<SYSTEM_TASK:>
Given the following text description, write Python code to implement the functionality described below step by step
<END_TASK>
<USER_TASK:>
Description:
 Recommendation Engine
In this tutorial we are going to build a simple recommender system using collaborative filtering. You'll be learning about the popular data analysis package pandas along the way.
1. The import statements
Step1:  2. The data
We will use Germany's data of the Last.fm Dataset. To read and explore the data we will use the pandas library
Step2:  The resulting DataFrame contains a row for each user and each column represents an artist. The values indicate whether the user listend to a song by that artist (1) or not (0). Note that the number of times a person listened to a specific artist is not listed.
3. Determining artist similarity
We want to figure out which artist to recommend to which user. Since we know which user listened to which artists we can look for artists or users that are similar. Humans can have vastly complex listening preferences and are very hard to group. Artists on the other hand are usually much easier to group. So it is best to look for similarities between artists rather than between users.
To determine if two artists are similar, you can use many different similarity metrics. Finding the best metric is a whole research topic on its own. In many cases though, the cosine similarity is used. The implementation we will use here is the sklearn.metrics.pairwise.cosine_similarity.
This function will create a matrix of similarity scores between elements in the first dimension of the input. In our dataset the first dimension holds the different users and the second the different artists. You can switch these dimensions with np.transpose().
Step3:  The cosine_similarity function returned a 2-dimensional numpy array. This array contains all the similarity values we need, but it is not labelled. Since the entire array will not fit the screen, we will use slicing to print a subset of the result.
Step4:  The artist names are both the row and column labels for the similarity_matrix. We can add these labels by creating a new DataFrame based on the numpy array. By using the pandas.DataFrame.iloc integer-location based indexer, we get the same slice as above, but with added labels.
Step5:  Pandas also provides a label based indexer, pandas.DataFrame.loc, which we can use to get a slice based on label values.
Step6:  As you can see above, bands are 100% similar to themselves and The White Stripes are nothing like Abba. 
We can further increase the usability of this data by making it a tidy dataset. This means we'll put each variable in a column, and each observation in a row. There's three variables in our dataset
Step7:  To view the first n rows, we can use the pandas.DataFrame.head method, the default value for n is 5.
Step8:  Note that we created a MultiIndex by specifying two columns in the set_index call.
Step9:  The use of the MultiIndex enables flexible access to the data. If we index with a single artist name, we get all compared artists. To view the last n rows for this result, we can use the pandas.DataFrame.tail method.
Step10:  We can index on multiple levels by providing a tuple of indexes
Step11:  4. Picking the best matches
Even though many of the artists above have a similarity close to 0, there might be some artists that seem to be slightly similar because somebody with a complex taste listened to them both. To remove this noise from the dataset we are going to limit the number of matches.
Let's first try this with the first artist in the list
Step13:  We can transform the task of getting the most similar bands for a given band to a function.
Step14:  Note that we also defined a docstring for this function, which we can view by using help() or shift + tab in a jupyter notebook.
Step15:  5. Get the listening history
To determine the recommendation score for an artist, we'll want to know whether a user listened to many similar artists. We know which artists are similar to a given artist, but we still need to figure out if any of these similar artists are in the listening history of the user. The listening history of a single user can be acquired by entering the user id with the .loc indexer.
Step16:  We now have the complete listening history, but we only need the history for the similar artists. For this we can use the index labels from the DataFrame returned by the most_similar_artists function. Index labels for a DataFrame can be retrieved by using the pandas.DataFrame.index attribute.
Step17:  We can combine the user id and similar labels in the .loc indexer to get the listening history for the most similar artists.
Step19:  Let's make a function to get the most similar artists and their listening history for a given artist and user. The function creates two DataFrames with the same index, and then uses pandas.concat to create a single DataFrame from them.
Step20:  6. Calculate the recommendation score.
Now that we have the most_similar_artists_history function, we can start to figure out which artists to advise to whom. We want to quantify how the listening history of a user matches artists similar to an artist they didn't listen to yet. For this purpose we will use the following recommendation score
Step21:  Remember what the DataFrame returned by the most_similar_artists_history function looks like
Step22:  Pandas provides methods to do column or row aggregation, like e.g. pandas.DataFrame.product. This method will calculate all values in a column or row. The direction can be chosen with the axis parameter. As we need the product of the values in the rows (similarity * history), we will need to specify axis=1.
Step23:  Then there's pandas.DataFrame.sum which does the same thing for summing the values. As we want the sum for all values in the column we would have to specify axis=0. Since 0 is the default value for the axis parameter we don't have to add it to the method call.
Step25:  Knowing these methods, it is only a small step to define the scoring function based on the output of most_similar_artists_history.
Step27:  Determine artists to recommend
We only want to recommend artists the user didn't listen to yet, which we'll determine by using the listening history.
Step29:  The last requirement for our recommender engine is a function that can score all unknown artists for a given user. We will make this function return a list of dictionaries, which can be easily converted to a DataFrame later on. The list will be generated using a list comprehension.
Step31:  From the scored artists we can easily derive the best recommendations for a given user.
Step32:  With this final function, it is a small step to get recommendations for multiple users. As our code hasn't been optimized for performance, it is advised to limit the number of users somewhat.
Step33:  We can now use the concat function again to get a nice overview of the recommended artists.
<ASSISTANT_TASK:>
Python Code:
import numpy as np
import pandas as pd
import sklearn.metrics.pairwise
Explanation: Recommendation Engine
In this tutorial we are going to build a simple recommender system using collaborative filtering. You'll be learning about the popular data analysis package pandas along the way.
1. The import statements
End of explanation
data = pd.read_csv('data/lastfm-matrix-germany.csv').set_index('user')
data.head()
data.shape
Explanation: 2. The data
We will use Germany's data of the Last.fm Dataset. To read and explore the data we will use the pandas library:
+ pandas.read_csv: reads a csv file and returns a pandas.DataFrame, a two-dimensional data structure with labelled rows and columns.
+ pandas.DataFrame.set_index: sets the DataFrame index (the row labels).
Pandas enables the use of method chaining: read_csv call returns a DataFrame, on which we can immediatly apply the set_index method by chaining it via dot notation.
End of explanation
### BEGIN SOLUTION
similarity_matrix = sklearn.metrics.pairwise.cosine_similarity(np.transpose(data))
### END SOLUTION
# similarity_matrix = sklearn.metrics.pairwise.cosine_similarity( ? )
assert similarity_matrix.shape == (285, 285)
print(similarity_matrix.ndim)
Explanation: The resulting DataFrame contains a row for each user and each column represents an artist. The values indicate whether the user listend to a song by that artist (1) or not (0). Note that the number of times a person listened to a specific artist is not listed.
3. Determining artist similarity
We want to figure out which artist to recommend to which user. Since we know which user listened to which artists we can look for artists or users that are similar. Humans can have vastly complex listening preferences and are very hard to group. Artists on the other hand are usually much easier to group. So it is best to look for similarities between artists rather than between users.
To determine if two artists are similar, you can use many different similarity metrics. Finding the best metric is a whole research topic on its own. In many cases though, the cosine similarity is used. The implementation we will use here is the sklearn.metrics.pairwise.cosine_similarity.
This function will create a matrix of similarity scores between elements in the first dimension of the input. In our dataset the first dimension holds the different users and the second the different artists. You can switch these dimensions with np.transpose().
End of explanation
similarity_matrix[:5, :5]
Explanation: The cosine_similarity function returned a 2-dimensional numpy array. This array contains all the similarity values we need, but it is not labelled. Since the entire array will not fit the screen, we will use slicing to print a subset of the result.
End of explanation
### BEGIN SOLUTION
artist_similarities = pd.DataFrame(similarity_matrix, index=data.columns, columns=data.columns)
### END SOLUTION
# artist_similarities = pd.DataFrame( ? , index=data.columns, columns= ? )
assert np.array_equal(artist_similarities.columns, data.columns)
assert artist_similarities.shape == similarity_matrix.shape
artist_similarities.iloc[:5, :5]
Explanation: The artist names are both the row and column labels for the similarity_matrix. We can add these labels by creating a new DataFrame based on the numpy array. By using the pandas.DataFrame.iloc integer-location based indexer, we get the same slice as above, but with added labels.
End of explanation
slice_artists = ['ac/dc', 'madonna', 'metallica', 'rihanna', 'the white stripes']
artist_similarities.loc[slice_artists, slice_artists]
Explanation: Pandas also provides a label based indexer, pandas.DataFrame.loc, which we can use to get a slice based on label values.
End of explanation
similarities = (
    # start from untidy DataFrame
    artist_similarities
    # add a name to the index
    .rename_axis(index='artist')
    # artist needs to be a column for melt
    .reset_index()
    # create the tidy dataset
    .melt(id_vars='artist', var_name='compared_with', value_name='cosine_similarity')
    # artist compared with itself not needed, keep rows where artist and compared_with are not equal.
    .query('artist != compared_with')
    # set identifying observations to index
    .set_index(['artist', 'compared_with'])
    # sort the index
    .sort_index()
)
Explanation: As you can see above, bands are 100% similar to themselves and The White Stripes are nothing like Abba. 
We can further increase the usability of this data by making it a tidy dataset. This means we'll put each variable in a column, and each observation in a row. There's three variables in our dataset:
+ first artist
+ second artist
+ cosine similarity
In our current DataFrame the second artist is determined by the column labels, and as consequence the cosine similarity observation is spread over multiple columns. The pandas.DataFrame.melt method will fix this. We make extensive use of method chaining for this reshaping of the DataFrame. If you want to know the effect of the different methods, you can comment / uncomment them and check the influence on the result.
End of explanation
similarities.head()
Explanation: To view the first n rows, we can use the pandas.DataFrame.head method, the default value for n is 5.
End of explanation
similarities.index
Explanation: Note that we created a MultiIndex by specifying two columns in the set_index call.
End of explanation
similarities.loc['the beatles', :].tail()
Explanation: The use of the MultiIndex enables flexible access to the data. If we index with a single artist name, we get all compared artists. To view the last n rows for this result, we can use the pandas.DataFrame.tail method.
End of explanation
similarities.loc[('abba', 'madonna'), :]
print(slice_artists)
similarities.loc[('abba', slice_artists), :]
Explanation: We can index on multiple levels by providing a tuple of indexes:
End of explanation
artist = 'a perfect circle'
n_artists = 10
### BEGIN SOLUTION
top_n = similarities.loc[artist, :].sort_values('cosine_similarity').tail(n_artists)
### END SOLUTION
# top_n = similarities.loc[?, :].sort_values('cosine_similarity') ?
print(top_n)
assert len(top_n) == 10
assert type(top_n) == pd.DataFrame
Explanation: 4. Picking the best matches
Even though many of the artists above have a similarity close to 0, there might be some artists that seem to be slightly similar because somebody with a complex taste listened to them both. To remove this noise from the dataset we are going to limit the number of matches.
Let's first try this with the first artist in the list: a perfect circle.
End of explanation
def most_similar_artists(artist, n_artists=10):
    Get the most similar artists for a given artist.
    
    Parameters
    ----------
    artist: str
        The artist for which to get similar artists
    n_artists: int, optional
        The number of similar artists to return
    
    Returns
    -------
    pandas.DataFrame
        A DataFrame with the similar artists and their cosine_similarity to
        the given artist
    
    ### BEGIN SOLUTION
    return similarities.loc[artist, :].sort_values('cosine_similarity').tail(n_artists)
    ### END SOLUTION
    # return similarities.loc[ ? ].sort_values( ? ) ?
print(most_similar_artists('a perfect circle'))
assert top_n.equals(most_similar_artists('a perfect circle'))
assert most_similar_artists('abba', n_artists=15).shape == (15, 1)
Explanation: We can transform the task of getting the most similar bands for a given band to a function.
End of explanation
help(most_similar_artists)
Explanation: Note that we also defined a docstring for this function, which we can view by using help() or shift + tab in a jupyter notebook.
End of explanation
user_id = 42
### BEGIN SOLUTION
user_history = data.loc[user_id, :]
### END SOLUTION
# user_history = data.loc[ ? , ?]
print(user_history)
assert user_history.name == user_id
assert len(user_history) == 285
Explanation: 5. Get the listening history
To determine the recommendation score for an artist, we'll want to know whether a user listened to many similar artists. We know which artists are similar to a given artist, but we still need to figure out if any of these similar artists are in the listening history of the user. The listening history of a single user can be acquired by entering the user id with the .loc indexer.
End of explanation
artist = 'the beatles'
### BEGIN SOLUTION
similar_labels = most_similar_artists(artist).index
### END SOLUTION
# similar_labels = most_similar_artists( ? ). ?
print(similar_labels)
assert len(similar_labels) == 10
assert type(similar_labels) == pd.Index
Explanation: We now have the complete listening history, but we only need the history for the similar artists. For this we can use the index labels from the DataFrame returned by the most_similar_artists function. Index labels for a DataFrame can be retrieved by using the pandas.DataFrame.index attribute.
End of explanation
user_id = 42
### BEGIN SOLUTION
similar_history = data.loc[user_id, similar_labels]
### END SOLUTION
# similar_history = data.loc[?, ?]
assert similar_history.name == user_id
print(similar_history)
Explanation: We can combine the user id and similar labels in the .loc indexer to get the listening history for the most similar artists.
End of explanation
def most_similar_artists_history(artist, user_id):
    Get most similar artists and their listening history.
    
    Parameters
    ----------
    artist: str
        The artist for which to get the most similar bands
    user_id: int
        The user for which to get the listening history
        
    Returns
    -------
    pandas.DataFrame
        A DataFrame containing the most similar artists for the given artist,
        with their cosine similarities and their listening history status for
        the given user.
    
    ### BEGIN SOLUTION
    artists = most_similar_artists(artist)
    history = data.loc[user_id, artists.index].rename('listening_history')
    ### END SOLUTION
    # artists = most_similar_artists( ? )
    # history = data.loc[ ? , ? ].rename('listening_history')
    return pd.concat([artists, history], axis=1)
example = most_similar_artists_history('abba', 42)
assert example.columns.to_list() == ['cosine_similarity', 'listening_history']
example
Explanation: Let's make a function to get the most similar artists and their listening history for a given artist and user. The function creates two DataFrames with the same index, and then uses pandas.concat to create a single DataFrame from them.
End of explanation
listening_history = np.array([0, 1, 0]) 
similarity_scores = np.array([0.3, 0.2, 0.1])
recommendation_score = sum(listening_history * similarity_scores) / sum(similarity_scores)
print(f'{recommendation_score:.3f}')
Explanation: 6. Calculate the recommendation score.
Now that we have the most_similar_artists_history function, we can start to figure out which artists to advise to whom. We want to quantify how the listening history of a user matches artists similar to an artist they didn't listen to yet. For this purpose we will use the following recommendation score: 
+ We start with the similar artists for a given artist, and their listening history for the user.
+ Then we sum the cosine similarities of artists the user listened to. 
+ In the end we divide by the total sum of similarities to normalize the score.
So when a user listened to 1 of 3 artists that are similar, for example [0, 1, 0] and their respective similarity scores are [0.3, 0.2, 0.1] you get the following recommendation score:
End of explanation
user_id = 42
artist = 'abba'
most_similar_artists_history(artist, user_id)
Explanation: Remember what the DataFrame returned by the most_similar_artists_history function looks like:
End of explanation
most_similar_artists_history(artist, user_id).product(axis=1)
Explanation: Pandas provides methods to do column or row aggregation, like e.g. pandas.DataFrame.product. This method will calculate all values in a column or row. The direction can be chosen with the axis parameter. As we need the product of the values in the rows (similarity * history), we will need to specify axis=1.
End of explanation
most_similar_artists_history(artist, user_id).product(axis=1).sum()
Explanation: Then there's pandas.DataFrame.sum which does the same thing for summing the values. As we want the sum for all values in the column we would have to specify axis=0. Since 0 is the default value for the axis parameter we don't have to add it to the method call.
End of explanation
def recommendation_score(artist, user_id):
    Calculate recommendation score.
    
    Parameters
    ----------
    artist: str
        The artist for which to calculate the recommendation score.
    user_id: int
        The user for which to calculate the recommendation score.
        
    Returns:
    float
        Recommendation score    
    
    df = most_similar_artists_history(artist, user_id)
    ### BEGIN SOLUTION
    return df.product(axis=1).sum() / df.loc[:, 'cosine_similarity'].sum()
    ### END SOLUTION
    # return df.?(axis=1).?() / df.loc[:, ? ].sum()
assert np.allclose(recommendation_score('abba', 42), 0.08976655361839528)
assert np.allclose(recommendation_score('the white stripes', 1), 0.09492796371597861)
recommendation_score('abba', 42)
Explanation: Knowing these methods, it is only a small step to define the scoring function based on the output of most_similar_artists_history.
End of explanation
def unknown_artists(user_id):
    Get artists the user hasn't listened to.
    
    Parameters
    ----------
    user_id: int
        User for which to get unknown artists
        
    Returns
    -------
    pandas.Index
        Collection of artists the user hasn't listened to.
    
    ### BEGIN SOLUTION
    history = data.loc[user_id, :]
    return history.loc[history == 0].index
    ### END SOLUTION
    # history = data.loc[ ? , :]
    # return history.loc[ ? == 0].index
    
print(unknown_artists(42))
assert len(unknown_artists(42)) == 278
assert type(unknown_artists(42)) == pd.Index
Explanation: Determine artists to recommend
We only want to recommend artists the user didn't listen to yet, which we'll determine by using the listening history.
End of explanation
def score_unknown_artists(user_id):
    Score all unknown artists for a given user.
    
    Parameters
    ----------
    user_id: int
        User for which to get unknown artists
        
    Returns
    -------
    list of dict
        A list of dictionaries.
    
    ### BEGIN SOLUTION
    artists = unknown_artists(user_id)
    return [{'recommendation': artist, 'score': recommendation_score(artist, user_id)} for artist in artists]
    ### END SOLUTION
    # artists = unknown_artists( ? )
    # return [{'recommendation': artist, 'score': recommendation_score( ? , user_id)} for artist in ?]
assert np.allclose(score_unknown_artists(42)[1]['score'], 0.08976655361839528)
assert np.allclose(score_unknown_artists(313)[137]['score'], 0.20616395469219984)
score_unknown_artists(42)[:5]
Explanation: The last requirement for our recommender engine is a function that can score all unknown artists for a given user. We will make this function return a list of dictionaries, which can be easily converted to a DataFrame later on. The list will be generated using a list comprehension.
End of explanation
def user_recommendations(user_id, n_rec=5):
    Recommend new artists for a user.
    
    Parameters
    ----------
    user_id: int
        User for which to get recommended artists
    n_rec: int, optional
        Number of recommendations to make
        
    Returns
    -------
    pandas.DataFrame
        A DataFrame containing artist recommendations for the given user,
        with their recommendation score.
    
    scores = score_unknown_artists(user_id)
    ### BEGIN SOLUTION
    return (
        pd.DataFrame(scores)
        .sort_values('score', ascending=False)
        .head(n_rec)
        .reset_index(drop=True)
    )
    ### END SOLUTION
    # return (
    #     pd.DataFrame( ? )
    #     .sort_values( ? , ascending=False)
    #     . ? (n_rec)
    #     .reset_index(drop=True)
    # )
assert user_recommendations(313).loc[4, 'recommendation'] == 'jose gonzalez'
assert len(user_recommendations(1, n_rec=10)) == 10
user_recommendations(642)
Explanation: From the scored artists we can easily derive the best recommendations for a given user.
End of explanation
recommendations = [user_recommendations(user).loc[:, 'recommendation'].rename(user) for user in data.index[:10]]
Explanation: With this final function, it is a small step to get recommendations for multiple users. As our code hasn't been optimized for performance, it is advised to limit the number of users somewhat.
End of explanation
np.transpose(pd.concat(recommendations, axis=1))
g_s = most_similar_artists_history('gorillaz', 642).assign(sim2 = lambda x: x.product(axis=1))
r_1 = g_s.sim2.sum()
total = g_s.cosine_similarity.sum()
print(total)
r_1/total
g_s
Explanation: We can now use the concat function again to get a nice overview of the recommended artists.
End of explanation
<END_TASK>