Beyond Gauss: Image-Set Matching on the Riemannian Manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifolds, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods

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

Similarity Search Over Graphs Using Localized Spectral Analysis

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the algorithm uses kernel method that embeds the data points into a low dimensional manifold. Unlike other kernel methods, which consider the entire data for the embedding, our method selects a specific set of kernel eigenvectors. The eigenvectors are chosen to separate between the data points and the reference data point so that similar data points can be easily identified as being distinct from most of the members in the dataset.Comment: Published in SampTA 201

Distribution matching for transduction

Many transductive inference algorithms assume that distributions over training and test estimates should be related, e.g. by providing a large margin of separation on both sets. We use this idea to design a transduction algorithm which can be used without modification for classification, regression, and structured estimation. At its heart we exploit the fact that for a good learner the distributions over the outputs on training and test sets should match. This is a classical two-sample problem which can be solved efficiently in its most general form by using distance measures in Hilbert Space. It turns out that a number of existing heuristics can be viewed as special cases of our approach.

GPU acceleration for statistical gene classification

The use of Bioinformatic tools in routine clinical diagnostics is still facing a number of issues. The more complex and advanced bioinformatic tools become, the more performance is required by the computing platforms. Unfortunately, the cost of parallel computing platforms is usually prohibitive for both public and small private medical practices. This paper presents a successful experience in using the parallel processing capabilities of Graphical Processing Units (GPU) to speed up bioinformatic tasks such as statistical classification of gene expression profiles. The results show that using open source CUDA programming libraries allows to obtain a significant increase in performances and therefore to shorten the gap between advanced bioinformatic tools and real medical practic

GPU cards as a low cost solution for efficient and fast classification of high dimensional gene expression datasets

The days when bioinformatics tools will be so reliable to become a standard aid in routine clinical diagnostics are getting very close. However, it is important to remember that the more complex and advanced bioinformatics tools become, the more performances are required by the computing platforms. Unfortunately, the cost of High Performance Computing (HPC) platforms is still prohibitive for both public and private medical practices. Therefore, to promote and facilitate the use of bioinformatics tools it is important to identify low-cost parallel computing solutions. This paper presents a successful experience in using the parallel processing capabilities of Graphical Processing Units (GPU) to speed up classification of gene expression profiles. Results show that using open source CUDA programming libraries allows to obtain a significant increase in performances and therefore to shorten the gap between advanced bioinformatics tools and real medical practic