Lianwei Zhao

Combining label information and neighborhood graph for semi-supervised learning

In this paper, we consider the problem of combining the labeled and unlabeled examples to boost the performance of semi-supervised learning. We first define the label information graph, and then incorporate it with neighborhood graph. We propose a new regularized semi-supervised classification algorithm, in which the regularization term is based on this modified Graph Laplacian. According to the properties of Reproducing Kernel Hilbert Space (RKHS), the representer theorem holds, so the solution can be expressed by the Mercer kernel of examples. Experimental results show that our algorithm can use unlabeled and labeled examples effectively.

Adapting k-means algorithm for discovering clusters in subspaces

Subspace clustering is a challenging task in the field of data mining. Traditional distance measures fail to differentiate the furthest point from the nearest point in very high dimensional data space. To tackle the problem, we design minimal subspace distance which measures the similarity between two points in the subspace where they are nearest to each other. It can discover subspace clusters implicitly when measuring the similarities between points. We use the new similarity measure to improve traditional k-means algorithm for discovering clusters in subspaces. By clustering with low-dimensional minimal subspace distance first, the clusters in low-dimensional subspaces are detected. Then by gradually increasing the dimension of minimal subspace distance, the clusters get refined in higher dimensional subspaces. Our experiments on both synthetic data and real data show the effectiveness of the proposed similarity measure and algorithm.

Fast and adaptive low-pass whitening filters for natural images

A fast and simple solution was suggested to reduce the inter-pixels correlations in natural images, of which the power spectra roughly fell off with the increasing spatial frequency f according to a power law; but the 1/f exponent, α, was different from image to image. The essential of the proposed method was to flatten the decreasing power spectrum of each image by using an adaptive low-pass and whitening filter. The act of low-pass filtering was just to reduce the effects of noise usually took place in the high frequencies. The act of whitening filtering was a special processing, which was to attenuate the low frequencies and boost the high frequencies so as to yield a roughly flat power spectrum across all spatial frequencies. The suggested method was computationally more economical than the geometric covariance matrix based PCA method. Meanwhile, the performance degradations accompanied with the computational economy improvement were fairly insignificant.

“What” and “where” information based attention guidance model

Visual system can be defined as consisting of two pathways. The classic definition labeled a “what” pathway to process object information and a “where” pathway to process spatial information. In this paper, we propose a novel attention guidance model based on “what” and “where” information. Context-centered “where” information is used to control top-down attention, and guide bottom-up attention which is driven by “what” information. The procedure of top-down attention can be divided into two stages: pre-attention and focus attention. In the stage of pre-attention, “where” information can be used to provide prior knowledge of presence or absence of objects which decides whether search operation is followed. By integrating the result of focus attention with “what” information, attention is directed to the region that is most likely to contain the object and series of salient regions are detected. Results of experiment on natural images demonstrate its effectiveness.

Learning overcomplete representations with a generalized gaussian prior

Overcomplete representations have been advocated because they allow a basis to better approximate the underlying statistical density of the data which can lead to representations that better capture the underlying structure in the data. The prior distributions for the coefficients of these models, however, are assumed to be fixed, not adaptive to the data, and hereby inaccurate. Here we describe a method for learning overcomplete representations with a generalized Gaussian prior, which can fit a broader range of statistical distributions by varying the value of the steepness parameter β. Using this distribution in overcomplete representations, empirical results were obtained for the blind source separation of more sources than mixtures, which show that the accuracy of the density estimation is improved.

Construction algorithm of principal curves in the sense of limit

Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.