Narrow Results

Subspace learning method has commonly been used as a popular way to understand high dimensional data such as face images. In this paper, a novel subspace learning method called Discriminative Local Learning Projection (DLLP) is proposed for face recognition. By characterizing the local structures and dissimilarities between the supervised data manifolds, a linear transformation that can maximize the dissimilarities between all manifolds and simultaneously minimize the local estimation error can be computed. Thus the proposed algorithm embeds the discriminative information as well as the local geometry of samples into the objective function. And the abilities of preserving the local structure in each manifold and classification are both combined into the algorithm. Extensive experiments on face databases demonstrate the effectiveness of DLLP.

Sparse subspace learning has drawn more and more attentions recently, however, most of them are unsupervised and unsuitable for classification tasks. In this paper, a new discriminant sparsity preserving analysis (DSPA) method by integrating sparse reconstructive weighting into Fisher criterion is proposed for face recognition. We first get sparsity preserving space spanned by the eigenvectors of sparsity preserving projections (SPP). Then, the optimal projection can be obtained by solving an eigenvalue and eigenvector problem of the between-class scatter matrix in sparsity preserving space. The method not only preserves the sparse reconstructive relationship of the data, but also encodes the discriminant information. Extensive experiments on four face image datasets (Yale, ORL, AR and CMU PIE) demonstrate the effectiveness of the proposed DSPA method.

Subspace learning has been widely utilized to extract discriminative features for classification task, such as face recognition, even when facial images are occluded or corrupted. However, the performance of most existing methods would be degraded significantly in the scenario of that data being contaminated with severe noise, especially when the magnitude of the gross corruption can be arbitrarily large. To this end, in this paper, a novel discriminative subspace learning method is proposed based on the well-known low-rank representation (LRR). Specifically, a discriminant low-rank representation and the projecting subspace are learned simultaneously, in a supervised way. To avoid the deviation from the original solution by using some relaxation, we adopt the Schatten $p$-norm and ${\ell }_p$-norm, instead of the nuclear norm and ${\ell }_1$-norm, respectively. Experimental results on two famous databases, i.e. PIE and ORL, demonstrate that the proposed method achieves better classification scores than the state-of-the-art approaches.

Electroencephalogram (EEG) is a pivotal diagnostic tool for epilepsy. EEG signals have complex sources, significant individual differences, and data distribution varies across different domains are also easily influenced by noise. This study develops a low-rank sparse representation-based transition subspace learning (LRSRTS) algorithm. Based on low-rank reconstruction transfer subspace learning, the LRSRTS algorithm uses subspace projection and low-rank constraints to ensure that multiple domains are aligned in the subspace and uses sparse constraints to ensure reconstruction from the source domain to the target domain. Separating the noise information in the subspace, the LRSRTS algorithm uses the source domain samples to establish a discriminative classifier. Since the label information is non-negative, the LRSRTS imposes non-negative constraints on the transition subspace. With the more flexible subspace and classifier, the LRSRTS algorithm demonstrates satisfactory recognition performance on the CHB-MIT dataset.

Multidimensional scaling (MDS) has been applied in many applications such as dimensionality reduction and data mining. However, one of the drawbacks of MDS is that it is only defined on "training" data without clear extension to out-of-sample points. Furthermore, since that MDS is based on Euclidean distance (which is a dissimilarity measure), it is not suitable for detecting the nonlinear manifold structure embedded in the similarities between data points. In this paper, we extend MDS to the correlation measure space, named correlation MDS (CMDS). CMDS employs an explicit nonlinear mapping between the input and reduced space while MDS using an implicit mapping. As a result, CMDS can directly provide prediction for new samples. In addition, correlation is a similarity measure, CMDS method can effectively capture the nonlinear manifold structure of data embedded in the similarities between the data points. Theoretical analysis also shows that CMDS has some properties similar to kernel methods and can be extended to feature space. The effectiveness of the approach provided in this paper are demonstrated by extensive experiments on various datasets, in comparison with serval existing algorithms.

Hyperspectral image (HSI) classification draws a lot of attentions in the past decades. The classical problem of HSI classification mainly focuses on a single HSI scene. In recent years, cross-scene classification becomes a new problem, which deals with the classification models that can be applied across different but highly related HSI scenes sharing common land cover classes. This paper presents a cross-scene classification framework combining spectral–spatial feature extraction and manifold-constrained feature subspace learning. In this framework, spectral–spatial feature extraction is completed using three-dimensional (3D) wavelet transform while manifold-constrained feature subspace learning is implemented via multitask nonnegative matrix factorization (MTNMF) with manifold regularization. In 3D wavelet transform, we drop some coefficients corresponding to high frequency in order to avoid data noise. In feature subspace learning, a common dictionary (basis) matrix is shared by different scenes during the nonnegative matrix factorization, indicating that the highly related scenes should share than same low-dimensional feature subspace. Furthermore, manifold regularization is applied to force the consistency across the scenes, i.e. all pixels representing the same land cover class should be similar in the low-dimensional feature subspace, though they may be drawn from different scenes. The experimental results show that the proposed method performs well in cross-scene HSI datasets.

Learning to hash is receiving increasing research attention due to its effectiveness in addressing the large-scale similarity search problem. Most of the existing hashing algorithms are focused on learning hash functions in the form of numeric quantization of some projected feature space. In this work, we propose a novel hash learning method that encodes features’ relative ordering instead of quantizing their numeric values in a set of low-dimensional ranking subspaces. We formulate the ranking-based hash learning problem as the optimization of a continuous probabilistic error function using softmax approximation and present an efficient learning algorithm to solve the problem. As a generalization of Winner-Take-All (WTA) hashing, the proposed algorithm naturally enjoys the numeric stability benefits of rank correlation measures while being optimized to achieve high precision with very compact code. Additionally, the proposed method can also be easily extended to nonlinear kernel spaces to discover ranking structures that can not be revealed in linear subspaces. We demonstrate through extensive experiments that the proposed method can achive competitive performances as compared to a number of state-of-the-art hashing methods.

With the incredible growth of high-dimensional data such as microarray gene expression data and web blogs from internet, the researchers are desirable to develop new clustering techniques to address the critical problem created by irrelevant dimensions. Properties of Nonnegative Matrix Factorization (NMF) as a clustering method were studied by relating its formulation to other methods such as K-means clustering. In this paper, by introducing clustering indicator constraints on NMF and incorporating manifold regularization to preserve geometric structures, we propose a novel manifold regularized NMF method that can simultaneously learn subspace and do clustering. As a result, our clustering results can directly assign cluster label to data points. Extensive experimental results show that our method outperforms related other methods.