Topic modeling is one of the most common tools to analyze a large volume of unlabeled documents that are usually represented with bag-of-words. This thesis firstly discusses the connections between the exchangeability property of bag-of-words, popular topic modeling algorithms, and the de Finetti-Hewitt-Savage theorem. We show that these algorithms are special cases of this theorem and the exchangeability of words, rather than independence of words, is the sufficient condition for applying them. Tasks are then focused on the latent Dirichlet allocation (LDA) because of its higher modeling capability. The investigation of asymmetric priors for LDA and derivation of per-document topic distribution for unseen documents are also presented. Since topics are often denoted by multinomial distributions of words, the semantic meaning cannot be easily understood especially when people are not familiar with the background of the studying corpus. To address this problem, automatic topic labeling is proposed to automatically generate understandable topic labels.;Apart from the text of a corpus, there are usually some meta information accompanied for analyses, e.g. author name, date, category, etc. Integrating them with text documents during topic modeling not only enables better topic analysis but also causes more information to be found. For instance, an author's interests can be identified if his/her name occurrences are tightly coupled to some words. Based on LDA and the author-topic model, we propose a Bayesian model with Dirichlet priors to combine text and author information to identify topics and interests associated with the corpus and the authors, respectively. With both the topics and the interests, generalization of the model is significantly improved. We also propose a composite model to combine identified topics and interests so that the overall composite topics of a corpus can be derived. These composite topics have a desirable property that the correlation between them is lower and hence they can represent more diverse aspects of the corpus.;Text corpus analyses and processing are often performed in low dimensional spaces rather than high dimensional spaces formed by bag-of-words. Dimensionality reduction can be achieved with principle component analysis (PCA) or some other algorithms. Nevertheless, most of them are unsupervised and complementary information such as the labels of documents is often ignored. Even there are some supervised dimensionality reduction algorithms such as supervised probabilistic PCA, they treat labels as real numbers but not nominal categories. We propose the classification probabilistic PCA (CPPCA) to incorporate label information of documents, in which labels are treated as categories. Documents can be projected into a lower dimensional space where variances and labels are considered simultaneously. Semi-supervised version of this algorithm was applied to domain adaptation problems and experimental results show that CPPCA performs significantly better than unsupervised and supervised probabilistic PCA.
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