Advanced Probabilistic Models for Clustering and Projection

Probabilistic modeling for data mining and machine learning problems is a fundamental research area. The general approach is to assume a generative model underlying the observed data, and estimate model parameters via likelihood maximization. It has the deep probability theory as the mathematical background, and enjoys a large amount of methods from statistical learning, sampling theory and Bayesian statistics. In this thesis we study several advanced probabilistic models for data clustering and feature projection, which are the two important unsupervised learning problems. The goal of clustering is to group similar data points together to uncover the data clusters. While numerous methods exist for various clustering tasks, one important question still remains, i.e., how to automatically determine the number of clusters. The first part of the thesis answers this question from a mixture modeling perspective. A finite mixture model is first introduced for clustering, in which each mixture component is assumed to be an exponential family distribution for generality. The model is then extended to an infinite mixture model, and its strong connection to Dirichlet process (DP) is uncovered which is a non-parametric Bayesian framework. A variational Bayesian algorithm called VBDMA is derived from this new insight to learn the number of clusters automatically, and empirical studies on some 2D data sets and an image data set verify the effectiveness of this algorithm. In feature projection, we are interested in dimensionality reduction and aim to find a low-dimensional feature representation for the data. We first review the well-known principal component analysis (PCA) and its probabilistic interpretation (PPCA), and then generalize PPCA to a novel probabilistic model which is able to handle non-linear projection known as kernel PCA. An expectation-maximization (EM) algorithm is derived for kernel PCA such that it is fast and applicable to large data sets. Then we propose a novel supervised projection method called MORP, which can take the output information into account in a supervised learning context. Empirical studies on various data sets show much better results compared to unsupervised projection and other supervised projection methods. At the end we generalize MORP probabilistically to propose SPPCA for supervised projection, and we can also naturally extend the model to S2PPCA which is a semi-supervised projection method. This allows us to incorporate both the label information and the unlabeled data into the projection process. In the third part of the thesis, we introduce a unified probabilistic model which can handle data clustering and feature projection jointly. The model can be viewed as a clustering model with projected features, and a projection model with structured documents. A variational Bayesian learning algorithm can be derived, and it turns out to iterate the clustering operations and projection operations until convergence. Superior performance can be obtained for both clustering and projection

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Advanced Probabilistic Models for Clustering and Projection

Probabilistic modeling for data mining and machine learning problems is a fundamental research area. The general approach is to assume a generative model underlying the observed data, and estimate model parameters via likelihood maximization. It has the deep probability theory as the mathematical background, and enjoys a large amount of methods from statistical learning, sampling theory and Bayesian statistics. In this thesis we study several advanced probabilistic models for data clustering and feature projection, which are the two important unsupervised learning problems. The goal of clustering is to group similar data points together to uncover the data clusters. While numerous methods exist for various clustering tasks, one important question still remains, i.e., how to automatically determine the number of clusters. The first part of the thesis answers this question from a mixture modeling perspective. A finite mixture model is first introduced for clustering, in which each mixture component is assumed to be an exponential family distribution for generality. The model is then extended to an infinite mixture model, and its strong connection to Dirichlet process (DP) is uncovered which is a non-parametric Bayesian framework. A variational Bayesian algorithm called VBDMA is derived from this new insight to learn the number of clusters automatically, and empirical studies on some 2D data sets and an image data set verify the effectiveness of this algorithm. In feature projection, we are interested in dimensionality reduction and aim to find a low-dimensional feature representation for the data. We first review the well-known principal component analysis (PCA) and its probabilistic interpretation (PPCA), and then generalize PPCA to a novel probabilistic model which is able to handle non-linear projection known as kernel PCA. An expectation-maximization (EM) algorithm is derived for kernel PCA such that it is fast and applicable to large data sets. Then we propose a novel supervised projection method called MORP, which can take the output information into account in a supervised learning context. Empirical studies on various data sets show much better results compared to unsupervised projection and other supervised projection methods. At the end we generalize MORP probabilistically to propose SPPCA for supervised projection, and we can also naturally extend the model to S2PPCA which is a semi-supervised projection method. This allows us to incorporate both the label information and the unlabeled data into the projection process. In the third part of the thesis, we introduce a unified probabilistic model which can handle data clustering and feature projection jointly. The model can be viewed as a clustering model with projected features, and a projection model with structured documents. A variational Bayesian learning algorithm can be derived, and it turns out to iterate the clustering operations and projection operations until convergence. Superior performance can be obtained for both clustering and projection

Cell Type-specific Analysis of Human Interactome and Transcriptome

Cells are the fundamental building block of complex tissues in higher-order organisms. These cells take different forms and shapes to perform a broad range of functions. What makes a cell uniquely eligible to perform a task, however, is not well-understood; neither is the defining characteristic that groups similar cells together to constitute a cell type. Even for known cell types, underlying pathways that mediate cell type-specific functionality are not readily available. These functions, in turn, contribute to cell type-specific susceptibility in various disorders

Mathematical and Data-driven Pattern Representation with Applications in Image Processing, Computer Graphics, and Infinite Dimensional Dynamical Data Mining

Patterns represent the spatial or temporal regularities intrinsic to various phenomena in nature, society, art, and science. From rigid ones with well-defined generative rules to flexible ones implied by unstructured data, patterns can be assigned to a spectrum. On one extreme, patterns are completely described by algebraic systems where each individual pattern is obtained by repeatedly applying simple operations on primitive elements. On the other extreme, patterns are perceived as visual or frequency regularities without any prior knowledge of the underlying mechanisms. In this thesis, we aim at demonstrating some mathematical techniques for representing patterns traversing the aforementioned spectrum, which leads to qualitative analysis of the patterns' properties and quantitative prediction of the modeled behaviors from various perspectives. We investigate lattice patterns from material science, shape patterns from computer graphics, submanifold patterns encountered in point cloud processing, color perception patterns applied in underwater image processing, dynamic patterns from spatial-temporal data, and low-rank patterns exploited in medical image reconstruction. For different patterns and based on their dependence on structured or unstructured data, we present suitable mathematical representations using techniques ranging from group theory to deep neural networks.Ph.D

Contributions au traitement des images multivariées

Ce mémoire résume mon activité pédagogique et scientifique en vue de l’obtention de l’habilitation à diriger des recherches