborhood and only at the, in a certain region, it's finding the relations. So, that's why it only found the inner structure. Yeah. So, that's probably is what is more powerful over here. So, in the aspect of clustering, this is a more efficient way basically. So, this can give us more clusters. The natural thing. Yeah. Yeah. So, but like in case of K means, I have to tell the K. So, I have to tell it the K is 4. So, I knew there were 4 clusters. So, I told it with the job. If I don't know what the K is, how would you solve the problem? So, if you know that there is a 4 clusters, then you can solve the problem basically. If you don't know, then it gets complex. So, that's a good idea. But, so we can use the property over here. So, I think that's the idea. The local neighborhood property can give us those structures if we can find the demarcation. We'll demarcate basically. So, that's where the next idea comes in. So, you must have heard I'm going to call DB scan. It's a simple. Yeah. Yeah. Yeah. It's Euclidean. Euclidean. So, I think yeah, so that's we can do that. So, that's the theoretical part. So, if we know the geometry, like in case we yes, we know that it's a curved space, we can simply apply geodesic. And we get the answer. So, that was the first part we were talking earlier. If you know that do it, it's easy, pretty easy basically. Yeah. But now, if we don't know it, we want to do it empirically as in like by doing testing. By applying algorithm and then basically testing it and finding a measure. So, we can also find like defined matrix. What is the number of clusters and like defined distance between intra-cluster distance and the inter-cluster distance. So, that will tell us basically how good the clusters are. So, we can measure the quality of clusters. So, empirically, if you have to find, we don't know the geometry, how we can solve that. So, this is the second approach where we do a test and trial and figure out those things. So, I think I was meaning this was the LLE, locally linear emitting. This was MDS, multi-dimensional scaling. Yeah. So, LLE is really powerful, the locally linear emitting. It is just looking at the neighborhood around that. So, that captures the real essence of data, the real information in the data that we had. So, we can generalize this concept and we may not need to create a manifold because it's a very computational intensive thing. It's not possible to create manifold always, basically. It's not easy also. Yeah. So, we can just pick the idea that look at the neighborhood and use an algorithm which works on neighborhood. That's like a DB scan. DB scan is a simple algorithm that works on looks at the neighborhood of data. It constructs a graph and it labels something called a core points. If I'll just go through the simple algorithm for people who doesn't know it, the points in the red are called core points. So, we are drawing a circle around those core points and let's say we are saying if there are three points within the circle, it's a core point. So, for all the red points, you'll find at least three points inside the red circle and that's what they're called a core point. Then there could be points inside the circle, but they don't have three more points. That's the yellow one, basically. These are the non-core points like B and C over here. So, they were part of some other core point. So, that's why they are still connected, but they are not core points themselves. Then we have the uncustered one, which are basically not connected to anyone. So, this is modeled as a graph. So, the same problem of local neighborhood can be basically imposed over here. But we need two things. First, if you have a distance matrix. So, if we have the distance of all pair of points, I think, yeah, that's starting point. We need that. And then we can maybe play on that. The second most thing is the epsilon or the radius. If we can somehow define the radius of this circle, what should be the size or what should be the minimum distance that I should cut upon to create the graph and basically prune the graph, then I'll get the clusters. So, this is the two main things that we need. If we can do those things, I think we have a totally automated clustering approach. We don't need to define any k, don't need to define anything, and just give that through the data and get the answers. So, the problem is, how do we automatically get this epsilon? So, that's where probably we're proposing a method, how to get those things. So, but before I get to solving this, I'll show one more case where we can apply the same technology. So, the second area is called different spaces. So, in the earlier part, I was talking about the curved spaces. So, let's say the one of the axes is curved, then you will see where the peak rises. These are, let's say, the projection of this on the one-dimension one. In a normal ruler, all the axes are equi-professional when you have a ruler, basically. One centimeter, two centimeter, three centimeter. But in case of a curved space, if you project a curve to a straight line, there would be non-uniform. So, not equidistance, basically. The one near the peaks would be close by. One near the planes would be far apart, basically. So, close and far, close and far. So, that makes it harder or complex to basically define geometry. So, one way, do the geodesic and do the curved geometry. But there is another solution possible. Use a reference space, something like a probability space. If you can match, map each point in this space to a point in some other space where you can define probabilities of a point belonging to some label, some class, or some basic cluster, then that's an easier way. I'll show an example, sorry. So, if you just look at a simple example, we have a users and movie categories. So, I don't know much about the users, their properties, or what they are basically belonging to, what they have, but I want to cluster them. Even if I don't know anything about the users, I can still cluster them based on their choices. I know the user watches the action movie or thriller movie. So, we can define probabilities in a simple way. We can do simple counting. If a user one is watching three action movies out of ten, probability is 0.3, as simple as that. User two is watching five comedy movies out of ten, probability is 0.5. So, we can have this conditional probability and create a bipartite graph. It's a simple thing. So, I just know the choice of the user and the counts of those choices. This can give me a vector. So, I can easily say that the user one a 0.1 times choose action, 0.2 times comedy, 0.3 drama, and 0.4 thriller. So, this way we can just easily create a probability vector for every user. So, it's a simple way. We create a bipartite graph, make the counting from the counts we create the probability. So, now we are actually mapping user to a probability space. We did not have any user information, but still we can use those vectors. So, now we have a new dimension. That's a four-dimensional probability space. Now, we're going to cluster on that. So, how we do that? I'll talk about later. But the idea is you got to a new space without looking at the parameters of the input data. You can also add those parameters if you have, let's say you have user groups based on A, H, X, language and location. So, you can create groups of users. Let's say having these properties. So, we can call these tuples basically. So, a group of user can have again a probability vector. So, in general we can say for any set of n-dimensional attributes we can map it to a p-dimensional probability vector. That's generic way basically. So, that's what we call as a different space. We are not looking at the original data, the original space, but referring it to somebody else and maybe his classes or his categories. So, this has a condition. So, this has a condition that we have a difference available, label available basically. So, that label can be utilized in the same fashion. So, in short, if we have a probability space, we have lots of matrix supply. These are some of the function names. Kale, Divergence, Patacharya, total variation and there are many more. You can also define a similarity measure like a same rank on a graph or something. But all these are not distances. These are similarities. This, Helinger distance, the distance metric basically. This is a true metric. It confirms to all the four properties I showed in the beginning, the matrix space basically. So, if we use this, then you can actually compute a geometry and get the right geometry of the data. This is a simple idea. And so, essentially, we just need to create a distance matrix by using this function and the vectors. So, now we get the distance matrix. And remember, this is what we needed for our dB scan. So, we already have one criteria fulfilled. So, if we generalize this, so what all do we have till now? So, to create for the purpose of clustering, we need a distance matrix. And we can get a matrix in both the scenarios. In case of a high dimensional data, we need a distance matrix. In case of probability space, we need a distance matrix. So, in both the cases, we can get a distance matrix. So, that's a simple thing. Now, the challenge is, one, how do we create the matrix in a bigger space? That you could have a million rows, 10 million, 100 million rows. So, n cross n n square is the distance metric size. So, 100 million cross 100 million. That's 10 to the power of 16. That's pretty huge. So, that's a challenge. So, how do we do that? That's one part. Second, if you got the distance matrix, how do you find the epsilon? So, how do you automatically basically get the clusters? That's the key idea. So, I'll talk about this first, because that's more important, given assuming we have the distance matrix, basically. So, I'll take back the example again, which we had earlier, the less curved S and the more curved S, or the hourglass, basically. Just do a simple histogram or a density plot of that. Just counting that we have a distance matrix. Just make a count of distances. So, this graph we're showing, maximum distance are at distance 2, because that's the max distance, basically. So, this is just showing a histogram for both the cases. It's showing a peak over here, similarly for there, but that's the idea. I can easily play with this same histogram or density plot and do more fine graining. If I do a plot at a different resolution, I get a different plot. If you see, notice, now you get a peak over here and a peak over here in the beginning also, which was not there earlier. So, this is called a smoothness of how much smooth density, kernel you want to fit over there, basically. So, you have different formation. So, in a more refined kernel, I got a peaks over here. So, that's the major idea. If there are clusters data, then majority of them would be very close by. These are very close, very close. All of you are very close. So, that small distance would be lying in a small range. So, the frequency of that would be very high, what you're seeing over here, basically. So, a small range would always having a high distance, a high frequency. And if you can capture that, so that is your epsilon, basically. So, if we just translate into words, the clustering epsilon is simply based assumption that we have clusters. Assuming the data is high dimensional and is organizing in some clusters, then we can apply this and simply just compute the distance matrix and find the frequency for that. And the inter-cluster distance should lie in narrow range because they have a cluster, they are very close by, basically. So, this assumption translated into a very simple thing. If we can find the peak of the first mode, then probably we have the clustering epsilon. But again, finding the peak may be easier, but finding the right curve is not easy. So, the problem comes to which is the right curve for the data, right frequency curve. So, that's where the problem comes in finding the right Gaussian kernel. So, let's say we are fitting a Gaussian kernel over the density plot, like multiple Gaussian curves. So, the first one is the one we need. That is the more inter-cluster density and the peak of that is the mean, is probably giving us the epsilon or forward clustering. So, there is a simple technique. Just using a grid search, give it us a multiple bandwidth parameters. These are like controlling the smoothness, basically. And give a list of those and do a simple Gaussian kernel estimation. These three things are just simply Gaussian kernel. That's it. Take a Fourier transform, inverse it and get the data back. And you can find the minima by maximizing the probability as simple as that. The probability of the entire curve, where is the maximum is, find that. Based on a scoring mechanism that uses log loss, standard technique, log loss over the distribution will give you the minima and that is the optimal bandwidth and the grid size. So, that was basically all. I'll just, in short, quickly... Yeah. So, one is a theoretical way. Second, you can basically play analytically and try different distance functions and then measure those parameters, like integral distance, integral distance. And we will find the best, most separated clusters and most dense clusters. That's the way. Yeah. Yeah, exactly. That's an integral way. A grid search on those things, basically, and minimizing those parameters for clustering. So, that's the idea. Sure, yeah. But that's hierarchical. So, it is basically doing in multiple hierarchies a bigger radius or bigger radius, basically. Here, it's more like finding the minimal distance. So, actually, yes. For example, in the case, basically, it's part of a big cluster, like the S1. So, in case of HDB scan, the bigger one would be the S. Smaller one would be basically this ODSC one. Yeah, yeah. So, I think that's one way of doing it, HDB scan, if you have a hierarchical structure over there. But at times, the structure may not be coming to clusters hierarchies. So, it's another way of doing it, basically. Just find epsilon later on. You don't have a different function. Get the epsilon is free to DB scan. It's the same DB scan. You can modify it, basically. Without modifying DB scan, just plug the epsilon and get the value. So, you will still have the answers. We'll quickly summarize how do you get the distance metric data? I'll let you about the challenges that we have. So, you do create a data frame and find the pair of distance, basically, between any two feature vectors. And the assumptions are, data is large. Large means dimensions could be 10,000 or more than 1,000, basically. And, like, dimensional in current world, like deep learning, it goes to even millions, also. So, dimensions could be very high. And features are definitely more than one million. So, in a very simple case, just one million case, computations is basically very high. It goes to n-square. And as the n increases, the n-square goes up pretty high. So, you have compute problem. You have storage problem. So, we can do a few quick things. I'll just summarize and give the idea. So, a most obvious way of doing a distance metric computation would be do a cross-joint in your spark. This is a simple spark code. And then apply distance function. But, as you know, going for n-square cross-joint is pretty bad. It will have a huge shuffle cost. And it will be basically, it will go on for days. So, in our cases, we had data which had more than 1,000 dimensions, and probably more than million rows, it went to days, finding all those things. So, and it will basically, still you can distribute that, make it horizontally scalable, but that is the limit. You can't go beyond some executors. It is a challenging problem. So, simple quick way. By reducing to reduce of operation is use the spark technique. What we call as basically, instead of doing a pair computation, or each pair do the row computation basically. Compute the whole row at a time. And that's a more optimal way. So, in this case, convert your feature vectors to a simple array. And then compute dot product of an element with the transpose of an array, as simple as that. That's a row compute computation. And, but the idea is, broadcast the array to all of the executors basically. So, now you just have the end length array being partitioned in data. And now you are also having the same end dimensional array as broadcasted in all the executors. Now, just multiply the array with the element. You have the row in each of those. So, simple you're doing this basically. Just collect the whole data. It's a sample code. The idea, I'll just skip the idea. So, I'll also share the code later on on a GitHub, so that you have the code. I just collect it, do a simple broadcast, and then basically apply distance function. So, this is now a row distance function that is simply taking an element and getting the whole row for that element. So, what happened over here? We did the entire row computation single thing. But, this also had issues. The issue was for broadcasting now. Now, that's the second issue that's got added. Because broadcasting is a new memory thing, we require RAM over there. So, for high dimensional vectors, these will cause more problems. So, idea is then change your dimensionality vector space to sparse. So, using your sparse vectors. So, like in our data, we have thousand dimensions, but most of times, only 70, 80 were populated. More, less than 10% were populated. Majority were empty. So, sparse vector was given the basically the space optimization that we had. So, that was one way. I'll just show what we obtained from that. Just give you a trade-off. So, the two techniques that we had. First one, which I talked earlier, the cross-joint technique. We were doing n-square computations with a cos c. C is the cost of shuffle, and the distance function basically. So, that's a very high thing. But, the space was optimal. We were just picking a record and finding a distance for that. So, it was space optimal, but not time complexity. The new technique, let's say, k is the sparsity of data. Like in our case, it was like 7%, 0.07%. So, now, time complexity is n to k into c. And the memory cost goes up. So, at the cost of memory, we save the time. So, the saving was basically nearly n by k. So, for n more than a million, nk less than 0.1 is easily a 10 million time save operations across just 7 million data. So, that's the one quick technique that we have. Then, I'll just quickly mention a few more. You can read the code later on. The way we found the epsilon in the earlier way, we can do something similar over here. Just take a data frame and find a histogram, basically. Take a random sample, take a sample of data. Let's say 0.1% or 0.01% of data and compute distance on the sample, just a sample. And assuming the sample captures the essence of data, get a histogram, and then find the first peak. So, it will again give you a broad or a broad epsilon to cut the distance matrix. So, you can also save only one percent of distance matrix and don't save the entire matrix. So, this will actually also save a storage cost over there. Two simple functions, basically take a sample from data frame and then, basically, compute distance matrix and eventually do a histogram. So, there is a function in a double RDD given by Spark that can give you a histogram for that, basically. So, if you get a histogram, simply just get the first peak. That will give you a cross cut-off epsilon, basically. So, you can save your storage spaces. And then, I think there are some typical scalar things. I'll just mention it for your benefit that in any of our operations, like finding a distance function or anything or any loops, don't use iterators for each map. Then, you're asking, what's left then, basically. So, we have loops over there. So, the best thing is, use a primitive while loop because there is an internal optimization that Spark does for every map, every for each. They basically do the whole operation again. The memory is refreshed and then, probably, the whole thing takes a lot of time. So, I don't go details of that. I leave for people to look upon. Just to give you a hint how to find those things, take simple stack cases. So, do a kil minus three on your Spark job. You'll get stack dumps and then, aggregate those stack dumps. Analyze those, you'll get the answer. Why these functions are pretty slow? And compare them with a dump for a while loop. So, while loop doesn't have all those fancy stuff. So, the scalar does lots of fancy stuff to make code look smarter and basically, more fancy. But you lose the performance over there. So, quick thing, use a primitive while loop. That's ten times faster. Yeah, I've measured that. And that gives you so much benefit. So, after doing all these things, like in our case, the whole thing competition came from days to like 30-40 minutes. It was like a 20-30x improvement that we had by using the broadcast-based join and then using the different optimizations, cutoff epsilon, all those things. So, you can easily get down like a 30x improvement by doing these basic things. So, I think I'll leave that. And this is a simple code for distributed DB scan. I think you can pick from later on from the slides. The idea is, if you want to do a distributed scan, use a graph frame basically. It's a distributed graph. Find the core points. And the same and loggy. Get the core points based on neighborhood, basically. If the neighborhood lies in some degree, let's say called num points, you have the core points. Find the core edges. And after core edges, create the graph again, basically. And then just do call graph-continued components. You have the clusters. So, this simple technique is the distributed clustering you can do on Spark. So, you have a distributed computation. You have a clustering technique on Big Data. So, now you can combine both and actually get the real geometry data and find the real clusters that you have. So, these are the findings that we have. Understand geometry of data. And so, you can actually capture the natural information data. If you don't modify it, you don't distort it. Analytical approach. First, figure out the geometry. Then apply the function. So, that's more like a theoretical study. You need to first understand how you can find or estimate distance function and how to test that. If you have that, that's the way. Other is, if you have a reference space where you can map each points to probably a label, then use a reference space. Use the probability vector of that and do a clustering on that. Third or fourth is the manifold. So, that gives you good essence of data. How data is organized. Is the global thing more important or local thing more important? So, that gives you a notion where to focus upon. And finally, for clustering, I think, yeah, more important is the local neighborhood. As we can see in LLE, we captured the real information data by looking at local structures. So, focus more on local part and for big data, I think, yeah, you do some optimizations. So, I think, yeah, these are the things that we can have and we can automatically do an unsupervised machine learning without knowing much about data. So, I think that's it. Yeah. So, one final quiz question. Can you defeat between the two images? If the answer is yes, then you're not a topologist. Because topology sees the thing as this way. So, the coffee mug and the torus are homeomorphic. Yeah. So, that's why you're not a topologist. If you can't, you can't defeat between them. So, it's a simple mathematical joke. Yeah.