Exemple #1
0
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
Exemple #2
0
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