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cur.py
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cur.py
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import numpy as np
from svd import computeSVD
import math
from utilmat import UtilMat
import pandas as pd
class CUR:
'''
Performs CUR decomposition of the given input utility matrix
'''
def __init__(self, utilmat, r):
'''
Arguments:
utilmat: Utility matrix object <class: UtilMat>
r: size of square matrix U in CUR decomposition
'''
self.r = r
self.utilmat = utilmat
# Probabilty of selecting columns
pc = {}
# Probability of selecting rows
pr = {}
um = utilmat.um
ium = utilmat.ium
# Frobenius norm
f = 0
for user in um:
for movie in um[user]:
if pr.get(user):
pr[user] += um[user][movie] ** 2
else:
pr[user] = um[user][movie] ** 2
if pc.get(movie):
pc[movie] += um[user][movie] ** 2
else:
pc[movie] = um[user][movie] ** 2
f += um[user][movie] ** 2
sumprob = 0
for user in pr:
pr[user] /= f
sumprob += pr[user]
for movie in pc:
pc[movie] /= f
# Select r columns and r rows
cols = []
rows = []
# Intersection matrix W
w = np.zeros((r, r))
for i in range(r):
chance = np.random.random()
probsum = 0
selected_movie = -1
for movie in pc:
probsum += pc[movie]
if probsum >= chance:
selected_movie = movie
break
assert(selected_movie != -1)
column = ium[selected_movie].copy()
# Normalizing chosen column by dividing it with sqrt(r * prob)
for user in column:
column[user] /= math.sqrt(r * pc[selected_movie])
cols.append((selected_movie, column))
chance = np.random.random()
probsum = 0
selected_user = -1
for user in pr:
probsum += pr[user]
if probsum >= chance:
selected_user = user
break
assert(selected_user != -1)
row = um[selected_user].copy()
# Normalizing chosen row
for movie in row:
row[movie] /= math.sqrt(r * pr[selected_user])
rows.append((selected_user, row))
# Creating W matrix
for i in range(r):
for j in range(r):
movie, column = cols[j]
user, row = rows[i]
val = 0
if um[user].get(movie):
val = um[user][movie]
w[i, j] = val
# Perform SVD on W
# W = X S Y.T
X, S, Y = computeSVD(w)
# Calculate moore-penrose inverse and square it
# i.e. S = (S+) ^ 2
# S+[i] = 1 / S[i] if S[i] > 0 else 0
s_plus_squared = np.zeros((r, r))
for i in range(r):
if S[i] > 0.0001:
S[i] = 1 / S[i]
S[i] = S[i] ** 2
s_plus_squared[i, i] = S[i]
# Compute U = Y (S+) ^ 2 X.T
U = np.dot(Y, s_plus_squared).dot(X.T)
self.C = cols
self.R = rows
self.U = U
def calc_error2(self, energy=1.):
r = self.r
M = 3953
N = 6041
I = np.zeros((N, M))
um = self.utilmat.um
for user in um:
for movie in um[user]:
I[user, movie] = um[user][movie]
C = np.zeros((N, r))
R = np.zeros((r, M))
for i, t in enumerate(self.C):
movie, c = t
for user in c:
C[user, i] = c[user]
for i, t in enumerate(self.R):
user, r = t
for movie in r:
R[i, movie] = r[movie]
Res = np.dot(C, self.U).dot(R)
rmse = math.sqrt(np.sum((Res - I) ** 2) / (N * M))
mae = np.sum(np.abs(Res - I)) / (N * M)
return rmse, mae
def calc_error(self, energy=1.):
# Multiply C * U
r = self.r
cu = np.full(r, {})
for y, t in enumerate(self.C):
c = t[1]
for x in c:
for i in range(r):
val = self.U[y, i] * c[x]
if val == 0:
continue
if cu[i].get(x):
cu[i][x] += val
else:
cu[i][x] = val
# Multiply CU * R
out = {}
for y, c in enumerate(cu):
for x in c:
r = self.R[y][1]
for k in r:
val = c[x] * r[k]
if val == 0:
continue
if out.get((x, k)):
out[(x, k)] += val
else:
out[(x, k)] = val
um = self.utilmat.um
rmse = 0
mae = 0
cnt = 0
for user in um:
for movie in um[user]:
pred = 0
if out.get((user, movie)):
pred = out[(user, movie)]
rmse += (pred - um[user][movie]) ** 2
mae += abs(pred - um[user][movie])
cnt += 1
rmse /= cnt
rmse = math.sqrt(rmse)
mae /= cnt
return rmse, mae
if __name__ == "__main__":
df = pd.read_csv('ratings.csv')
utilmat = UtilMat(df)
cur = CUR(utilmat, 2000)
rmse, mae = cur.calc_error2()
print('Reconstruction Error (RMSE, MAE): ', rmse, mae)