def snmf_bcd(cfg_matr,
alpha,
beta,
fac_subnet_init,
fac_coef_init,
max_iter,
verbose=True):
"""
Compute Sparse-NMF based on Kim and Park (2011).
By default, enforces a sparse penalty on the coefficients matrix H
and regularizes the sub-network, basis matrix W.
A -> cfg_matr.T
W -> fac_subnet.T
H -> fac_coefs
Parameters
----------
cfg_matr: numpy.ndarray
The network configuration matrix
shape: [n_win x n_conn]
alpha: float
Regularization parameter on W
beta: float
Sparsity parameter on H
fac_subnet_init: numpy.ndarray
Initial sub-network basis matrix
shape: [n_fac x n_conn]
fac_coef_init: numpy.ndarray
Initial coefficients matrix
shape: [n_fac x n_win]
max_iter: int
Maximum number of optimization iterations to perform
Typically around 100
verbose: bool
Print progress information to the screen
Returns
-------
fac_subnet_init: numpy.ndarray
Final sub-network basis matrix
shape: [n_fac x n_conn]
fac_coef_init: numpy.ndarray
Final coefficients matrix
shape: [n_fac x n_win]
rel_err: numpy.ndarray
Froebenius norm of the error matrix over iterations
shape: [n_iter,]
"""
# Standard param checks
errors.check_type(cfg_matr, np.ndarray)
errors.check_type(alpha, float)
errors.check_type(beta, float)
errors.check_type(fac_subnet_init, np.ndarray)
errors.check_type(fac_coef_init, np.ndarray)
errors.check_type(max_iter, int)
errors.check_type(verbose, bool)
# Check input dimensions
if not len(cfg_matr.shape) == 2:
raise ValueError('%r does not have two dimensions' % cfg_matr)
n_win = cfg_matr.shape[0]
n_conn = cfg_matr.shape[1]
if not len(fac_subnet_init.shape) == 2:
raise ValueError('%r does not have two dimensions' % fac_subnet_init)
n_fac = fac_subnet_init.shape[0]
if not fac_subnet_init.shape[1] == n_conn:
raise ValueError('%r should have same number of connections as %r' %
(fac_subnet_init, cfg_matr))
if not len(fac_coef_init.shape) == 2:
raise ValueError('%r does not have two dimensions' % fac_coef_init)
if not fac_coef_init.shape[0] == n_fac:
raise ValueError('%r should specify same number of factors as %r' %
(fac_coef_init, fac_subnet_init))
if not fac_coef_init.shape[1] == n_win:
raise ValueError('%r should have same number of windows as %r' %
(fac_coef_init, cfg_matr))
# Initialize matrices
# A - [n_conn x n_win]
# W - [n_conn x n_fac]
# H - [n_win x n_fac]
A = cfg_matr.T.copy()
W = fac_subnet_init.T.copy()
H = fac_coef_init.T.copy()
# Regularization matrix
# alpha_matr - [n_fac x n_fac]
alpha_matr = np.sqrt(alpha) * np.eye(n_fac)
alpha_zeros_matr = np.zeros((n_conn, n_fac))
# Sparsity matrix
# beta_matr - [1 x n_fac]
beta_matr = np.sqrt(beta) * np.ones((1, n_fac))
beta_zeros_matr = np.zeros((1, n_win))
# Capture error minimization
rel_error = np.zeros(max_iter)
norm_A = matr_util.norm_fro(A)
my_display('\nBeginning Non-Negative Matrix Factorization\n', verbose)
t_iter_start = time.time()
for ii in xrange(max_iter):
# Use the Block-Pivot Solver
# First solve for H
W_beta = np.vstack((W, beta_matr))
A_beta = np.vstack((A, beta_zeros_matr))
Sol, info = nnls.nnlsm_blockpivot(W_beta, A_beta, init=H.T)
H = Sol.T
# Now, solve for W
H_alpha = np.vstack((H, alpha_matr))
A_alpha = np.hstack((A, alpha_zeros_matr))
Sol, info = nnls.nnlsm_blockpivot(H_alpha, A_alpha.T, init=W.T)
W = Sol.T
t_iter_elapsed = time.time() - t_iter_start
err = matr_util.norm_fro_err(A, W, H, norm_A) / norm_A
rel_error[ii] = err
str_header = 'Running -- '
str_iter = 'Iteration %4d' % (ii + 1)
str_err = 'Relative Error: %0.5f' % err
str_elapsed = 'Elapsed Time: %0.3f sec' % t_iter_elapsed
my_display(
'{} {} | {} | {} \r'.format(str_header, str_iter, str_err,
str_elapsed), verbose)
my_display('\nDone.\n', verbose)
W, H, weights = matr_util.normalize_column_pair(W, H)
return W.T, H.T, rel_error
def iter_solver(self, A, W, H, k, it):
Sol, info = nnlsm_blockpivot(W, A, init=H.T)
H = Sol.T
Sol, info = nnlsm_blockpivot(H, A.T, init=W.T)
W = Sol.T
return (W, H)