from glrm import GLRM from glrm.convergence import Convergence from glrm.util import pplot from numpy.random import randn, choice, seed from numpy import sign from itertools import product from math import ceil seed(1) # Generate problem data m, n, k = 100, 100, 10 data = randn(m,k).dot(randn(k,n)) data = data - data.min() data = (data/data.max()*6).round() + 1 # approx rank k #data = choice(range(7), (m,n)) + 1 # not inherently rank k # Initialize model A = data loss = OrdinalLoss regX, regY = QuadraticReg(0.1), QuadraticReg(0.1) glrm_ord = GLRM(A, loss, regX, regY, k) # Fit glrm_ord.fit(eps=1e-3, max_iters=1000) # Results X, Y = glrm_ord.factors() A_hat = glrm_ord.predict() # glrm_pca.predict(X, Y) works too; returns decode(XY) ch = glrm_ord.convergence() # convergence history pplot([A, A_hat, A-A_hat], ["original", "glrm", "error"])
m, n, k = 20, 20, 5
eta = 0.1 # noise power
X_true, Y_true = abs(randn(m, k)), abs(randn(k, n))
data = X_true.dot(Y_true) + eta * randn(m, n) # noisy rank k
# Initialize model
A = data
loss = QuadraticLoss
regX, regY = NonnegativeReg(0.1), NonnegativeReg(0.1)
glrm_nn = GLRM(A, loss, regX, regY, k)
# Fit
glrm_nn.fit()
# Results
X, Y = glrm_nn.factors()
A_hat = glrm_nn.predict(
) # glrm_pca.predict(X, Y) works too; returns decode(XY)
ch = glrm_nn.convergence() # convergence history
pplot([A, A_hat, A - A_hat], ["original", "glrm", "error"])
# Now with missing data
missing = list(
product(range(int(0.25 * m), int(0.75 * m)),
range(int(0.25 * n), int(0.75 * n))))
glrm_nn_missing = GLRM(A, loss, regX, regY, k, missing)
glrm_nn_missing.fit()
A_hat = glrm_nn_missing.predict()
pplot([A, missing, A_hat, A - A_hat], \
["original", "missing", "glrm", "error"])
# Generate problem data (draw smiley with -1's, 1's)
m, n, k = 500, 500, 8
data = -ones((m, n))
for i,j in product(list(range(120, 190)), list(range(120, 190))):
d = (155-i)**2 + (155-j)**2
if d <= 35**2:
data[i,j] = 1
data[i, m-j] = 1
for i,j in product(list(range(300, 451)), list(range(100, 251))):
d = (250 - i)**2 + (250-j)**2
if d <= 200**2 and d >= 150**2:
data[i,j] = 1
data[i,m-j] = 1
# Initialize model
A = data
loss = HingeLoss
regX, regY = QuadraticReg(0.1), QuadraticReg(0.1)
converge = Convergence(TOL = 1e-2)
glrm_binary = GLRM(A, loss, regX, regY, k, converge = converge)
# Fit
glrm_binary.fit()
# Results
X, Y = glrm_binary.factors()
A_hat = glrm_binary.predict() # glrm_pca.predict(X, Y) works too; returns decode(XY)
ch = glrm_binary.convergence() # convergence history
pplot([A, A_hat, A - A_hat], ["original", "glrm", "error"])
# Generate problem data
m, n, k = 20, 20, 5
eta = 0.1 # noise power
X_true, Y_true = abs(randn(m,k)), abs(randn(k,n))
data = X_true.dot(Y_true) + eta*randn(m,n) # noisy rank k
# Initialize model
A = data
loss = QuadraticLoss
regX, regY = NonnegativeReg(0.1), NonnegativeReg(0.1)
glrm_nn = GLRM(A, loss, regX, regY, k)
# Fit
glrm_nn.fit()
# Results
X, Y = glrm_nn.factors()
A_hat = glrm_nn.predict() # glrm_pca.predict(X, Y) works too; returns decode(XY)
ch = glrm_nn.convergence() # convergence history
pplot([A, A_hat, A - A_hat], ["original", "glrm", "error"])
# Now with missing data
missing = list(product(list(range(int(0.25*m), int(0.75*m))), list(range(int(0.25*n), int(0.75*n)))))
glrm_nn_missing = GLRM(A, loss, regX, regY, k, missing)
glrm_nn_missing.fit()
A_hat = glrm_nn_missing.predict()
pplot([A, missing, A_hat, A - A_hat], \
["original", "missing", "glrm", "error"])
A = [data_real, data_ord, data_bool]
loss = [QuadraticLoss, OrdinalLoss, HingeLoss]
regX, regY = QuadraticReg(0.01), QuadraticReg(0.01)
converge = Convergence(TOL=1e-2,
max_iters=1000) # optional (default TOL = 1e-3)
glrm_mix = GLRM(A, loss, regX, regY, k, converge=converge)
# Fit
glrm_mix.fit()
# Results
X, Y = glrm_mix.factors()
A_hat = glrm_mix.predict(
) # glrm_pca.predict(X, Y) works too; returns decode(XY)
ch = glrm_mix.convergence() # convergence history
pplot([hstack(A), A_hat, hstack(A) - A_hat], ["original", "glrm", "error"])
# Now with missing data
missing = [
list(product(range(35, 50), range(n1 - 5, n1))),
list(product(range(35, 50), range(0, n2))),
list(product(range(35, 50), range(0, n3 - 5)))
]
glrm_mix_missing = GLRM(A, loss, regX, regY, k, missing)
glrm_mix_missing.fit()
A_hat = glrm_mix_missing.predict()
# translate missing list into something that we can plot
new_missing = unroll_missing(missing, [n1, n2, n3])
pplot([hstack(A), new_missing, A_hat,
asym_noise = sqrt(k)*randn(m,n) + 3*abs(sqrt(k)*randn(m,n)) # large, sparse noise rate = 0.3 # percent of entries that are corrupted by large, outlier noise corrupted_entries = sample(list(product(range(m), range(n))), int(m*n*rate)) data = randn(m,k).dot(randn(k,n)) A = data + sym_noise for ij in corrupted_entries: A[ij] += asym_noise[ij] # Initialize model loss = HuberLoss regX, regY = QuadraticReg(0.1), QuadraticReg(0.1) glrm_huber = GLRM(A, loss, regX, regY, k) # Fit glrm_huber.fit() # Results X, Y = glrm_huber.factors() A_hat = glrm_huber.predict() # glrm_pca.predict(X, Y) works too; returns decode(XY) ch = glrm_huber.convergence() # convergence history pplot([data, A, A_hat, data-A_hat], ["original", "corrupted", "glrm", "error"]) # Now with missing data from numpy.random import choice missing = list(product(range(int(0.25*m), int(0.75*m)), range(int(0.25*n), int(0.75*n)))) glrm_huber_missing = GLRM(A, loss, regX, regY, k, missing) glrm_huber_missing.fit() A_hat = glrm_huber_missing.predict() pplot([data, A, missing, A_hat, data-A_hat], ["original", "corrupted", "missing", "glrm", "error"])
asym_noise = sqrt(k)*randn(m,n) + 3*abs(sqrt(k)*randn(m,n)) # large, sparse noise rate = 0.3 # percent of entries that are corrupted by large, outlier noise corrupted_entries = sample(list(product(list(range(m)), list(range(n)))), int(m*n*rate)) data = randn(m,k).dot(randn(k,n)) A = data + sym_noise for ij in corrupted_entries: A[ij] += asym_noise[ij] # Initialize model loss = HuberLoss regX, regY = QuadraticReg(0.1), QuadraticReg(0.1) glrm_huber = GLRM(A, loss, regX, regY, k) # Fit glrm_huber.fit() # Results X, Y = glrm_huber.factors() A_hat = glrm_huber.predict() # glrm_pca.predict(X, Y) works too; returns decode(XY) ch = glrm_huber.convergence() # convergence history pplot([data, A, A_hat, data-A_hat], ["original", "corrupted", "glrm", "error"]) # Now with missing data from numpy.random import choice missing = list(product(list(range(int(0.25*m), int(0.75*m))), list(range(int(0.25*n), int(0.75*n))))) glrm_huber_missing = GLRM(A, loss, regX, regY, k, missing) glrm_huber_missing.fit() A_hat = glrm_huber_missing.predict() pplot([data, A, missing, A_hat, data-A_hat], ["original", "corrupted", "missing", "glrm", "error"])
data_ord = (data_ord/data_ord.max()*6 + 1).round()# ordinal data, e.g., Likert scale
data_bool = sign(data[:,n1+n2:])
# Initialize model
A = [data_real, data_ord, data_bool]
loss = [QuadraticLoss, OrdinalLoss, HingeLoss]
regX, regY = QuadraticReg(0.01), QuadraticReg(0.01)
converge = Convergence(TOL = 1e-2, max_iters = 1000) # optional (default TOL = 1e-3)
glrm_mix = GLRM(A, loss, regX, regY, k, converge = converge)
# Fit
glrm_mix.fit()
# Results
X, Y = glrm_mix.factors()
A_hat = glrm_mix.predict() # glrm_pca.predict(X, Y) works too; returns decode(XY)
ch = glrm_mix.convergence() # convergence history
pplot([hstack(A), A_hat, hstack(A)-A_hat], ["original", "glrm", "error"])
# Now with missing data
missing = [list(product(list(range(35, 50)), list(range(n1-5, n1)))), list(product(list(range(35,
50)), list(range(0, n2)))), list(product(list(range(35, 50)), list(range(0, n3-5))))]
glrm_mix_missing = GLRM(A, loss, regX, regY, k, missing)
glrm_mix_missing.fit()
A_hat = glrm_mix_missing.predict()
# translate missing list into something that we can plot
new_missing = unroll_missing(missing, [n1, n2, n3])
pplot([hstack(A), new_missing, A_hat, hstack(A)-A_hat], ["original", "missing", "glrm", "error"])
