Open Digital Asset News to get top stories and cryptocurrency digital assets and break them down to bite-sized pieces today We've got some pretty bullish news And it really doesn't come from any type of article or any type of little piece that we had picked up But this is actually from the Pompeiano podcast where he is interviewing Micro-Strategy CEO Michael Saylor and the things that he says about why his company Invested near a half a billion dollars into Bitcoin when just so many years ago He was talking about Bitcoin was going to die Was just it just blew my mind and it made me realize just how lucky we are to be here right now And what he talks about when he says there's gonna be something happening in two three and four months Really made me pay attention So I'm gonna break down this entire hour and a half interview into five parts So we're gonna condense into six minutes also great news if you had ever used Uniswap before today Because they're gonna give you 400 tokens which when I was making this video started out around 250 And when I ended the video it start it was about three dollars and 52 cents So we'll go over both those things but first let's talk a look at the market So today it is Thursday September 17th almost high in New, Texas time and it looks like Bitcoin is hitting up a little bit Of a stride but still down one and a half percent It was above 11,000 yesterday, but we just took a little tumble with hey I'll take ten eight no problem. It's up. It's up six percent for seven day. Happy with that Ethereum 380. I'm waiting for the 400. I think you can hit it. I think you can do it Heather's tether Nobody cares XRP. Hey up two percent to three percent twenty five cents. Wow Okada up six percent five thirty three. I take that Bitcoin cash in that six spot again and potentially going well It'll go for their hard for it in November also chain link down 1.8 It might fall below that $10 mark We will see finance coin. Oh how far we've fallen six percent Although up seven percent and they've dipped their toes in the DeFi space isn't working out to for them too much crypto.com Down 2.6 percent again doing the same thing didn't really work out so hot Cardano 2.4. That's pretty nice. What's up five percent for trying graduates is trying holders I don't hold any anymore, but you held it congratulations. Neo same thing don't hold any more Cosmos I hear good things about this projects and interoperability need to take a look at that a little bit harder You're in finance down 32. What are you gonna do the chain up eight percent almost a two cents? Wow Uma you may down six another project for DeFi also Ave down a little bit Zcash ontology synthetics also down some like the DeFi space down a little bit But that's how it is theta my new not my new hole that I've been holding this for a while I'm really bullish on this one. I think it's gonna do great again. This is good news It's up 1.7 percent. I think this project will do well It's got an advisor one of the advisors is the ex YouTube founders And they're doing a lot of good things and they're actually have a working project right now And I'm going to be doing live streams over theta kusama. I've heard about this product of 14% didn't take a look at that That one looks pretty good. Dogecoin That one at percent Digibytes who are going down deep today Qtm waves and then this little guy right here over the last hour It is up 13% when I was looking at this this morning was like 250 now. It's at 381. It's up 13% over 24 hours 117% so yeah, not too shabby and everything's looking pretty good. Also, ooh, one of my favorites my one-two punch Celsius Up 2% 34% percent for seven days. Wow 57 cents boy, I wish I could buy more of that, but I live in Texas.  Anyhow, let's jump in today's top story So next up continue on with my bromance of Anthony Pompliano here. I got to tell you this guy Smart guy has some really fantastic guests. If you didn't watch the video that we did with Jim Kramer Yeah, I broke it down. It was an hour and seven minute long podcast We broke down into five snippets and it was just the crux of the information. This one was even longer So first of all, if you haven't seen our video on micro strategy We've been covering this for the last week to two weeks micro strategy is a billion-dollar company. That's data analytics And it's run there by Michael Saylor the CEO and what they are doing is they bought Darn near half a billion dollars worth of Bitcoin and it kind of shook everybody because the first time was 250 million And then they came about and then they by another hundred and seventy plus million dollars worth of Bitcoin And the question I have was why why now why after all this time? What's going on? Why did this company buy all this Bitcoin right now? And the question I have was did they use their analytics advantage to just crunch a bunch of data and go This is the best thing to do or was it some other information or piece that they had behind the scenes and and actually I After listening this this podcast it comes down to a bit of both pieces of information So we're gonna break this down in just the five parts because the first you can watch the whole thing I'll link in the description Mr. Saylor here love to talk about himself, which is fine. He's a super smart guy He is a work for Dupont. He had a scholarship at MIT. He was in the Air Force He's a fellow veteran. He started up his company at 24 years old You pretty much badger Dupont to give him a quarter of a million dollars back in the 80s So he could start up his own company, which is insane But here we are and he has taken that company at 24 years old to a million dollars 30 million dollars then all Way here we are at a billion dollar company and what he talks about here is just what is going on Not just inside the company, but inside other companies and at a macro level about what's gonna happen And after I listened to this I thought to myself man I mean I invest in Bitcoin pretty heavily I thought I should probably be investing a little more and it really comes down to what he talks about in the very first part here Which is asset inflation versus monetary inflation. It makes a ton of sense when he when he says it So let's just take a listen and the economy went to the worst place. I've seen in 30 years at that point you started having a thought with yourself, which is What is what is the true inflation rate and and we should probably coin a different term, right? If you if you looked at asset inflation on a good year for the last decade it's 7% a year normal, right this year You can make an argument. It was 25% Right. I mean if you look at the long bond index and if you look at these equities You can make an argument that the asset inflation rate leaps through 25 and 30% depending and and now What does that mean to me metaphorically? Well, here's how I feel I felt like I had five hundred million dollars of cash in the bank safe And it was yielding two three percent and I'm ready for a rainy day And then I'm starting to do stuff with it and then every month some banker sends me a note saying the interest went down It went down. Now there is no interest and Then someone took my cash out of the bank and they put it in the backyard in pallets and then they open my back gate and Then every month someone comes along and starts burning 2% of the money and then I started thinking well, you know in 12 months 25% of the money is going to be gone and Then you know that I started thinking What is the point of all this? What am I doing wrong and of course the answer is you can't hold cash And so you can't hold cash and it's one of those things where I have always talked about how cash is king And when I listen to this, I'm like that's very true. I mean it's very true assets are I mean the inflation rate is huge and he talks about bonds and equities But just take a look at the at the housing market right now If you go out there and try to buy a house for some reason even the economy is in the toilet and people lose their jobs Left and right and 60% of small business. They're gonna go under and not real open Houses are going through the roof and that's just not in America. I verify this in places for subscribers in Europe also Canada and It's just a very odd thing So when he talks about hey, I shouldn't be have my money into or my money in money That's a very good point, especially with all the assets. So what it all comes down to is you need a product that is a hedge So next up he's gonna get into COVID or the coronavirus and how it didn't just change the perception of The day-to-day operation of a business and what the actual outcome should be But it's really about how it changed the perception for everything including Bitcoin And this was the most fascinating to me because my question was how did you get? How did you arrive to put in half a billion dollars almost into Bitcoin now the corporate standard? Everyone was whichever to zoom starting tomorrow Right. That's how and by the way the same CEO that said I don't believe in remote work You got to show up to the office or else you're not working for me and I would have sworn up and down I hated remote work until COVID crisis hit Flip and so that same idea happened with the balance sheet They're all these strongly held views. You got to be conservative You got to invest in cash and short term T bills and you don't contemplate anything else And then all of a sudden you contemplate other things. So I mean you're an expert You tell me if you had 500 million dollars of cash right now Where would you invest it? I'm cheating because you and I see eye-to-eye now is I'd go buy a lot of Bitcoin and of course Yeah, palms gonna say that that's just how it is. That's well That's exactly how I think we would all kind of come to that conclusion But really if you start to think about it this guy Michael Saylor Part of a billion dollar company CEO if he came to this conclusion and he's talking about all these things Or how much time do you think it's gonna take before other CEOs CFOs are going to come up and go You know what we are just burning cash and we can't have this here We could we need to get in some type of assets some type of hedge assets that we can really get into and Well, let's see micro strategy did something like that and they're doing pretty good so far How much time do you think it is before all these companies start to pile in it's already starting It's already starting you got the Jim Kramer's you got the Paul Tudor Jones You got the Michael Saylor's you got the TD Ameritrade's you got the Fidelity digital assets I mean the tide is coming and I think it's gonna come faster than what we think it is So the next part here is this was a question that I got in the comment section Which was all these businesses are buying all this Bitcoin, but it's like the price doesn't move that much So what the heck is going on? Well, Saylor here is going to open up the curtain and kind of reveal How he bought not him but him and his team bought so much Bitcoin and didn't really move the price at all Which to me was really eye-opening We've wrapped it all so Substantially 95% of that money is either invested in our stock or in Bitcoin and we've accomplished that in short order, right? Like over the course of six weeks or four weeks now Regarding acquiring that much Bitcoin first of all I Can't give you like exact low by blow details because I've got security issues and the world is watching and I I Can't but what I can do is is is I can describe to you if you were running a company How you should think about this? You know if you were in my position, which is you're gonna go and you're odd You're going to audition a bunch of a bunch of institutional grade exchanges You're going to work through and look for institutional grade custodians Yeah, yeah, you're going to look at you know all all of the security issues all the technology issues, etc You're gonna you're gonna think about the team You're gonna build a relationship with them And then you're gonna buy if you're gonna buy that much you're going to buy it in Thousands or tens of thousands or 100,000 plus small transactions day and night minute by minute over that like over the course of many many many days, so So it's not like we're going in I'll sit and I'll watch this happening and I've got a great team You know a great team that I've worked with and some excellent professionals They are brilliant geniuses or what they do, but let me tell you they've got great technology, too Right, it's like and you got to have the right technology You got to have the right team and then you have to be very patient like very very patient, you know, I go I'll watch people walk in on Monday morning And I was like okay some dude just got up at 9 a.m. Decided to buy some Bitcoin at the price Spikes, you know whenever I see that I'm like well that guy won't be in the market very long because no one that really wanted to buy a lot of Bitcoin would be so silly as To spike the price so hard, you know, I can tell you this which is we bought $425,000,000 worth of it and we never ran the price not a dollar Like you don't know impressive. Yeah, it's pretty impressive. I'm in the market you wouldn't know that I'm trading against you ever because That's just That's not how you get stuff done right let the market come to you So there's a couple things unpacked there first of all when he talks about how he didn't run up the price And he didn't see how white people would do that There's people out there there whales and they love volatility So, you know what they can do is they can buy a ton and then the price will skyrocket Then they'll sell off and then I'll go back down again. They'll buy for cheap I mean that's just that's just how those guys work But in here and in his situation what he's thinking of I believe is that hey I want to hold this for the long haul and he talks about holding Bitcoin for like a hundred years So this gentleman here is all in and his business So there is that part and the second part is is that he had to take I think he said is like between three and six months I forgot which how much it actually took or six weeks But he did a lot him and his team did a lot of work and they're every super patient Just to get the Bitcoin to where they wouldn't move the price, you know at all or just a little bit So that's just one company. That's just one billion dollar company now Just start to extrapolate that out how many other companies big businesses conglomerates are going to get into this space and try to do Exactly what micro strategy did they're not to be able to do it at us for a very long amount of time There's only so much Bitcoin out there. The price will go up It's just that these guys were very slick and they got an early So when people ask me, well, well, how why does it not, you know move up? Well, there has to come a point when you are buying so many Bitcoin There's only like 18 and a half million out there when you're buying so much that Eventually the price is going to rise and is going to go crazy And it just takes a small fluctuation and that's not that much 500 a thousand dollar increase Which I mean percentage wise is pretty big But if you have all these players and they're all trying to do the same thing Which is not move the price and one screws up and it only takes one screw up where they're like I'll shoot we bought way too much and then the price goes up a little bit and then some Retail investors go hey the price is going up and they start to buy and other companies like wait wait These companies are buying too much. We got to get in there now and all of a sudden to the moon So that's what I think will happen just that you know hats off to Michael sale and his team Those guys are just slick enough to do without anybody knowing about it. Okay next up I am hoping that Peter Schiff is listening to my channel Peter. Hello This is where he talks about Bitcoin is a hundred to maybe even a thousand times better than gold and When businesses all figure it out It's gonna take him a very short amount of time to actually get their positions And we're gonna see some fireworks and he lets something slip and I'm gonna I hope you can pick it up when he says listen I just want you to listen to this maybe two three four months Just listen for that in this little snippet inflation edge. This is this is if it's not tax better than gold It's a hundred X maybe it's a thousand X better go we could go on for hours I could tell you why I think it's a thousand X better than gold But let's just assume since we're preaching to the choir that it's a thousand X better than gold Once you realize that it's a thousand X better than gold from that point it's minimum 12 weeks if you went like a bad out of hell and probably six months And I kind of feel that if people were waiting to see if this was possible Well, they kind of saw our announcement august. So the six month clock starts in august if if they were Super if they were just perfectly configured if they had all the same characteristics as us Then they start focusing on this in may Or june Nobody's thinking about this in march or april which is so busy trying to keep the doors open and and their bells getting wrong So take august and say august september october I you know december january february. I think that what you're going to see is over the next two three four months something interesting and um You know, I the the other point right that's not not lost upon me is There's 3,500 public traded companies. There's five trillion dollars in their treasuries and it's all melting and And yeah, at some point you have a fiduciary obligation to not lose the money Okay Yeah, I get it's it used but it used to be acceptable to be conservative But that was before the asset inflation rate went from six percent to 40 percent And there he said it There's a bunch of different companies and they have five trillion dollars in their treasury and it's on fire What do you think they're going to do once they hear this story about micro strategy? And how they not only save the cash But they actually grew their position with this type of asset Which is also the best performing asset over the last decade I don't know what would you think but uh, I got my opinion. Okay, lastly I just want to throw this in because he talks about volatility and he talks about how it's not so much that It's actually volatile out there But people like him and his companies are going to dampen that volatility Of course when it skyrockets and then he talks about how crypto is just fantastic and again How gold is far inferior. So peter pay attention. I think you could have chosen Um, and when we talk about volatility, it's not like hey make up to two percent or down two percent You can have double digit percentage days up or down Does that change your strategy? Is this just your long term holding it for, you know years and years kind of how do you think about that? Well, so first of all, I think the volatility is falling and I I think I gotta do is look at the chart And I there's a narrative like everybody's like everybody wants to say that they know something about crypto wants to jump up and say Well, you know, it's volatile Well, what was volatile in 2017? You know when like individuals are trading it on their mobile phones But yeah, think about what I just what I just said about how we acquired it We buy 175 million dollars I'm in the market every minute of the day for multiple days in a row. I'm damping the volatility one person Like me right in every every trading day that I'm in the market I'm damping it to the upside and the downside and I'm damping it with large sums of money right and and so How many of how many institutions does it take before they damp it? Right, like I'm the I'm the dude. I'm like, okay. I'll pay an extra whatever but stop this thing I'm holding it for a hundred fricking years, right? It's like I'm not really I'm not the day trader guy that's worried about it So I think that as the institutions come in and as they buy a bigger amount They're damping the volatility. That's my first observation. My second observation is crypto trades 168 hours a week Every other asset trades 35 hours a week at best and sometimes less on holidays, right? You're trading I look at this thing in all, you know, when I look at these exchanges Saturday night 9 30 p.m And I'm watching The thing stream and I'm like, this is the most magical hardest working security in the history of the world And and I would think everybody ought to be in awe that the thing's not going haywire It's remarkably non-volatile in that regard Like in my opinion you could go and you could go into the market And you could liquidate 50 or 100 million dollars worth of this stuff In the matter of an hour any hour of the day any day of the week on a holiday and maybe you take a 3 percent haircut But don't try to liquidate 100 million dollars of gold on a Saturday afternoon in istanbul on the street side And that's just it so that is it for that little segment I will just say this when he said he said look I'm not the day trader that has to worry about it and uh, you know, I'm just going to be here for 100 years that's pretty much how I am And what I've been talking about since I began this channel when I first got into this this market It was all about you need a day trade and you need a day trade and you can do that all you want to that's fine But for me personally and Maybe for you, it's just about dollar cost averaging putting the money in and then off you go Um, I don't believe that bitcoin go to zero. I think that is a ridiculous statement And I know that we will go up and down and we will have our turbulence points, but Just looking at what it was in 2017 where it was just pretty much Hope and white papers And now what we have today And what I mean the type of participation that we have from I mean big big big players and big people And uh, the track has been laid and everything that's going on. I just don't see how this doesn't take off That's all I have to say. So let me know what you think in the comment section. Let's move on to our next piece All right, so getting one of the big stories Introducing uni and this was from yesterday probably late at night. I'm not for sure But I just saw this today and this was actually put out to me from sergeant crypto And also crazy for cryptos. He had actually put that out. So both of these guys, uh, thank you so much for the heads up So what exactly is going on here? So first of up, uh, uniswap the token the governor's token just got listed on coin gecko And we take a look we talked about before So this is in the number 70 position and we can see in the last 24 hours It's gone up 64 whatever that means because I think we just listed. So sure Over seven days, of course has been out seven days. So we don't know but uh, it's already at $2.89 Which is gonna be important to us in a little bit So this is coming right from uniswap.org forward slash blog. I'll list this in the description below And that's what's happening. So 60 of the uniswap genesis supply is allocated to uniswap community members A quarter of which 15 percent of total supply has already been distributed to past users. So Essentially, what's going on here is that if you've ever used uniswap before the 16th You're going to get free tokens, which is always nice. So what's it does pay to be a little bit early And uh, this is how we're going to do it. So let's go through the article first just to make sure we know exactly What's going on so to start Uni is available through four liquidity mining pools Uni holders may vote to add more pools after an initial 30 day governance grace period, which starts today So this is what they're all talking about. Uh, they have been as they put it inspired by ethereum's vision They've long committed the ideals of permissionless access security and immutability All indispensable components for a future where anyone in the world can access financial services without fear Of discrimination or counterparty risk and I think that they are actually living up to this credo A little bit more than what sushi swap did that's for darn sure Now it states here rivaling centralized incumbents on daily volume and a couple of days ago We actually had talked about this how they had overtaken coinbase and other large exchanges To be one of the biggest Exchanges whether that be centralized or decentralized out there at present And this is what they've been doing over the past two years. They've supported over 20 billion volume They've secured over 1 billion liquidity deposited over 49,000 unique liquidity providers or LPs Earning 56 million fees in the process and emergence as a foundational defi infrastructure.  I mean They've probably been doing this for a long time. It's just that, uh, you know how it goes It's a it's an overnight success that took a long time and here we are In the forefront of defi. So this is how it's all going to work union allocation. So 60 percent Is going to the uniswap community members or 600 million union and this is Exactly how you're supposed to do it. So you create something you have a you have mining for or that the genesis block And you know what 60 percent is going on to the community members, which is where it should go So think about a lot of other projects that you can think of right now where they mined it and guess where it went to It went to the founders. It went to some investors It went to a very small portion which makes it in my opinion centralized so if they're going to say, hey, we're going to mine all this and uh, 60 percent goes out So we don't have control of it. Thanks so much That's kind of like the whole idea behind decentralization and I can support that for sure 21% are going to team members and future employees with four-year vesting Hey, I'm okay with that if you're giving away a ton of it 60 percent And then 21 percent goes to uh members and people who are actually gonna, uh, you know Keep the whole project going and flowing fine fantastic 70 to investors with four-year vesting and 0.069 to advisors with four-year vesting So they are actually putting money into it. I'm good with that This is interesting a perpetual inflation rate of 2 per year will start after four years This is ensuring continued participation and contribution to uniswap at the expense of passive unit holder So you can't just sit back and don't do anything. You got to be involved in the community. That's great Moving down a retrospective Uniswap owes its success to the thousands of community members that have joined its journey over the past two years people like you and me These early community members will naturally serve as responsible stewards of uniswap 49 knowing you and uni are claimable by historical liquidity providers So it all looks good. Let's see. There's going to be liquidity mining an initial liquidity mining program will go live September 18th, so we're looking at what is that tomorrow The initial program will run until November 17th and target the following four pools on uniswap v2 ETH USDT ETH USDC ETH DIE ETH RAP BITCOIN 5 million uni will be allocated per pool to LPs Which roughly translates to 83 000 plus per pool per day or 55 uni per pool per block So in the meantime uni holders uh until this actually happens We'll have immediate ownership of the governance token uni community treasury, which is big Pay attention to sushi swap the protocol fee switch Uniswap default list and the socks liquidity token. So here's the next step all historical users Liquidity priors and socks redeemers can claim their uni now. So Just to make sure to get the right web address. I have this on my exchange and wallet fees This is in the description of every one of my videos There's a link that looks just like this and this goes over every wallet and exchange and decentralized exchange that I use and recommend I also break down all the different fees and things like that You can use the affiliate links or not You can go right to it if you don't want to use it That's fine. But if you use the alinks that give you 10 25 dollars just to sign up And as you know, I recommend to sign up to as many as possible Especially when a parabolic bull run comes so you're not left out like a lot of people were in 2017 So over here as we go forward finance up fold abra simple swap uni swap So here is the actual website address. We're going to click on that. So when you first come here, there's nothing really magical It's not going to be able to just go here's your tokens You have to connect to a wallet and this has got wallet that you have used in the past for uni swap So they can actually verify that you have used this in the past So we're going to click on a connect to wallet and for me, I use metamask before it was pretty simple It was uh connected to my brave browser and you can't get any more Easier than that. That's why I love brave because they make it so simple and you get to earn that token Just for surfing around the internet.  Thanks for being part of the uniswap community claim uni tokens Sure, I will do that. So again, you can read more about uni and that was the same article that we just went over I'm going to claim uni So of course for here, there's always a gas fee and unfortunately right now it is quite high. However Uh to get 400 uni at almost three dollars. Yeah, sure. I'm going to confirm that So right now it's pending. It's going through the whole process and then as I come back It's been about 10 minutes 15 minutes or so It looks like the balance was claimed of 400 unclaimed 0.00 Wow, uni price already up to 387. So not a bad day. Uh, just do a little bit of work I will take it. So there we are now what we need to do is make sure that it's actually in our wallet So let's take a look at whatever wallet that you have for me. It's in my brave browser It's my metamask. I'm going to take a look at my wallet to see if it's actually there, but you can see right here Um The wallet address is pasted right here. That's the one that is is connected to so it should be the same one Let's open it up. So what I'm going to do and brave is open up a new new tab Click on the brave icon the upper left hand corner, which you can't see go to preferences And you can't see that but uh, there's all my information right there on the very right hand side It says crypto wallets. I'm going to open that guy up and let's see what we got Let me turn this down and there it is 400 uni at 15 29 So uh, just to be aware of this is that um, just give it some time And it may look like things aren't working too well in the beginning But just give a little bit of time because remember this is all through, you know Ethereum and the transaction fees are high and it just takes a long time. So uh, the more you wait Probably the more the fees are going to jump up and uh, who knows if you know, you know There was enough to go around so if my recommendation is definitely do this as soon as possible And get this done so you can have your uni right there and then you can uh, save it spend it Whatever you want to do. All right, so that's it for today So I hope that last piece helped you out with the uniswap platform and I gotta tell you I gotta tell you uh, that is one of those ways of how you build a community Now you don't pull some type of you know Masterchef sushi swap thing where you know the money's just out there Uh, you just you set it all up in the beginning and say hey, this is what we're gonna do This is how we're gonna do things and you lay it all out very clearly I was on a show yesterday. It was uh, with uh, being crypto It was as me crypto love and hasho she and hasho she um, he said it very clearly So, you know The whole sushi swap situation could have been prevented if the master chef just would have laid it all out and said Hey, I'm going to take x amount of dollars because that is going to be my salary And that's why I need to actually live on but I'm going to do all the things that I promise to do And just you know set out as a tweet or on any kind of social media on telegram And he said it would have been no big deal because people would have understood now There's a big difference between they can like 200 000 for a salary as opposed to you know 12 13 million or whatever else it was But I would say that the way that they did this as far as uniswap did Was a fantastic way like look we're going to give 60 percent of the community We're not going to hoard it We're not going to just give it to the founders and just let you know some whales buy it all up So there's 96 percent in a very concentrated Little piece of the pie We are going to give it all out there and let it for the community and that to me Is the whole point of decentralization Let me know what you think but that's just how I see it and then the next one or in actually the very beginning And we talked about the pompomiano podcast With mr. sailor there, which who was the CEO of micro strategy Again, it's a fantastic thing It's just a great look as to how businesses are actually seeing Bitcoin cryptocurrency digital assets and if you have That person and that huge billion dollar company making strides What do you think is going to happen when all the other companies who are just sitting back and our spectators going I wonder how it's all going to work out and then it does work out and then all of a sudden they're like, hmm All those trillions of dollars they have in their treasury like we talked about Maybe we should do something with that. Maybe we should get into a deflationary asset That is not quantitative easing, but it's quantitative hardening. So uh, that is it for today If you would be so kind Make sure you check out um, uh, antony pompiano's podcast. He's got a youtube show. It's fantastic I highly recommend it. I'll put it. I'll put at the very end So you can click and check out the whole thing again. It's an hour and a half So, uh, just be ready to you know, listen to whole stuff and it's a lot about uh sailor there talking about himself Which is fine And uh, and that is it for today. So thanks so much for watching all the way to the end really appreciate it There's no cue the day section. We went through a lot of stuff But if you like those types of videos, I'm going to put two more at the very top You can check those out and that is it So thanks so much for watching to the very end and I'll see you on the next one


If you thought regression analysis was a little bit esoteric, I have news for you. It's getting really esoteric now. We're going to talk about dimension reduction, moving in and out of higher dimensions and reducing dimensions. So the foundation of dimension reduction is often a procedure called principal component analysis. And we'll talk about how principal component analysis can be useful for dimension reduction. And I hope that by the end of this unit you'll be able to perform PCA on your own data and interpret the results. So not just do it but also understand what you're doing. And be able to use the results to identify interesting aspects of the data. And we'll also talk about some alternatives such as projection methods and embedding methods. So what's a dimension anyway when we talk about dimensions of data? So we're not talking about something that would appear in the X files appearing from higher dimensions. What are we referring to? What does the word dimension mean in the first place? I'm hearing an attribute. What word is embedded in the etymology of dimension axis? Yes, the idea is there. But etymologically, looking at the word, it's got a prefix d i and then something with mention measure something. It's something about measurement. Not necessarily independent. When we're talking about dimensions the values can be very dependent on each other and something. So that's something that we would like to figure out. Can we make them independent? Then why should that be so? But basically a dimension is something that can be measured. And two dimensions are orthogonal to each other if none of the measurements has information about the other measurements. So orthogonal dimensions describe independent aspects of our data. Another way to look at the concept of dimensions is to call them features. And that's become a term that is used a lot currently when we talk about machine learning of data. Machine learning basically is the art of using features of data and then drawing conclusions about the data in terms of grouping the data or making decisions of whether the data overall have a non-observed property. And this kind of looking at PCA and dimension analysis conceptually has a lot to do with feature engineering for machine learning. So what we're trying to do is often we're working with data that is quite high dimensional. So for example if you look at a gene expression profile across different types of stimuli then each of these stimulus say heat shock, acid shock, induction with some cytokine and so on and so on could be a different dimension along which this particular gene expression value varies. And they're not necessarily correlated in any way with each other or perhaps the correlation is something we would like to find out. Or we might have gene expression data that are collected in a time series at different time points and that's an odd kind of correlation with special properties that we can discuss. So these features together if they're the same feature we can think about them as being plotted on the same axis i.e. corresponding to the same kind of measurement. And the goal of principle component analysis is to take such possibly correlated variables or such features or such dimensions and transform the data overall, the entire data set so that we can describe what's important about the data with fewer dimensions. And if we have everything that's important about the data presented with fewer dimensions it becomes easier to discern structures. We're as humans really not very good to find structures in four and five and six dimensional space. That's not usually most of us anyway where we are situated when we think. We're very very good at finding structures in two dimensional images. We are often better than any kind of computer algorithm that we've discovered so far. We can even find structure in two dimensional images when there's none there. That's how good we are. We just imagine it. If you do a Google search for par idolia that's an example of seeing faces everywhere. Quite funny. So what we're trying to do is we're trying to take two high dimensional data and transform it into a smaller number of dimensions because it's easier to analyze. And to do that without losing anything that's essential about the data. So that's the idea. And the way we can do that is if the data is correlated in some way we can use the fact of that correlation to remove it. So if like in our regression example before we have a perfect linear correlation between two variables then we don't need the x and the y. We just take the y axis divided by the slope, subtract the intercept and then we come up with the x axis. So either using the x or the y values has exactly the same information. We can just throw the other dimension away. Now that's not often not always possible so we need to look at the data in a different way. The idea is to use this mathematical procedure principle component analysis to transform the data into these so-called PC's or principle components that are orthogonal to each other i.e. they are now uncorrelated. So here's the deal about that. Never mind the code we're going to reproduce that in code. So if we have a histogram of random values of x and y we could get a random plot that looks like this one down here. If we have a random plot of x and y2 where y2 is computed from a linear relationship plus some errors of y1 this looks not very much at all like this year. This would have a very low correlation coefficient. This would have a rather high correlation coefficient. However, if we only look at the histograms of x and the histograms of y2 we can't actually distinguish the two. They look the same to us. So the idea of correlation analysis is to take data sets such as these and rotate them or view them in a way where we maximize the variance along one dimension and then we may hopefully be able to ignore the variance along the other dimension. So kind of you're trying to rotate this in space in this case it would be in two dimensional space. You're trying to rotate it so that when you shine a light from the top the shadow in one direction is maximized and then that's what you analyze. So you take a data set and you rotate it in space along the dimensions. In this case this would be since it's a two dimensional data set in 2D space but it could be in high dimensional space. You rotate it and you try to rotate it in such a way that the variance along one of these dimensions is maximized and then once that is done you rotate it around that orthogonal to it so that the variance in another dimension is also maximized and so on. And it then turns out that the more you do that the less information is still remaining in the dimensions that you didn't treat like that. So in this two dimensional example if I rotate this parallel to the x-axis there's not very much more going on in the y-axis at all and then I can say well there's not much going on in the y-axis maybe I'll just throw it out and then just keep on analyzing with the x-axis data which is then one dimensional data. So the interpretation of these principal components even though it's a mathematical technique that's not very hard but to properly understand it you need a little bit of linear algebra but the intuitive interpretation is the first principal component shown in red here corresponds to a line that passes through the mean and minimizes the sum of squares of the distances of the points from the line that sounds familiar right it's just regression analysis along the first dimension and then you take that line and you treat that as the new x-axis and the second principal component is calculated in the same way after the correlation with the first principal component has been subtracted out. So apply to our data set where the histograms are indistinguishable between the original data and the data plus error terms after principal component analysis this histogram would correspond to the projection along the red vector it's most of the variance is now explained here and on the same scale this histogram corresponds to the components along the blue axis there's not a lot of variation left here. So what we can then often do is ignore this part and continue the analysis only with this part. In R we have two alternatives they're very similar PR comp and print comp for historical reasons there's two different approaches to that they can be used in very different ways but they use slightly different terminology which you might come across when you read tutorials that uses either of them. The center is basically the vector that was subtracted to center the data i.e. the whole multi-dimensional data set you calculate the mean of that and then transform translate the data set to the origin so it's then rotated around the zero point of the coordinate system. The standard deviations for each dimension of the rotated data basically tell you how much variance is explained by one of the principal components the what PR comp calls rotations or what print comp calls loadings are the actual principal components. So these actual principal components are vector that have the same length as the number of dimensions and they basically say how much each original dimension contributes to the new vector. And that's kind of interesting because it says after we've done this analysis and we look at the principal components we actually cannot interpret what these principal components are to a very significant degree. All of the dimensions can equally contribute to one of these new dimensions. So imagine that your data would be a perfect correlation along a high dimensional diagonal through the hyper cube then all of the dimensions would then contribute perfectly equally to the one dimension that the resulting data would require to be perfectly represented. So that's one of the downsides of principal component analysis. We get a mathematically very robust procedure to work with our data but we lose a certain amount of interpretability. Not all interpretability. We can still look at the data and then make some conclusions as we'll see when we look at actual data. So the actual principal components are called rotations or loadings depending on which program you use. PR comp uses X for the rotated data i.e. the data after principal component analysis and print comp uses scores. But these are the same things they're just called differently. One thing one should mention is that principal component analysis is sensitive to scaling. So it makes a difference on whether we report, for example, temperatures in Kelvin or in degrees Celsius or even in that arcane other measurements that we sometimes use in North America. Even though temperature is both, is equally similar to what we really well described with all of these systems, the fact that the numbers are different has an influence on the principal components. You can imagine if I say I have data of heights and weights and the weights are given in tons and the heights are given in micrometers. So these of people, these would be very, very different scales. So all of the variance in the data would be dominated by the numeric values of the micrometers. And the principal components would correspondingly just focus on the weight scale and the other information would be lost. So how do we fix that? Well, what we usually do is we use some kind of variance normalization. We calculate the variance of the data. We divide each individual dimension by its variance and then everything is on an equal scale. That's a good approach if the dimensions are independent. If they are not independent on each other, we can introduce some artifacts in this way. But as a good first approach, it's often reasonable to do a variance normalization with your data. So basically just use SD or the var on the data and divide the entire data column by that value. Well, okay, so again, let's do some, let's do some code. Let's play with it. It's the same procedure that our studio project is called our EDA dimension reduction. This is the script. I'll pull it out again. And let's start with the same synthetic data example. 500 normally distributed samples each uncorrelated. So build a vector of X1 and Y1 of normally distributed samples. And then we generate this Y2, which is correlated with or dependent on X1. So Y2 is just two times X1 plus Y1. And when we do that, we notice that we have a significantly large mean so we subtract the mean from that data. And now it's virtually zero. And we also notice that we have a standard deviation, which is not equal to one. So we divide the data by the standard deviation. And now it is equal to one. And then we plot. So basically what we've done here is we've generated data that has a linear correlation and an error term. And then we've normalized it so that the mean is the same as X and the standard deviation is equal to one. So let's plot this. I've shown you how to plot things and then add elements to the plot with commands like text, or line, or points, or map lines, or other additions. But what we can also do is we can plot more than one plot into the same graphics window. And that uses one of the graphics parameters. There's a quite large set of graphics parameters that you can set globally for your session. For example, you can set the number of rows and columns that will then determine where R is going to plot its next plot. So if I have two rows and two columns, the first next plot will go into the top left, the next plot will go into the top right, the next plot bottom lift, and then bottom right. So then I have four plots in the same window. Of course we need to reset that if we want to plot different things. But the graphics parameters are sticky. So in order to reset that, it wouldn't be automatically reset when we make a new plot or a new plot. We have to reconstruct our graphic state as beforehand. And so this parameter function has a side effect of setting the graphic state. And it has also an effect of returning the previous value of the graphic states, which is kind of crafty. It doesn't return what it did. It returns the way it was previously. But in this way, we can run this function to set a new graphic state, and we can save the old graphic state in a variable. This is old parameters. And then if we are done with our plots, we can reconstruct the previous graphic states, i.e. again get back to the function that one plot fills one entire plot window. We can reconstruct that by defining par equals opar, or par as a function of opar. So that restores the graphic state parameters. Now I usually get that wrong. I either forget to reset the graphic state or I have a typo or I forget how to properly use this. One way of how to basically reset the graphic state is simply to close your plotting window. And then once a new plotting window is opened, it will come with default parameters. So in this case, once we execute this, we can put four plots in the same window. The first plot should be a histogram of our X1. So that's this histogram. And it goes into the top left. The next plot should be a histogram of Y2. The histogram of our new data. Remember, we've normalized it. So the means are the same. The standard deviations are the same. And simply from looking at the histograms, we could not tell in this data set whether X or Y would be more important or what's going on with the data. Now if we plot X1 against Y1, we see that this data set is essentially uncorrelated. And if we plotted again X1 against Y2, we see that there's a large linear component in there. Now calculating the principal component analysis of X1 and Y2, i.e. the principal component analysis of this plot is very easy. Simply run PR comp on these two columns. So once a matrix, what we have are two independent vectors, but we can generate a matrix with the C bind command. C bind binds two columns together, or binds a column to a matrix. C bind is short for column bind, and there's a cognate R bind to bind rows together, which we can also use. So if we do that, we get an object which I've now called PCA sample. What is this? Well that's the data we get here. Standard deviations of the PCA sample are 1.3 and 0.3. So you already see that after rotation with principal components analysis, most of the variation in the data is only in the first principal component here. So you have to think of these principal components as the new X and Y axis. The one X and Y axis we get after rotating the data, or that would correspond to the rotated data. And the rotations are defined here. Minus 0.7 and so basically this corresponds to a 45 degree rotation. Now as I've shown you in that PowerPoint slide, there are a number of values that are available in that PCA sample object. There's the standard deviations, there's the rotation, and so on. So let's look at that. Standard deviations is something that was printed by default. We can get at the rotations like that individually. We can get using the summary command. Remember the summary command gave us minimum values and quantiles and means and medians for vectors. It has a special version of summary for PCA object so it behaves differently. And it gives us the importance of the components. So the proportion of variance here is that 95% of the variance is now found in PC1 after rotation. And only 4, about 5% of the variance is found in PC2 after rotation. So we see that PC1 is 20 times more important than PC2. And that is something that might lead us to conclude, well we can just toss out PC2 and keep working with PC1. PCA sample $x gives us the rotated values. And if we plot them, we get this here. See did I forget to run this? I don't remember why I set it explicitly. Maybe just for nicer numbers here, of course it would work in the same way. Without that. Ah, yes. Okay, so that's why. So what's the difference? Right, so it's random, but the scale is very different. So what the plot does by default is it optimizes the axis so that we see the most amount of data in both axes. But with the plot I did previously, I wanted to emphasize that now all of the variance is just in one dimension. So plotting it in this way shows me that because now the y-axis limits are on the same scale as the x-axis limits. I'm wasting a lot of space. Well in this case I'm not wasting space, but I'm demonstrating something through empty space. Okay, so if we compare the histograms before and after rotation, essentially this is the plot that we've seen before. This was before rotation, the two histograms. This is after rotation. Most of the variance of the data is in the first principle component and much less of it is in the second principle component. If we plot the sample along the principle components as axes, that's what that looks like. So this is now a plot of the rotated sample using the axes. The object PCA sample is list five elements, standard deviation, rotation, center scale and x. Some of these have attributes, dimension names x1, y2, PC1, PC2 and the class is PRComp. So plot recognizes that PRComp is a special kind of class and treats it accordingly. So that's a very simple synthetic example, a very simple data set. Let's look at something that's a bit more biological. I remember when I was a medical student I was volunteering in the department of physiology and looking what people were doing there. And some people were interested in salmon. Kidney physiology of salmon is actually quite interesting because they spend part of their life in salt water and part of their life in sweet water and the kidneys have to adapt to that. So they were studying that and as a side effect, every now and then they had a large batch of salmon. They took out the kidneys for study and then of course the rest of the fish had to be otherwise disposed of. So we had excellent salmon at that time. Now these researchers here apparently like to go scuba diving and they're in West Australia, nice place for scuba diving probably, and they study crabs. The question they had is if we do a morphometric study of crabs, can we distinguish the species and the sex of the crabs? God, I can never remember. Is it actually two genders or two sexes? I think with crabs it's sex and not genders. So if I use them interchangeably, it doesn't really mean anything. Okay so there's blue and orange of these crabs and there's males and females and we can take a number of measurements. So we catch a crab and then we measure its frontal lobe size. That's this measurement here and we measure its rear width with calipers all the time trying very hard not to get pinched because the crab doesn't agree. The carapace length and the carapace width and the body depth. So these measurements should somehow characterize the crab from its shape. They're related species but maybe they're different enough. The question then is once we've done these morphometric measurements can we infer which crabs is which? And the data set is included as one of the sample data sets with all our distributions. You simply type library mass and load the data set crabs. Now that's interesting. Here as in terms of data set crabs has been loaded but nothing actually exists yet. It's a promise. One of the ways that R is able to do things very efficiently is because it defers activities that it doesn't actually need yet or is able to defer activities that it doesn't actually need yet as promises. So we've loaded the data set only in principle but since we're not actually using it yet we're not reserving space in memory or reserving process of cycles to do anything with it. So it's just there in principle. If we look at the header of this we see the species blue in the first six rows, the sex, the index, the counting index and then the measurement for frontal low rear width carapace length. And now the promise has changed into an actual data set. So we've used it so at that point R said okay now we actually need to load it and we need to access it. So let's have a look at that. First of all I'd like to be able to annotate the data. And in order to annotate the data I want to have a code that characterizes them. We have letters for species B and O and we have letters for the sex M and F. So B-O should be for, B-M should be for blue males and O-F should be for orange females and so on. And in order to get that we use the paste function to take the letters from the first column and the letters from the first column and the first column and the first column and the first column and the first column paste function to take the letters from the first column and the letters from the second column and just paste them together. So these are little labels that characterize our crabs. And as you can see the first set of crabs are all blue males then we have all blue females then all orange males and all orange females and we have 50 of each. Now that's very nicely cleaned up data usually it's messier but just keep that in mind. 50 blue males, 50 blue females and so on. Now this is one time we actually want to use factors. Now if we take these labels here and turn them into factors, assign that to the variable FAC, you see the first six measurements are now B dot M as labels, they're factors now, no longer strings so they don't have quotation marks around them. And whenever you print some factors it will always tell you what all of the possible levels are. So this is B-M, we also have B-F, O-F and O-M. If we look at the different factors like these four, the factor of the first, the 51st, the 101st and the 151st, these are now two, one, four, three, that's the contents of the factor. And we can turn them into numbers, two, one, four, three and we can use these numbers to get different colors or different plot symbols or different line types and thus make plots where the types of crabs are distinguished as we plot them. So in that they're not all circles, they might be different plot symbols. So that's what we do here. We plot crabs column 428 where the plotting character is the factors that we've just determined turned into numbers. So that's what our labels, what our actual data look like. Quite highly correlated. I didn't draw a legend here so I can't tell you offhand which ones are the circles, which ones are the X's, which ones are the pluses and which ones are the triangles, but one of them each is blue males and another one orange females and so on. So now the challenge is here's the two dimensional information. We have five dimensional data sets. We have two dimensional information essentially like this and the question is how do we take this information to actually distinguish between the crabs or can we do that? And what you see immediately is that there's a lot of overlap. So the question is can principal component analysis or some other procedure help us to remove the overlap based on these measurements? So if you assume that probably because we're working on this example it's true that some combination of the morphometric measurements is able to distinguish the different crabs here. It is not possible to do it with the original measurements and the correlations of these original measurements in two dimensions. There's simply too much overlap. Can we imagine which combination of these dimensions we would need to do that? No. This is where our capability to visualize and to imagine data breaks down. So we can do this easily in two dimensions but none of the two dimensional presentations here actually help us. So let's apply principal component analysis to the five dimensions. So the dimensions we want to work with is not column one and two because that characterizes the crabs, not column three. That's just an index but column four, five, six, seven and eight. So principal components analysis PCA crabs on columns four to eight. And we plot that. And we see that the principal components analysis is quite successful. There's a huge first principal component that has all of the variance and a lot of other information in the other principal components. So what does this mean and what does it do? So if we look at the summary here, the principal part of interest in these summaries is often the cumulative proportion. So basically this is taking the first principal component, the one with the largest variance and then saying what proportion of variance do we have in that? Then we add the next and the next and the next so we can basically pursue how the 100% variance is generated. So with the first component we have 0.98, adding the second component goes to 0.99, adding the third component goes to 0.99, 9 and so on. So almost all of the information is in the first component. Now there's a standard plot that we use for such scatter plots and that's the so-called by plot. The by plot plots the principal components in the rotations from PCA crabs and it also adds the projections of the individual principal components so we can have a look at how they are oriented and how the data, the rotated data lies along the new principal components. We can add, okay. So these are now the numbers, one is the blue males, two is the blue females, three is the orange males and that's the by plot of the first principal component and the second principal component. So after principal component analysis, we see that actually the data is separable to a certain degree. We have very large variance overlap between 1 and 4 and we can't distinguish it perfectly and it's kind of all odd going in that trend. So let's look at plotting along the other principal components. So this is 1 against 2, this is 1 against 3, the first against the third principal component and it's separated in a different way. Again, there's a very large amount of overlap here. So number one was the strongest principal component, number three is the third largest, the one relatively small principal component and that's what we see here. Now here's what we see when we plot 2 against 3, the two smaller principal components. What do we have here? What's going on? We have almost perfect separation of our four categories if we plot principal components 2 against 3. Didn't we just say that all of the information is actually in the first principal component? So we can get separation if we look at the noise but not if we look at the data or am I misrepresenting something here. What's going on? Any idea? Why do we have these huge correlations in the first place and why can we look at the categories in a representation that doesn't even look at the huge correlations? Well, actually all of the units were highly correlated with something. So what we have in a very similar way and Brandon's actually absolutely right, they were all correlated with a confounding factor that we didn't take into account here and that could be something like weight or volume or age of the crab, the older they get, the larger they get but all of the dimensions grow essentially in the same way and we didn't distinguish, we didn't require that all of these crabs would have exactly 50 grams or 500. I don't know how large they actually get. They do look tasty. So that's what's happening here. We have this huge correlation but it's due to a confounding factor and once we can remove that out through principal components analysis then the actual information in the data becomes apparent. So what we're doing now in the second and third principal components is essentially classifying them not by this correlation here but overall shape independent of what the absolute values of the size is. We could probably have a similar effect if we take an average of all the values and then simply divide everything by that average set of values then we would get more information here. But this principal component analysis nicely pulls out and is able to remove the confounding factor. Now that's a special example. It's not always the case that you have to throw out the first principal component because it corresponds to a confounding factor. That would certainly be false. But if there's a confounding factor it is often very strong in all of the data points because it affects all of the data points equally. So that's one way to detect it. Mohamed. Machine learning at least based on my vague understanding from an undergrad course that we often look at the components with the highest variation and actually keep those components and throw smaller variations away. It depends. Go on. Sorry I was just wondering. This example very nicely shows the counter example of what is often done in machine learning. In other words here we should throw away the largest variation and keep smaller ones. Yeah. So it depends both on the type of machine learning you do and the kind of computational resources that you have. Some types of machine learning are quite sensitive to features that are not informative like the confounding factor here. So in that case we would do a pre-analysis and find that the first principal component should be removed and then we would only work with the second and the third principal component. This reduces the number of dimensions and reduces information that's erroneous. If we have fewer dimensions we can run more cycles of optimization on the classifier and then we can get better classifiers and then everything will work better. However, that's not actually true anymore for the modern machine learning approaches like deep neural networks. They don't care. We just throw all the numbers we have on a deep neural network and let the neural network figure it out. As long as your training data is well conditioned and covers all of the possibilities and is correctly annotated you are likely to get good results. Of course training runs will still be longer if you have uninformative features but it's not necessarily the case that uninformative features will lead to less accurate results. So I don't know. There's this modern perspective where we might not really need data science anymore. We just need large clusters and large machines. We don't need to worry about features as much as we used to do. But I don't think the data analysis will go out of style very quickly for a number of reasons. You still have to prepare the features in some way and understand which features are available in the first place. The most important part is asking intelligent questions. You never mechanically treat data in that way. You analyze it in different ways and you interpret what you see. So as I said this is an example that's interesting because we can identify a confounding factor here. But to say we just throw small factors away and keep large ones that would not be correct. So what I would do is I would drive it from the performance of the classifiers. So I would try different ways of preparing features and feeding them into the machine learning algorithm and then see which ones give the best reductions and the best classifications in the end. Keeping maybe the top ones. We do a genetics for example. If you want to control the population stratification, you actually want to look at the population and see if you're separating out. And that's how you decide to keep them. Here we're classifying. So we're looking at the top ones and we saw that the top ones don't decouple or decompose the different types. So we move down to lower ones as well. So I would say that it's never one size fits all. I think you have to look at your data. Look at your data, play with it, learn about it. Simply looking at the first and third and first and second plot that we had before, it wasn't clear that we could separate the data at all. This might have gone on for all of the dimensions. And then that would have said, you know, what we're measuring here is what we're measuring here, but it doesn't really correspond to our categories. Okay. I have a small task for you. And that is to plot this last plot, i.e. this kind of plot. Not as a by plot, but simply as a scatter plot of the rotated values in a way where your plotting symbols correspond to the sex and the type of the crap. Orange and blue circles for females and triangles for males. Orange and blue triangles. The reason behind that is that interpreting scatter plots is often tremendously helped by identifying which data points we're actually looking at. So if we see outliers on the scatter plot and the outliers are just circles, that doesn't tell us a whole lot. But if the outliers are labeled with gene names, then we can perhaps identify all of these are known cell cycle genes. And that then tells us something. So one of the things that I would like to start doing here is when we do scatter plots, decorate the values with information that we have about the values. So in this case, the information would be encoding the categories of species and sex into the shape and the color of the plotting symbols. And I'm being deliberately vague. You don't know how to make circles and triangles in a way that you can color them. We've talked a little bit about specifying colors and so on. But we're talking crap, so I'm throwing you into the deep end. Try not to get pinched. See if you can solve this. And before you despair, put up a red postage so we can help you out.  So I'd like to walk you through one possible way to do it. If you have very different ideas, then we'll discuss this as we go along. So the problems we need to solve is first we need a plotting frame that will accommodate all of the data. And then we'll need to find a way to plot the points individually. And then we'll need to find a way to assign a particular shape and color to some of the points that we plot. So plotting the value in the first place requires nothing more than plotting $x of the PCA crabs, column one and column two. So that's essentially the underlying plot that we had. But right now, they're all circles. So in order to plot some of the values with different symbols, we can plot, for example, only the first 50 values. So all the first 50 I think are blue males. So that's what that looks like. Now, R automatically adjusts the size of the plotting frame when we do that. So now we would have no more space to plot orange males and blue females and so on. So that's not good. We need to define a plotting window that will actually accommodate all of our data. We talked about x limits and y limits before. So can we use x limits and y limits? Yes, in principle. If we do range on PCA crabs x one, we get the smallest and largest value. So we can plot the same thing, column one, column two, and specify that the x limits should be the range of all the values in column one and the y limits should be the range of all values in column two. And that creates a plotting window that is large enough to accommodate everything. So that's one way to set the plot window large enough. There's another way which is probably preferred, much easier. And that is simply to plot the window without plotting or showing anything as an empty window and then adding everything we want to show through appropriate commands of points and lines and text and whatever. And if I remember correctly, we simply need to specify type equals n for none. So now we plot all of the values, but we don't actually show anything empty. And now we can use not plot, but points. The points command works exactly like the plotting commands, except it doesn't set a new plot window. It writes nothing into the margins. It doesn't do access ticks and labels or anything. It just plots symbols for whatever data we tell it to. Oh, yeah, of course. Well, if that is wrong, if I limit it, of course there's no difference. So here's my empty plotting frame and here's plotting the first 50 values as points. And doing this in a very pedestrian way with the... I hope you understand very well that there's a lot of possibilities of adding typos here, doing things wrong. This is quick and dirty, but quick. We can get the categories here. Okay, so that's our second set of points, our third set of points, and our final set of points. What did we gain again? Well, several things. First of all, this was wrong anyway. We didn't want one and two. We should have had... What was it? Two and three. Okay, so let's change that. Two and three. Oh, if you haven't seen this yesterday, we can use the Alt key in our studio editor to select things from columns in the text editor or to enter things in the text editor in columns and delete them and replace them. If things are lined up, this is quite quick and easy. Okay, so let's do this again. Plotting the empty frame, plotting the first data set, the second data set, the third data set, and the fourth data set. Yay, it looks just like before. So what did we gain? Well, what we gained is that we're now doing it independently and we can write additional commands into these points to do different things. So for example, we can define different plotting characters. What plotting characters should we use? Triangles for males. How do we specify that? What's the plotting character for color-filled triangles? How do we know? Do we do question mark or PCH? I'm not sure that would work. It's there? For PCH? Question mark, PCH works? Awesome. Okay, very good. So the triangles would be 17 and the circles would be 16. We need the filled ones because we went to fill them with a color. Okay, so which of these groups are the males? I think it was the first and the third one, right? And then that was 16 and 16. Okay, so the first triangles, second circles, third triangles, and the fourth circles. Okay, now accept that they're not colored yet. Should we hex it? Yeah, let's hex it. I'm going to remove some spaces here so it doesn't wrap. Okay, so the first one is blue. Let's use something of a light blue with a little bit of cyan. And then we get two orange ones. Let's also make it something like this. The orange is very light. It's more like a dark yellow. Let's make it deeper. There we go. Okay, so now we can actually see that the separation is very good. There's actually only one overlap that we can see here. Everything else we could potentially draw a line through the convex shape that covers all of the points and none of the others. So that's a very good separation. That solves this task. Would you have done it fundamentally differently? Any other ideas? Anything confusing about this? Could you do this for your own data? There's more elegant ways to achieve these things, but I think this is very pedestrian, doing nothing that we haven't done before, no special new tricks. Yeah, right. Awesome. Exactly. So basically the way you do that is you generate a vector that contains the individual color values, and you use that vector for the colors or for the plotting characters. I'll write up a little sample solution tonight that we can just run by tomorrow, and I'll also add a little bit of code, because that's quite informative here, that scales the plotting character by the average weight or the average size of the individual measurements. So the hypothesis is that the young animals would not be easily distinguished, so the smaller they are, the more closely they should lie together, and the larger they become, the more characteristic the differences become. That's what I would hypothesize about data like that, and we can easily test it and show it on a plot like that if we scale the plots by average size. So we'll look at that function tomorrow.


Hi stampers, I'm Jill and I'm part of the Stampin' Jill Creative Team here to show you a new layout idea. And actually I got this layout idea from one of our trade cards that we received and this is just basic layout here with a strip and two circles and a saying. And so I want to kind of show you a bunch of different ways to actually use this layout idea. So I'm using the perennial essence designer series paper and if you notice on one side it's kind of more like a watercolor or oil painting and then the other side is just solid colors. It's just beautiful. So I'm gonna use this layout idea in a couple different ways. So I went ahead and already kind of cut these out so you can see. Okay so let me go into what is actually used in this.  So that's basically it and then just a quarter of it smaller around the card. So I'm gonna go ahead and put this one together and it's going. You can decide whatever side of paper you want to use. I'm just gonna use the more muted side on this particular card and have the quarter of inch go all the way around. So then I'm gonna take the strip and some of the strips I've used just plain and some of them I added the cardstock around to frame it. So it just depends on what you like. So I'm gonna go ahead and add that in the center and that just kind of splits the card. Now we're gonna have a focal point. We need to decide to have a focal point on this side, the left side of the card, or the right side of the card. It doesn't really matter and so I'm gonna go ahead and put this down and this is our paper stacks of designer series paper and they come in all the colors. And now I'm gonna go ahead and either put a same right where I stamp it right on that or I can use another one and double that like this particular one was. So it just depends on the stamp set. This floral essence stamp set has a couple different ones and I think I'm just gonna go ahead and use the all days. Stamp this in flirty flamingo. I've already cut out the circles and one's a punch and one's not. So this is all the days are beautiful with you. So there you go and you've got just a very simple and you can pop that up with your dimensionals and this is just very simple layout ideas right here. I'm not really embellishing them a lot. You can put other embellishments and ribbon on it too but this is more for layouts. So there you've got a simple layout where you've got a focal point and dividing your DSP. Okay this one I've went ahead and did the whole DSP opposite going up and down and the Blackberry Bliss is the background. Okay and then we've got the back of this which is great contrast and then after that and I just did a strip on that and then this is beautiful. Love the Blackberry Bliss color and we can pop that up. Now if you want to take your stamps and go ahead around the edges in a different color. Let's go ahead and show you how that would work so I could take this and with the old olive just step it up a little bit by filling the circle in with another color. Okay so that adds a little bit of different color and now I'm going to put that on with some dimensionals and there we've got a layout idea of the same thing just in a different direction. Super simple. Okay so we've got this one that's opens this way and this one that opens this way. Okay one more. This one is the same paper and I'm going to use not the floral but I'm going to use it the opposite way. Let's turn it around here and this is balmy blue and the old olive and we'll just go ahead and put the floral on so it's super simple. Now you can decide like let's say I'm gonna move it down here and do the circle so you can actually move that strip just a little bit to change it up a little bit. I love that's what you can do with layouts is use the same papers just by moving it changes the look of the card. Okay so we've got this and then we've got a same so let me put this one down. I've got a side where I want if I want the smaller flowers or if I want the bigger flower to show so I'm gonna move this over here. Okay and then I can either do this in blue or I can do this in white so you can decide kind of what you want to do. So let's look at this and I love how you have these clear because then you can stamp something long if you want to. Another thing is see these flowers. Okay if I wanted to stamp this on one of the circles I could stamp that and put it right there with the center and you've got a whole different look of a card and then you could put a saying on the inside so it's just giving you the ideas of the shapes so you could use that right here. So let me go ahead and do that so you can see the difference in the two. Here's the flower and we can do that in this blushing bride. Sometimes I like to stamp off blushing bride because it's pretty dark. Let me get this over here. Stamp it off. Let's look at the two. Okay so then you've got the center so I'm gonna pop that up and so this is not even a saying but we're just using a focal point of a flower. So it creates that focal point for you and now I'm going to go ahead and use these centers which come with this sweet and they really go with the paper if you notice they're in the middle of the flowers in the paper. So that's just showing you a simple way of doing the flower. Let me bring all these back in so you can look at all the layouts. Super simple layouts. We'll bring the original card in and then this is just showing you some simple layouts that you can do with that whole layout idea. You can add ribbon to it or little accessory but just showing you how easy with DSP you can make a new layout of card ideas. Hope you've enjoyed this video. Go to stampinjill.com if you'd like to order these products and we'll see you next time on Watch a Leaping One.


Soil erosion is amongst the most pressing issues regarding global food security. Around 40% of the world's agricultural land is already seriously degraded through non-renewable land use. This number, however, is still rising fast. This directly diminishes agricultural production, with severe consequences on a social and economic level in most regions around the world. Lack of grazing management and conventional farming methods with plowing, monocultures and non-renewal of the organic matter leaves the soil uncovered. Wind and rainfall then lead to progressive soil erosion. This is especially serious for farmland on slopes. In order to reduce erosion on slopes, several methods can be applied. Most of them aim at reducing the water runoff velocity or volume. Common erosion control techniques include swales and terraces. Swales are constructed by digging trenches along contour lines and by mounting soil on the downhill side. This way runoff is collected in trenches and can better infiltrate into the ground. Terraces are quite similar to swales. They are constructed along the contour lines by reshaping the slope into multiple steps that are usually fortified with stones. The runoff is slowed down and has more time to infiltrate. Vegetation cover must be established from the beginning. Terraces and swales demand labour and constant maintenance. Therefore, drought resistant fast growing plants with a fast income generation like moringa trees should be chosen. Mutually supportive plants should be combined, but there is still a lack of knowledge. To build a living terrace, tree rows are established along the contour lines of the slope. When they have grown to several metres in height, they are cut off and laid horizontally between the tree stumps in order to get a woven structure of vertical and horizontal elements. By choosing trees that are propagated by cuttings, the cut-off branches will form roots where they have contact with the ground and sprout. This way the whole structure will be alive, productive, long-lasting and more stable due to the roots. By converting erosion control techniques into a productive system, multiple benefits and positive synergies accumulate. These include soil restoration and agroforestry, which produce an extra income for farmers, making slope farming more sustainable and profitable.