def _cross_val(param_dict):
# Display output
display.my_display('Optimizing parameter set: {} \n'.format(param_dict['param_id']), True, param_dict['str_path'])
# Derive params from dict
n_train_win, n_train_conn = param_dict['train_cfg_matr'].shape
n_test_win, n_test_conn = param_dict['test_cfg_matr'].shape
# Run NMF on training set
fac_subnet_init = np.random.uniform(low=0.0, high=1.0,
size=(param_dict['rank'], n_train_conn))
fac_coef_init = np.random.uniform(low=0.0, high=1.0,
size=(param_dict['rank'], n_train_win))
train_fac_subnet, train_fac_coef, train_err = nmf.snmf_bcd(param_dict['train_cfg_matr'],
alpha=param_dict['alpha'],
beta=param_dict['beta'],
fac_subnet_init=fac_subnet_init,
fac_coef_init=fac_coef_init,
max_iter=25, verbose=False)
# Solve single least squares estimate for coefficients on held-out fold
fac_coef_init = np.random.uniform(low=0.0, high=1.0,
size=(param_dict['rank'], n_test_win))
_, test_fac_coef, _ = nmf.snmf_bcd(param_dict['test_cfg_matr'],
alpha=param_dict['alpha'],
beta=param_dict['beta'],
fac_subnet_init=train_fac_subnet,
fac_coef_init=fac_coef_init,
max_iter=1, verbose=False)
# Compute error
norm_test_cfg_matr = matrix_utils.norm_fro(param_dict['test_cfg_matr'].T)
err = matrix_utils.norm_fro_err(param_dict['test_cfg_matr'].T,
train_fac_subnet.T,
test_fac_coef.T,
norm_test_cfg_matr) / norm_test_cfg_matr
return {'param_id': param_dict['param_id'],
'error': err}
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 run(self, A, k, init=None, max_iter=None, max_time=None, verbose=0):
""" Run a NMF algorithm
Parameters
----------
A : numpy.array or scipy.sparse matrix, shape (m,n)
k : int - target lower rank
Optional Parameters
-------------------
init : (W_init, H_init) where
W_init is numpy.array of shape (m,k) and
H_init is numpy.array of shape (n,k).
If provided, these values are used as initial values for NMF iterations.
max_iter : int - maximum number of iterations.
If not provided, default maximum for each algorithm is used.
max_time : int - maximum amount of time in seconds.
If not provided, default maximum for each algorithm is used.
verbose : int - 0 (default) - No debugging information is collected, but
input and output information is printed on screen.
-1 - No debugging information is collected, and
nothing is printed on screen.
1 (debugging/experimental purpose) - History of computation is
returned. See 'rec' variable.
2 (debugging/experimental purpose) - History of computation is
additionally printed on screen.
Returns
-------
(W, H, rec)
W : Obtained factor matrix, shape (m,k)
H : Obtained coefficient matrix, shape (n,k)
rec : dict - (debugging/experimental purpose) Auxiliary information about the execution
"""
info = {'k': k,
'alg': str(self.__class__),
'A_dim_1': A.shape[0],
'A_dim_2': A.shape[1],
'A_type': str(A.__class__),
'max_iter': max_iter if max_iter is not None else self.default_max_iter,
'verbose': verbose,
'max_time': max_time if max_time is not None else self.default_max_time}
if init != None:
W = init[0].copy()
H = init[1].copy()
info['init'] = 'user_provided'
else:
W = random.rand(A.shape[0], k)
H = random.rand(A.shape[1], k)
info['init'] = 'uniform_random'
if verbose >= 0:
print '[NMF] Running: '
print json.dumps(info, indent=4, sort_keys=True)
norm_A = mu.norm_fro(A)
total_time = 0
if verbose >= 1:
his = {'iter': [], 'elapsed': [], 'rel_error': []}
start = time.time()
# algorithm-specific initilization
(W, H) = self.initializer(W, H)
for i in range(1, info['max_iter'] + 1):
start_iter = time.time()
# algorithm-specific iteration solver
(W, H) = self.iter_solver(A, W, H, k, i)
elapsed = time.time() - start_iter
if verbose >= 1:
rel_error = mu.norm_fro_err(A, W, H, norm_A) / norm_A
his['iter'].append(i)
his['elapsed'].append(elapsed)
his['rel_error'].append(rel_error)
if verbose >= 2:
print 'iter:' + str(i) + ', elapsed:' + str(elapsed) + ', rel_error:' + str(rel_error)
total_time += elapsed
if total_time > info['max_time']:
break
W, H, weights = mu.normalize_column_pair(W, H)
final = {}
final['norm_A'] = norm_A
final['rel_error'] = mu.norm_fro_err(A, W, H, norm_A) / norm_A
final['iterations'] = i
final['elapsed'] = time.time() - start
rec = {'info': info, 'final': final}
if verbose >= 1:
rec['his'] = his
if verbose >= 0:
print '[NMF] Completed: '
print json.dumps(final, indent=4, sort_keys=True)
return (W, H, rec)
def run(self, A, k, init=None, max_iter=None, max_time=None, verbose=0):
""" Run a NMF algorithm
Parameters
----------
A : numpy.array or scipy.sparse matrix, shape (m,n)
k : int - target lower rank
Optional Parameters
-------------------
init : (W_init, H_init) where
W_init is numpy.array of shape (m,k) and
H_init is numpy.array of shape (n,k).
If provided, these values are used as initial values for NMF iterations.
max_iter : int - maximum number of iterations.
If not provided, default maximum for each algorithm is used.
max_time : int - maximum amount of time in seconds.
If not provided, default maximum for each algorithm is used.
verbose : int - 0 (default) - No debugging information is collected, but
input and output information is printed on screen.
-1 - No debugging information is collected, and
nothing is printed on screen.
1 (debugging/experimental purpose) - History of computation is
returned. See 'rec' variable.
2 (debugging/experimental purpose) - History of computation is
additionally printed on screen.
Returns
-------
(W, H, rec)
W : Obtained factor matrix, shape (m,k)
H : Obtained coefficient matrix, shape (n,k)
rec : dict - (debugging/experimental purpose) Auxiliary information about the execution
"""
info = {
'k': k,
'alg': str(self.__class__),
'A_dim_1': A.shape[0],
'A_dim_2': A.shape[1],
'A_type': str(A.__class__),
'max_iter':
max_iter if max_iter is not None else self.default_max_iter,
'verbose': verbose,
'max_time':
max_time if max_time is not None else self.default_max_time
}
if init != None:
W = init[0].copy()
H = init[1].copy()
info['init'] = 'user_provided'
else:
W = random.rand(A.shape[0], k)
H = random.rand(A.shape[1], k)
info['init'] = 'uniform_random'
if verbose >= 0:
print '[NMF] Running: '
print json.dumps(info, indent=4, sort_keys=True)
norm_A = mu.norm_fro(A)
total_time = 0
if verbose >= 1:
his = {'iter': [], 'elapsed': [], 'rel_error': []}
start = time.time()
# algorithm-specific initilization
(W, H) = self.initializer(W, H)
for i in range(1, info['max_iter'] + 1):
start_iter = time.time()
# algorithm-specific iteration solver
(W, H) = self.iter_solver(A, W, H, k, i)
elapsed = time.time() - start_iter
if verbose >= 1:
rel_error = mu.norm_fro_err(A, W, H, norm_A) / norm_A
his['iter'].append(i)
his['elapsed'].append(elapsed)
his['rel_error'].append(rel_error)
if verbose >= 2:
print 'iter:' + str(i) + ', elapsed:' + str(
elapsed) + ', rel_error:' + str(rel_error)
total_time += elapsed
if total_time > info['max_time']:
break
W, H, weights = mu.normalize_column_pair(W, H)
final = {}
final['norm_A'] = norm_A
final['rel_error'] = mu.norm_fro_err(A, W, H, norm_A) / norm_A
final['iterations'] = i
final['elapsed'] = time.time() - start
rec = {'info': info, 'final': final}
if verbose >= 1:
rec['his'] = his
if verbose >= 0:
print '[NMF] Completed: '
print json.dumps(final, indent=4, sort_keys=True)
return (W, H, rec)
def run_xval_paramset(cfg_matr, param_dict):
"""
Run NMF cross-validation using a single parameter dictionary generated from
gen_random_sampling_paramset
Parameters
----------
cfg_matr: numpy.ndarray, shape:(n_win, n_conn)
The network configuration matrix
param_dict: dict with keys: {param_id, alpha, beta, rank, fold_id,
train_ix, test_ix, str_path}
Single entry of list of dicts returned by gen_random_sampling_paramset
Return
------
qmeas_dict: dict with keys: {param_id, err,
pct_sparse_subnet, pct_sparse_coef}
Quality measures associated with param_dict
"""
# Check input dimensions of cfg_matr
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]
# Derive params from dict
train_cfg_matr = cfg_matr[param_dict['train_ix'], :]
test_cfg_matr = cfg_matr[param_dict['test_ix'], :]
n_train_win, n_train_conn = train_cfg_matr.shape
n_test_win, n_test_conn = test_cfg_matr.shape
# Display output
display.my_display(
'Optimizing parameter set: {} \n'.format(param_dict['param_id']), True,
param_dict['str_path'])
# Run NMF on training set
fac_subnet_init = np.random.uniform(low=0.0,
high=1.0,
size=(param_dict['rank'],
n_train_conn))
fac_coef_init = np.random.uniform(low=0.0,
high=1.0,
size=(param_dict['rank'], n_train_win))
train_fac_subnet, train_fac_coef, train_err = nmf.snmf_bcd(
train_cfg_matr,
alpha=param_dict['alpha'],
beta=param_dict['beta'],
fac_subnet_init=fac_subnet_init,
fac_coef_init=fac_coef_init,
max_iter=25,
verbose=False)
# Solve single least squares estimate for coefficients on held-out fold
fac_coef_init = np.random.uniform(low=0.0,
high=1.0,
size=(param_dict['rank'], n_test_win))
_, test_fac_coef, _ = nmf.snmf_bcd(test_cfg_matr,
alpha=param_dict['alpha'],
beta=param_dict['beta'],
fac_subnet_init=train_fac_subnet,
fac_coef_init=fac_coef_init,
max_iter=1,
verbose=False)
# Compute error
norm_test_cfg_matr = matrix_utils.norm_fro(test_cfg_matr.T)
err = matrix_utils.norm_fro_err(test_cfg_matr.T, train_fac_subnet.T,
test_fac_coef.T,
norm_test_cfg_matr) / norm_test_cfg_matr
# Compute sparsity of the subgraphs and coefficients
pct_sparse_subnet = (train_fac_subnet == 0).mean(axis=1).mean()
pct_sparse_coef = (test_fac_coef == 0).mean(axis=1).mean()
qmeas_dict = {
'param_id': param_dict['param_id'],
'error': err,
'pct_sparse_subgraph': pct_sparse_subnet,
'pct_sparse_coef': pct_sparse_coef
}
return qmeas_dict
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