def udfs(X, **kwargs):
"""
This function implements l2,1-norm regularized discriminative feature
selection for unsupervised learning, i.e., min_W Tr(W^T M W) + gamma ||W||_{2,1}, s.t. W^T W = I
Input
-----
X: {numpy array}, shape (n_samples, n_features)
input data
kwargs: {dictionary}
gamma: {float}
parameter in the objective function of UDFS (default is 1)
n_clusters: {int}
Number of clusters
k: {int}
number of nearest neighbor
verbose: {boolean}
True if want to display the objective function value, false if not
Output
------
W: {numpy array}, shape(n_features, n_clusters)
feature weight matrix
Reference
Yang, Yi et al. "l2,1-Norm Regularized Discriminative Feature Selection for Unsupervised Learning." AAAI 2012.
"""
# default gamma is 0.1
if 'gamma' not in kwargs:
gamma = 0.1
else:
gamma = kwargs['gamma']
# default k is set to be 5
if 'k' not in kwargs:
k = 5
else:
k = kwargs['k']
if 'n_clusters' not in kwargs:
n_clusters = 5
else:
n_clusters = kwargs['n_clusters']
if 'verbose' not in kwargs:
verbose = False
else:
verbose = kwargs['verbose']
# construct M
n_sample, n_feature = X.shape
M = construct_M(X, k, gamma)
D = np.eye(n_feature)
max_iter = 1000
obj = np.zeros(max_iter)
for iter_step in range(max_iter):
# update W as the eigenvectors of P corresponding to the first n_clusters
# smallest eigenvalues
P = M + gamma*D
eigen_value, eigen_vector = scipy.linalg.eigh(a=P)
W = eigen_vector[:, 0:n_clusters]
# update D as D_ii = 1 / 2 / ||W(i,:)||
D = generate_diagonal_matrix(W)
obj[iter_step] = calculate_obj(X, W, M, gamma)
if verbose:
print 'obj at iter ' + str(iter_step+1) + ': ' + str(obj[iter_step])
if iter_step >= 1 and math.fabs(obj[iter_step] - obj[iter_step-1]) < 1e-3:
break
return W
def erfs(X, Y, **kwargs):
"""
This function implementS efficient and robust feature selection via joint l21-norms minimization
min_W||X^T W - Y||_2,1 + gamma||W||_2,1
Input
-----
X: {numpy array}, shape (n_samples, n_features)
input data
Y: {numpy array}, shape (n_samples, n_classes)
input class label matrix, each row is a one-hot-coding class label
kwargs: {dictionary}
gamma: {float}
parameter in RFS
verbose: boolean
True if want to display the objective function value, false if not
Output
------
W: {numpy array}, shape(n_samples, n_features)
feature weight matrix
Reference
---------
Nie, Feiping et al. "Efficient and Robust Feature Selection via Joint l2,1-Norms Minimization" NIPS 2010.
"""
# default gamma is 1
if 'gamma' not in kwargs:
gamma = 1
else:
gamma = kwargs['gamma']
if 'verbose' not in kwargs:
verbose = False
else:
verbose = kwargs['verbose']
n_samples, n_features = X.shape
A = np.zeros((n_samples, n_samples + n_features))
A[:, 0:n_features] = X
A[:, n_features:n_features+n_samples] = gamma*np.eye(n_samples)
D = np.eye(n_features+n_samples)
max_iter = 1000
obj = np.zeros(max_iter)
for iter_step in range(max_iter):
# update U as U = D^{-1} A^T (A D^-1 A^T)^-1 Y
D_inv = LA.inv(D)
temp = LA.pinv(np.dot(np.dot(A, D_inv), A.T)) # (A D^-1 A^T)^-1
U = np.dot(np.dot(np.dot(D_inv, A.T), temp), Y)
# update D as D_ii = 1 / 2 / ||U(i,:)||
D = generate_diagonal_matrix(U)
obj[iter_step] = calculate_obj(X, Y, U[0:n_features, :], gamma)
if verbose:
print 'obj at iter ' + str(iter_step+1) + ': ' + str(obj[iter_step])
if iter_step >= 1 and math.fabs(obj[iter_step] - obj[iter_step-1]) < 1e-3:
break
# the first d rows of U are the feature weights
W = U[0:n_features, :]
return W