svdX = []
svdY = []
u, s, vT = scipy.linalg.svd(train)
for k in xrange(1, 100):
low_s = [s[i] for i in xrange(k)] # + (min(u.shape[0], vT.shape[1]) - k) * [0]
print 'Exact SVD with low-rank approximation {}'.format(k)
svdX.append(k)
svdY.append(get_error(u, np.diag(low_s), vT, train, test))
plt.plot(svdX, svdY, label="SVD", color='black', linewidth='2', linestyle='--')
"""
print
print 'Testing incremental SVD'
for num in xrange(400, 1001, 300):
print '... with block size of {}'.format(num)
X, Y = [], []
for k in xrange(1, 91, 10):
print k
u, s, vT = incremental_SVD(train, k, num)
X.append(k)
Y.append(get_error(u, s, vT, train, test, prod_avg))
plt.plot(X, Y, label='iSVD u={}'.format(num))
##
plt.title('Recommendation system RMSE on {}x{} matrix'.format(*train.shape))
plt.xlabel('Low rank approximation (k)')
plt.ylabel('Root Mean Squared Error')
#plt.ylim(0, max(svdY))
plt.legend(loc='best')
plt.savefig('recommend_rmse_{}x{}.pdf'.format(*train.shape))
plt.show(block=True)
svdY = []
u, s, vT = scipy.linalg.svd(train)
for k in xrange(1, 100):
low_s = [s[i] for i in xrange(k)] # + (min(u.shape[0], vT.shape[1]) - k) * [0]
print 'Exact SVD with low-rank approximation {}'.format(k)
svdX.append(k)
svdY.append(get_error(u, np.diag(low_s), vT, train, test))
plt.plot(svdX, svdY, label="SVD", color='black', linewidth='2', linestyle='--')
"""
print
print 'Testing incremental SVD'
for num in xrange(400, 1001, 300):
print '... with block size of {}'.format(num)
X, Y = [], []
for k in xrange(1, 91, 10):
print k
u, s, vT = incremental_SVD(train, k, num)
X.append(k)
Y.append(get_error(u, s, vT, train, test, prod_avg))
plt.plot(X, Y, label='iSVD u={}'.format(num))
##
plt.title(
'Recommendation system RMSE on {}x{} matrix'.format(*train.shape))
plt.xlabel('Low rank approximation (k)')
plt.ylabel('Root Mean Squared Error')
#plt.ylim(0, max(svdY))
plt.legend(loc='best')
plt.savefig('recommend_rmse_{}x{}.pdf'.format(*train.shape))
plt.show(block=True)
#print err
#print
svdX.append(k)
svdY.append(err)
orthoX.append(k)
orthoY.append(check_orthogonality(u))
plt.plot(svdX, svdY, label="SVD", color='black', linewidth='2', linestyle='--')
print
print 'Testing incremental SVD'
incr_ortho = []
for num in xrange(100, 1001, 300):
print '... with block size of {}'.format(num)
X, Y = [], []
incr_orthoY = []
uL, sL, vTL = incremental_SVD(train, range(1, 101), num)
for i in xrange(len(uL)):
reconstruct = uL[i].dot(sL[i].dot(vTL[i]))
err = np.linalg.norm(train - reconstruct, 'fro')
X.append(i + 1)
Y.append(err)
incr_orthoY.append(check_orthogonality(uL[i]))
incr_ortho.append(['iSVD u={}'.format(num), X, incr_orthoY])
plt.plot(X, Y, label='iSVD u={}'.format(num))
"""
print 'Testing raw SVD => exact reconstruction'
svT = scipy.linalg.diagsvd(s, u.shape[0], vT.shape[1]).dot(vT)
for y in xrange(train.shape[0]):
for x in xrange(train.shape[1]):
colU = u[y, :]
rowV = svT[:, x]