The source code mf.py is an implementation of the matrix factorization algorithm in Python, using stochastic gradient descent. An article with detailed explanation of the algorithm can be found at http://www.albertauyeung.com/post/python-matrix-factorization/.
Below is an example of using the algorithm:
import numpy as np
from mf import MF
# A rating matrix with ratings from 5 users on 4 items
# zero entries are unknown values
R = np.array([
[5, 3, 0, 1],
[4, 0, 0, 1],
[1, 1, 0, 5],
[1, 0, 0, 4],
[0, 1, 5, 4],
])
# Perform training and obtain the user and item matrices
mf = MF(R, K=2, alpha=0.1, beta=0.01, iterations=20)
training_process = mf.train()
print(mf.P)
print(mf.Q)
print(mf.full_matrix())
# Prints the following:
'''
[[ 1.45345236 0.06946249]
[ 1.12922538 0.2319001 ]
[-1.21051208 0.94619099]
[-0.93607816 0.43182699]
[-0.6919936 -0.93611985]]
[[ 1.42787151 -0.20548935]
[ 0.84792614 0.29530697]
[ 0.18071811 -1.2672859 ]
[-1.4211893 0.20465575]]
[[ 4.98407556 2.99856476 3.96309763 1.01351377]
[ 3.99274702 2.27661831 3.20365416 1.0125506 ]
[ 1.0064803 1.00498576 2.37696737 4.98530109]
[ 1.00999456 0.59175173 2.58437035 3.99597255]
[ 2.26471556 1.01985428 4.9871617 3.9942251 ]]
'''