Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the ExpectationMaximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.

Abstract. This paper presents a novel statistical method for factor analysis of binary and count data which is closely related to a technique known as Latent Semantic Analysis. In contrast to the latter method which stems from linear algebra and performs a Singular Value Decomposition of co-occurrence tables, the proposed technique uses a generative latent class model to perform a probabilistic mixture decomposition. This results in a more principled approach with a solid foundation in statistical inference. More precisely, we propose to make use of a temperature controlled version of the Expectation Maximization algorithm for model fitting, which has shown excellent performance in practice. Probabilistic Latent Semantic Analysis has many applications, most prominently in information retrieval, natural language processing, machine learning from text, and in related areas. The paper presents perplexity results for different types of text and linguistic data collections and discusses an application in automated document indexing. The experiments indicate substantial and consistent improvements of the probabilistic method over standard Latent Semantic Analysis.

. Unlabeled document collections are becoming increasingly common and available; mining such data sets represents a major contemporary challenge. Using words as features, text documents are often represented as high-dimensional and sparse vectors--a few thousand dimensions and a sparsity of 95 to 99% is typical. In this paper, we study a certain spherical k-means algorithm for clustering such document vectors. The algorithm outputs k disjoint clusters each with a concept vector that is the centroid of the cluster normalized to have unit Euclidean norm. As our first contribution, we empirically demonstrate that, owing to the high-dimensionality and sparsity of the text data, the clusters produced by the algorithm have a certain "fractal-like" and "self-similar" behavior. As our second contribution, we introduce concept decompositions to approximate the matrix of document vectors; these decompositions are obtained by taking the least-squares approximation onto the linear subspace spanned...

Dyadic data refers to a domain with two finite sets of objects in which observations are made for dyads, i.e., pairs with one element from either set. This includes event co-occurrences, histogram data, and single stimulus preference data as special cases. Dyadic data arises naturally in many applications ranging from computational linguistics and information retrieval to preference analysis and computer vision. In this paper, we present a systematic, domain-independent framework for unsupervised learning from dyadic data by statistical mixture models. Our approach covers different models with flat and hierarchical latent class structures and unifies probabilistic modeling and structure discovery. Mixture models provide both, a parsimonious yet flexible parameterization of probability distributions with good generalization performance on sparse data, as well as structural information about data-inherent grouping structure. We propose an annealed version of the standard Expectation Maximization algorithm for model fitting which is empirically evaluated on a variety of data sets from different domains.

Unsupervised learning of linguistic structure is a difficult problem. A common approach is to define a generative model and maximize the probability of the hidden structure given the observed data. Typically, this is done using maximum-likelihood estimation (MLE) of the model parameters. We show using part-of-speech tagging that a fully Bayesian approach can greatly improve performance. Rather than estimating a single set of parameters, the Bayesian approach integrates over all possible parameter values. This difference ensures that the learned structure will have high probability over a range of possible parameters, and permits the use of priors favoring the sparse distributions that are typical of natural language. Our model has the structure of a standard trigram HMM, yet its accuracy is closer to that of a state-of-the-art discriminative model (Smith and Eisner, 2005), up to 14 percentage points better than MLE. We find improvements both when training from data alone, and using a tagging dictionary. 1

Abstract. In many applications of natural language processing (NLP) it is necessary to determine the likelihood of a given word combination. For example, a speech recognizer may need to determine which of the two word combinations “eat a peach ” and “eat a beach ” is more likely. Statistical NLP methods determine the likelihood of a word combination from its frequency in a training corpus. However, the nature of language is such that many word combinations are infrequent and do not occur in any given corpus. In this work we propose a method for estimating the probability of such previously unseen word combinations using available information on “most similar ” words. We describe probabilistic word association models based on distributional word similarity, and apply them to two tasks, language modeling and pseudo-word disambiguation. In the language modeling task, a similarity-based model is used to improve probability estimates for unseen bigrams in a back-off language model. The similaritybased method yields a 20 % perplexity improvement in the prediction of unseen bigrams and statistically significant reductions in speech-recognition error. We also compare four similarity-based estimation methods against back-off and maximum-likelihood estimation methods on a pseudo-word sense disambiguation task in which we controlled for both unigram and bigram frequency to avoid giving too much weight to easy-to-disambiguate high-frequency configurations. The similaritybased methods perform up to 40 % better on this particular task.

Language modeling is the art of determining the probability of a sequence of words. This is useful in a large variety of areas including speech recognition, optical character recognition, handwriting recognition, machine translation, and spelling correction (Church, 1988; Brown et al., 1990; Hull, 1992; Kernighan et al., 1990; Srihari and Baltus, 1992). The most commonly used language models are very simple (e.g. a Katz-smoothed trigram model). There are many improvements over this simple model however, including caching, clustering, higherorder n-grams, skipping models, and sentence-mixture models, all of which we will describe below. Unfortunately, these more complicated techniques have rarely been examined in combination. It is entirely possible that two techniques that work well separately will not work well together, and, as we will show, even possible that some techniques will work better together than either one does by itself. In this...

We present a technique for automatic induction of slot annotations for subcategorization frames, based on induction of hidden classes in the EM framework of statistical estimation. The models are empirically evalutated by a general decision test. Induction of slot labeling for subcategorization frames is accomplished by a further application of EM, and applied experimentally on frame observations derived from parsing large corpora. We outline an interpretation of the learned representations as theoretical-linguistic decompositional lexical entries.

. We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combination---or mixture---of simpler dynamical models. The parameters in these models admit a simple probabilistic interpretation and can be fitted iteratively by an Expectation-Maximization (EM) procedure. We derive a set of generalized Baum-Welch updates for factorial hidden Markov models that make use of this parameterization. We also describe a simple iterative procedure for approximately computing the statistics of the hidden states. Throughout, we give examples where mixed memory models provide a useful representation of complex stochastic processes. Keywords: Markov models, mixture models, discrete time series 1. Introduction The modeling of time series is a fundamental problem in machine learning, with widespread applications. These include speech recognition (Rabiner, 1989), natu...

In this paper we present a novel framework for extracting the ratable aspects of objects from online user reviews. Extracting such aspects is an important challenge in automatically mining product opinions from the web and in generating opinion-based summaries of user reviews [18, 19, 7, 12, 27, 36, 21]. Our models are based on extensions to standard topic modeling methods such as LDA and PLSA to induce multi-grain topics. We argue that multi-grain models are more appropriate for our task since standard models tend to produce topics that correspond to global properties of objects (e.g., the brand of a product type) rather than the aspects of an object that tend to be rated by a user. The models we present not only extract ratable aspects, but also cluster them into coherent topics, e.g., waitress and bartender are part of the same topic staff for restaurants. This differentiates it from much of the previous work which extracts aspects through term frequency analysis with minimal clustering. We evaluate the multi-grain models both qualitatively and quantitatively to show that they improve significantly upon standard topic models.