Ha Quang Minh

Mercer’s theorem, feature maps, and smoothing

We study Mercers theorem and feature maps for several positive definite kernels that are widely used in practice. The smoothing properties of these kernels will also be explored.

Semi-supervised multi-feature learning for person re-identification

Person re-identification is probably the open challenge for low-level video surveillance in the presence of a camera network with non-overlapped fields of view. A large number of direct approaches has emerged in the last five years, often proposing novel visual features specifically designed to highlight the most discriminant aspects of people, which are invariant to pose, scale and illumination. On the other hand, learning-based methods are usually based on simpler features, and are trained on pairs of cameras to discriminate between individuals. In this paper, we present a method that joins these two ideas: given an arbitrary state-of-the-art set of features, no matter their number, dimensionality or descriptor, the proposed multi-class learning approach learns how to fuse them, ensuring that the features agree on the classification result. The approach consists of a semi-supervised multi-feature learning strategy, that requires at least a single image per person as training data. To validate our approach, we present results on different datasets, using several heterogeneous features, that set a new level of performance in the person re-identification problem.

Kernel-based classification for brain connectivity graphs on the Riemannian manifold of positive definite matrices

An important task in connectomics studies is the classification of connectivity graphs coming from healthy and pathological subjects. In this paper, we propose a mathematical framework based on Riemannian geometry and kernel methods that can be applied to connectivity matrices for the classification task. We tested our approach using different real datasets of functional and structural connectivity, evaluating different metrics to describe the similarity between graphs. The empirical results obtained clearly show the superior performance of our approach compared with baseline methods, demonstrating the advantages of our manifold framework and its potential for other applications.

Multivariate Slow Feature Analysis and Decorrelation Filtering for Blind Source Separation

We generalize the method of Slow Feature Analysis (SFA) for vector-valued functions of several variables and apply it to the problem of blind source separation, in particular to image separation. It is generally necessary to use multivariate SFA instead of univariate SFA for separating multi-dimensional signals. For the linear case, an exact mathematical analysis is given, which shows in particular that the sources are perfectly separated by SFA if and only if they and their first-order derivatives are uncorrelated. When the sources are correlated, we apply the following technique called Decorrelation Filtering: use a linear filter to decorrelate the sources and their derivatives in the given mixture, then apply the unmixing matrix obtained on the filtered mixtures to the original mixtures. If the filtered sources are perfectly separated by this matrix, so are the original sources. A decorrelation filter can be numerically obtained by solving a nonlinear optimization problem. This technique can also be applied to other linear separation methods, whose output signals are decorrelated, such as ICA. When there are more mixtures than sources, one can determine the actual number of sources by using a regularized version of SFA with decorrelation filtering. Extensive numerical experiments using SFA and ICA with decorrelation filtering, supported by mathematical analysis, demonstrate the potential of our methods for solving problems involving blind source separation.

A regularized spectral algorithm for Hidden Markov Models with applications in computer vision

Hidden Markov Models (HMMs) are among the most important and widely used techniques to deal with sequential or temporal data. Their application in computer vision ranges from action/gesture recognition to videosurveillance through shape analysis. Although HMMs are often embedded in complex frameworks, this paper focuses on theoretical aspects of HMM learning. We propose a regularized algorithm for learning HMMs in the spectral framework, whose computations have no local minima. Compared with recently proposed spectral algorithms for HMMs, our method is guaranteed to produce probability values which are always physically meaningful and which, on synthetic mathematical models, give very good approximations to true probability values. Furthermore, we place no restriction on the number of symbols and the number of states. On various pattern recognition data sets, our algorithm consistently outperforms classical HMMs, both in accuracy and computational speed. This and the fact that HMMs are used in vision as building blocks for more powerful classification approaches, such as generative embedding approaches or more complex generative models, strongly support spectral HMMs (SHMMs) as a new basic tool for pattern recognition.

Slow feature analysis and decorrelation filtering for separating correlated sources

We generalize the method of Slow Feature Analysis for vector-valued functions of multivariables and apply it to the problem of blind source separation, in particular image separation. For the linear case, exact mathematical analysis is given, which shows in particular that the sources are perfectly separated by SFA if and only if they and their first order derivatives are uncorrelated. When the sources are correlated, we apply the following technique called decorrelation filtering: use a linear filter to decorrelate the sources and their derivatives, then apply the separating matrix obtained on the filtered sources to the original sources. We show that if the filtered sources are perfectly separated by this matrix, then so are the original sources. We show how to numerically obtain such a decorrelation filter by solving a nonlinear optimization problem. This technique can also be applied to other linear separation methods, whose output signals are decorrelated, such as ICA.

Approximate Log-Hilbert-Schmidt Distances between Covariance Operators for Image Classification

This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features, in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides a rich representation of image features by exploiting their non-linear correlations, using the power of kernel methods and Riemannian geometry. Theoretically, we provide an approximate formulation for the Log-Hilbert-Schmidt distance between covariance operators that is efficient to compute and scalable to large datasets. Empirically, we apply our framework to the task of image classification on eight different, challenging datasets. In almost all cases, the results obtained outperform other state of the art methods, demonstrating the competitiveness and potential of our framework.

Affine-Invariant Riemannian Distance Between Infinite-Dimensional Covariance Operators

This paper studies the affine-invariant Riemannian distance on the Riemann-Hilbert manifold of positive definite operators on a separable Hilbert space. This is the generalization of the Riemannian manifold of symmetric, positive definite matrices to the infinite-dimensional setting. In particular, in the case of covariance operators in a Reproducing Kernel Hilbert Space (RKHS), we provide a closed form solution, expressed via the corresponding Gram matrices.

Trusting Skype: Learning the Way People Chat for Fast User Recognition and Verification

Identity safekeeping on chats has recently become an important problem on social networks. One of the most important issues is identity theft, where impostors steal the identity of a person, substituting her in the chats, in order to have access to private information. In the literature, the problem has been addressed by designing sets of features which capture the way a person interacts through the chats. However, such approaches perform well only on the long term, after a long conversation has been performed, this is a problem, since in the early turns of a conversation, much important information can be stolen. This paper focuses on this issue, presenting a learning approach which boosts the performance of user recognition and verification, allowing to recognize a subject with considerable accuracy. The proposed method is based on a recent framework of one-shot multi-class multi-view learning, based on Reproducing Kernel Hilbert Spaces (RKHS) theory. Our technique reaches a recognition rate of 76.9% in terms of AUC of the Cumulative Matching Characteristic curve, with only 10 conversational turns considered, on a total of 78 subjects. This sets the new best performances on a public conversation benchmark.

The regularized least squares algorithm and the problem of learning halfspaces

We provide sample complexity of the problem of learning halfspaces with monotonic noise, using the regularized least squares algorithm in the reproducing kernel Hilbert spaces (RKHS) framework.