From Point to Set: Extend the Learning of Distance Metrics

Most of the current metric learning methods are proposed for point-to-point distance (PPD) based classification. In many computer vision tasks, however, we need to measure the point-to-set distance (PSD) and even set-to-set distance (SSD) for classification. In this paper, we extend the PPD based Mahalanobis distance metric learning to PSD and SSD based ones, namely point-to-set distance metric learning (PSDML) and set-to-set distance metric learning (SSDML), and solve them under a unified optimization framework. First, we generate positive and negative sample pairs by computing the PSD and SSD between training samples. Then, we characterize each sample pair by its covariance matrix, and propose a covariance kernel based discriminative function. Finally, we tackle the PSDML and SSDML problems by using standard support vector machine solvers, making the metric learning very efficient for multiclass visual classification tasks. Experiments on gender classification, digit recognition, object categorization and face recognition show that the proposed metric learning methods can effectively enhance the performance of PSD and SSD based classification. 1

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Tensor Regression

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table

EXTRACTING NEURONAL DYNAMICS AT HIGH SPATIOTEMPORAL RESOLUTIONS: THEORY, ALGORITHMS, AND APPLICATION

Analyses of neuronal activity have revealed that various types of neurons, both at the single-unit and population level, undergo rapid dynamic changes in their response characteristics and their connectivity patterns in order to adapt to variations in the behavioral context or stimulus condition. In addition, these dynamics often admit parsimonious representations. Despite growing advances in neural modeling and data acquisition technology, a unified signal processing framework capable of capturing the adaptivity, sparsity and statistical characteristics of neural dynamics is lacking. The objective of this dissertation is to develop such a signal processing methodology in order to gain a deeper insight into the dynamics of neuronal ensembles underlying behavior, and consequently a better understanding of how brain functions. The first part of this dissertation concerns the dynamics of stimulus-driven neuronal activity at the single-unit level. We develop a sparse adaptive filtering framework for the identification of neuronal response characteristics from spiking activity. We present a rigorous theoretical analysis of our proposed sparse adaptive filtering algorithms and characterize their performance guarantees. Application of our algorithms to experimental data provides new insights into the dynamics of attention-driven neuronal receptive field plasticity, with a substantial increase in temporal resolution. In the second part, we focus on the network-level properties of neuronal dynamics, with the goal of identifying the causal interactions within neuronal ensembles that underlie behavior. Building up on the results of the first part, we introduce a new measure of causality, namely the Adaptive Granger Causality (AGC), which allows capturing the sparsity and dynamics of the causal influences in a neuronal network in a statistically robust and computationally efficient fashion. We develop a precise statistical inference framework for the estimation of AGC from simultaneous recordings of the activity of neurons in an ensemble. Finally, in the third part we demonstrate the utility of our proposed methodologies through application to synthetic and real data. We first validate our theoretical results using comprehensive simulations, and assess the performance of the proposed methods in terms of estimation accuracy and tracking capability. These results confirm that our algorithms provide significant gains in comparison to existing techniques. Furthermore, we apply our methodology to various experimentally recorded data from electrophysiology and optical imaging: 1) Application of our methods to simultaneous spike recordings from the ferret auditory and prefrontal cortical areas reveals the dynamics of top-down and bottom-up functional interactions underlying attentive behavior at unprecedented spatiotemporal resolutions; 2) Our analyses of two-photon imaging data from the mouse auditory cortex shed light on the sparse dynamics of functional networks under both spontaneous activity and auditory tone detection tasks; and 3) Application of our methods to whole-brain light-sheet imaging data from larval zebrafish reveals unique insights into the organization of functional networks involved in visuo-motor processing

Sparse variational regularization for visual motion estimation

The computation of visual motion is a key component in numerous computer vision tasks such as object detection, visual object tracking and activity recognition. Despite exten- sive research effort, efficient handling of motion discontinuities, occlusions and illumina- tion changes still remains elusive in visual motion estimation. The work presented in this thesis utilizes variational methods to handle the aforementioned problems because these methods allow the integration of various mathematical concepts into a single en- ergy minimization framework. This thesis applies the concepts from signal sparsity to the variational regularization for visual motion estimation. The regularization is designed in such a way that it handles motion discontinuities and can detect object occlusions