HybridSVD example

hybridsvd.py

from scipy.sparse import csr_matrix
import scipy as sp
import numpy as np
from scipy.sparse.linalg import spsolve_triangular

# rating matrix
a = np.array([[1, 0, 1, 1, 0],
              [1, 1, 0, 1, 0],
              [1, 0, 0, 1, 0]])

# vector of a new user's preferences
p = np.array([1, 0, 0, 1, 1])

# ========== Standard Model ==========

rank = 2
u, s, vt = np.linalg.svd(a, full_matrices=False)
v = vt.T[:, :rank]

# recommendations for the user with standard folding-in approach
recs = p.dot(v).dot(v.T)
recs
# output: [ 0.8904344 ,  0.31234752,  0.31234752,  0.8904344 ,  0.        ]

# ========== Hybrid Model ==========

d = 0.5 # off-diagonal similarity factor

# item similarity matrix
# non-zero off-diagonal values denote similarity between items 3 and 5
s = np.array([[1, 0, 0, 0, 0],
              [0, 1, 0, 0, 0],
              [0, 0, 1, 0, d],
              [0, 0, 0, 1, 0],
              [0, 0, d, 0 ,1]])

# finding Cholesky factors
L = np.linalg.cholesky(s)
u2, s2, v2 = np.linalg.svd(a.dot(L), full_matrices=False)
v2 = v2.T[:, :rank]

# preparing for hybrid folding-in calculation
lv = L.dot(v2)
rv = spsolve_triangular(csr_matrix(L.T), v2, lower=False)

# recommendations for the user with hybrid model
recs2 = p.dot(lv).dot(rv.T)
recs2
# output: [0.96852129, 0.08973892, 0.58973892, 0.96852129, 0.        ]