SVD Example

svd_example.py

from scipy import linalg
import numpy as np
from scipy.spatial.distance import cosine

#Let's define the matrix
user_ids = np.array(['Amanda', 'Anna', 'Bruno', 'Ricardo'])
item_ids = np.array(['Back to The Future', 'Conan',
                    'Lord of the Rings', 'Star Wars'])

matrix = np.matrix([
        #Amanda, Anna, Bruno, Ricardo
         [3, 4, 3, 1], #Back to The Future
         [1, 3, 2, 6], #Conan
         [2, 4, 1, 5], #Lord of The Rings
         [3, 3, 5, 2] #Star Wars
])

#Compute the SVD Decomposition
u, s, vt = linalg.svd(matrix)

#Now let's get the decomposed matrixes (2-rank)
#The first and second columns of u (4x2)
u2 = u[:, 0:2]
#The first and second columns of vt transposed (4x2)
vt2 = vt.T[:, 0:2]
#Finally the first two eigen-values (2x2)
eig2 = np.diag(s.T[0:2])

#Now let's come with Marcel, the new user.
marcel = np.matrix([0, 3, 0, 4])
marcel_2D = marcel * u2 * linalg.inv(eig2)

#Compute the cosine similarity between Marcel and
#every other User in our 2-D space
#Perfect similarity = 1.0  No Similarity = 0.0
users_2D = [line * u2 * linalg.inv(eig2)  for line in matrix.T]
users_sim = np.array([1 - cosine(marcel_2D, user_2D).flatten()
                        for user_2D in users_2D]).flatten()

# Remove all users who fall below the 0.90 cosine similarity
#cutoff and sort by similarity
#users_sim = users_sim[users_sim]
most_similar = np.where(users_sim >= 0.9)
most_similar_scores = users_sim[most_similar]
most_similar_users = user_ids[most_similar]

for userno, user_id in enumerate(most_similar_users):
    print "%s x Marcel: %.2f" % (user_id, most_similar_scores[userno])


#For computing the recommendations we will use the strategy:
# 1) Select the most similar user
# 2) Compare all the items rated by this user against your own and select
#     the items that you have not yet rated
# 3) Return the ratings for items I have not yet seen,
#     but the most similar user has rated.
sorted_scores = np.lexsort((most_similar_scores,))[::-1]
most_similar_user = most_similar_users[sorted_scores][0]

recommendable_items = np.logical_xor(
                        matrix[np.where(user_ids == most_similar_user)],
                        marcel)

#If is there any recommendations.
print most_similar_user + ' recommends for Marcel:'

if np.any(recommendable_items):
    preferences = matrix[np.where(user_ids ==  \
                most_similar_user)][recommendable_items].getA().flatten()
    item_ids = item_ids[recommendable_items.getA().flatten()]
    for index in range(preferences.size):
        print 'I gave for the movie %s the rating %d' \
        % (item_ids[index], preferences[index])
else:
    print "All the movies you also watched."