Dirichlet process mixture models for text and video analysis

Managing large collections of information is a central goal of modern electrical and computer engineering. Text and image data sets have become widely accessible with the help of the world wide web, thus necessitating elaborate methods of retrieval, organization and exploration. This thesis considers the problem of inferring and modeling topics in a large sequence of documents with known publication dates and introduces two novel frameworks with applications in video: (i) automatic clustering and data segmentation into groups that are smooth along the time axis, and ( ii) unusual-event detection.;With respect to the analysis of topics in large collections of text, a novel model is introduced, based on an extension of the hierarchical Dirichlet process (HDP), termed the dynamic HDP. The details of this general framework may take different forms, depending on the specifics of the model. For the examples considered here we examine base measures based on independent multinomial-Dirichlet measures for representation of topic-dependent word counts. It is assumed that each paragraph is associated with a particular topic, and the probability of a given topic being manifested in a specific document evolves dynamically between contiguous time-stamped documents. Natural simplifications of the dHDP allow fully variational Bayesian (VB) inference, of interest for large-scale problems. We demonstrate results and make comparisons to HDP (i.e., without dynamic topic evolution) and latent Dirichlet allocation (LDA), considering a database of NIPS papers as well as the United States presidential State of the Union addresses from 1790 to 2008.;The video segmentation and clustering work presented here introduces a novel framework for automatic clustering of time-evolving data into contiguous segments in time, with specific application to video. The video is represented in terms of subsequences of discrete observations, and each subsequence is modeled as a mixture of hidden Markov models (HMMs), with time-evolving mixing weights. A fully Bayesian formulation is constituted, with variational Bayes (VB) inference employed to approximate an infinite-dimensional hierarchical Dirichlet process mixture model. Invariant subspace analysis (ISA) is used to extract features from the video. In addition to providing model and inference details, comparisons are made to modeling based on Dirichlet process HMM mixtures, that do not explicitly account for the known time dependence between subsequences in the video.;Finally, we address the problem of unusual-event detection in a video sequence. The time-evolving properties of the ISA extracted features from video are modeled via an infinite hidden Markov model (iHMM), which is trained using "normal"/"typical" video. The iHMM retains a full posterior density function on all model parameters, including the number of underlying HMM states. Anomalies (unusual events) are detected subsequently if a low likelihood is observed when associated sequential features are submitted to the trained iHMM. A hierarchical Dirichlet process (HDP) framework is employed in the formulation of the iHMM. The evaluation of posterior distributions for the iHMM is achieved in two ways: via MCMC and using a variational Bayes (VB) formulation. Comparisons are made to modeling based on conventional maximum-likelihood-based HMMs, as well as to Dirichlet-process-based Gaussian-mixture models.