KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization

We consider the image classification problem via kernel collaborative representation classification with locality constrained dictionary (KCRC-LCD). Specifically, we propose a kernel collaborative representation classification (KCRC) approach in which kernel method is used to improve the discrimination ability of collaborative representation classification (CRC). We then measure the similarities between the query and atoms in the global dictionary in order to construct a locality constrained dictionary (LCD) for KCRC. In addition, we discuss several similarity measure approaches in LCD and further present a simple yet effective unified similarity measure whose superiority is validated in experiments. There are several appealing aspects associated with LCD. First, LCD can be nicely incorporated under the framework of KCRC. The LCD similarity measure can be kernelized under KCRC, which theoretically links CRC and LCD under the kernel method. Second, KCRC-LCD becomes more scalable to both the training set size and the feature dimension. Example shows that KCRC is able to perfectly classify data with certain distribution, while conventional CRC fails completely. Comprehensive experiments on many public datasets also show that KCRC-LCD is a robust discriminative classifier with both excellent performance and good scalability, being comparable or outperforming many other state-of-the-art approaches

Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning

Graph-based Semi-supervised Learning: Algorithms and Applications.

114 p.Graph-based semi-supervised learning have attracted large numbers of researchers and it is an important part of semi-supervised learning. Graph construction and semi-supervised embedding are two main steps in graph-based semi-supervised learning algorithms. In this thesis, we proposed two graph construction algorithms and two semi-supervised embedding algorithms. The main work of this thesis is summarized as follows:1. A new graph construction algorithm named Graph construction based on self-representativeness and Laplacian smoothness (SRLS) and several variants are proposed. Researches show that the coefficients obtained by data representation algorithms reflect the similarity between data samples and can be considered as a measurement of the similarity. This kind of measurement can be used for the weights of the edges between data samples in graph construction. Each column of the coefficient matrix obtained by data self-representation algorithms can be regarded as a new representation of original data. The new representations should have common features as the original data samples. Thus, if two data samples are close to each other in the original space, the corresponding representations should be highly similar. This constraint is called Laplacian smoothness.SRLS graph is based on l2-norm minimized data self-representation and Laplacian smoothness. Since the representation matrix obtained by l2 minimization is dense, a two phrase SRLS method (TPSRLS) is proposed to increase the sparsity of graph matrix. By extending the linear space to Hilbert space, two kernelized versions of SRLS are proposed. Besides, a direct solution to kernelized SRLS algorithm is also introduced.2. A new sparse graph construction algorithm named Sparse graph with Laplacian smoothness (SGLS) and several variants are proposed. SGLS graph algorithm is based on sparse representation and use Laplacian smoothness as a constraint (SGLS). A kernelized version of the SGLS algorithm and a direct solution to kernelized SGLS algorithm are also proposed. 3. SPP is a successful unsupervised learning method. To extend SPP to a semi-supervised embedding method, we introduce the idea of in-class constraints in CGE into SPP and propose a new semi-supervised method for data embedding named Constrained Sparsity Preserving Embedding (CSPE).4. The weakness of CSPE is that it cannot handle the new coming samples which means a cascade regression should be performed after the non-linear mapping is obtained by CSPE over the whole training samples. Inspired by FME, we add a regression term in the objective function to obtain an approximate linear projection simultaneously when non-linear embedding is estimated and proposed Flexible Constrained Sparsity Preserving Embedding (FCSPE).Extensive experiments on several datasets (including facial images, handwriting digits images and objects images) prove that the proposed algorithms can improve the state-of-the-art results