Singularwaardedecompositie (SVD)

Aanbevelingssystemen bouwen in Python

Rob O'Callaghan

Director of Data

Wat SVD doet

Spaarzame rechthoekige matrix

Wat SVD doet

Spaarzame rechthoekige matrix naast de eerste factor

Wat SVD doet

Spaarzame rechthoekige matrix naast twee factoren

Wat SVD doet

Spaarzame rechthoekige matrix naast zijn factoren

Data voorbereiden

print(book_ratings_df.shape)

(220, 500)

avg_ratings = book_ratings_df.mean(axis=1)

print(avg_ratings)

array([[4.5 ],
       [3.5],
       [2.5],
       [3.5],
        ... 
       [2.2]])

Data voorbereiden

user_ratings_pivot_centered = user_ratings_df.sub(avg_ratings, axis=0)
user_ratings_df.fillna(0, inplace=True)

print(user_ratings_df)

          The Great Gatsby    The Catcher in the Rye    Fifty Shades of Grey                    
User_233               0.0                       0.0                     0.0
User_651               0.0                       0.5                    -0.5
User_965               0.5                      -0.5                     0.0
     ...               ...                       ...                     ...

SVD toepassen

from scipy.sparse.linalg import svds

U, sigma, Vt = svds(user_ratings_pivot_centered)

print(U.shape)

(610, 6)

print(Vt.shape)

(6, 1000)

SVD toepassen

print(sigma)

[3.0, 4.8, -12.6, -3.8, 8.2, 7.3]

sigma = np.diag(sigma)
print(sigma)

array([   3.0    ,   0.     ,   0.     ,   0.     ,   0.     ,   0.     ],
       [  0.     ,   4.8    ,   0.     ,   0.     ,   0.     ,   0.     ],
       [  0.     ,   0.     , -12.6    ,   0.     ,   0.     ,   0.     ],
       [  0.     ,   0.     ,   0.     ,  -3.8    ,   0.     ,   0.     ],
       [  0.     ,   0.     ,   0.     ,   0.     ,   8.2    ,   0.     ],
       [  0.     ,   0.     ,   0.     ,   0.     ,   0.     ,   7.3    ]),

De eindmatrix krijgen

De drie factormatrices uit SVD

De eindmatrix krijgen

De drie factormatrices uit SVD

De eindmatrix krijgen

De drie factormatrices uit SVD

De eindmatrix krijgen

De drie factormatrices uit SVD naast hun product

Product berekenen in Python

recalculated_ratings =        np.dot(U, sigma)

Product berekenen in Python

recalculated_ratings = np.dot(np.dot(U, sigma), Vt)
print(recalculated_ratings)

[[  0.1      -0.9       -3.6.     ...   ]
 [ -2.3       0.5       -0.5      ...   ]
 [  0.5      -0.5        2.0      ...   ]
 [ ...        ...        ...      ...   ]]

Gemiddelden terugzetten

recalculated_ratings = recalculated_ratings + avg_ratings.values.reshape(-1, 1)
print(recalculated_ratings)

[[  4.6       3.6        0.9      ...   ]
 [  1.8       4.0        3.0      ...   ]
 [  3.0       2.0        4.5      ...   ]
 [ ...        ...        ...      ...   ]]

print(book_ratings_df)

[[  5.0       4.0         NA      ...   ]
 [   NA       4.0        3.0      ...   ]
 [  3.0       2.0         NA      ...   ]
 [ ...        ...        ...      ...   ]]

Laten we oefenen!

Aanbevelingssystemen bouwen in Python