We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

/pdf/latent-dirichlet-allocation-4gmscb06en.pdf

Latent dirichlet allocation

We propose a generative model for text and other collections of discrete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams [6], and Hof-mann's aspect model, also known as probabilistic latent semantic indexing (pLSI) [3]. In the context of text modeling, our model posits that each document is generated as a mixture of topics, where the continuous-valued mixture proportions are distributed as a latent Dirichlet random variable. Inference and learning are carried out efficiently via variational algorithms. We present empirical results on applications of this model to problems in text modeling, collaborative filtering, and text classification.

/pdf/latent-dirichlet-allocation-rkwbqihm3p.pdf

Latent Dirichlet Allocation

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

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A tutorial on spectral clustering

https://www.stat.washington.edu/mmp/Papers/compare-jmva-revised.pdf

Comparing clusterings---an information based distance

This paper describes the mixtures-of-trees model, a probabilistic model for discrete multidimensional domains. Mixtures-of-trees generalize the probabilistic trees of Chow and Liu (1968) in a different and complementary direction to that of Bayesian networks. We present efficient algorithms for learning mixtures-of-trees models in maximum likelihood and Bayesian frameworks. We also discuss additional efficiencies that can be obtained when data are "sparse," and we present data structures and algorithms that exploit such sparseness. Experimental results demonstrate the performance of the model for both density estimation and classification. We also discuss the sense in which tree-based classifiers perform an implicit form of feature selection, and demonstrate a resulting insensitivity to irrelevant attributes.

/pdf/learning-with-mixtures-of-trees-26rlzw5kuc.pdf

Learning with mixtures of trees

We present a new view of clustering and segmentation by pairwise similarities. We interpret the similarities as edge ows in a Markov random walk and study the eigenvalues and eigenvectors of the walk's transition matrix. This view shows that spectral methods for clustering and segmentation have a probabilistic foundation. We prove that the Normalized Cut method arises naturally from our framework and we provide a complete characterization of the cases when the Normalized Cut algorithm is exact. Then we discuss other spectral segmentation and clustering methods showing that several of them are essentially the same as NCut.

/pdf/a-random-walks-view-of-spectral-segmentation-472de45dtz.pdf

A Random Walks View of Spectral Segmentation.

This paper proposes an information theoretic criterion for comparing two partitions, or clusterings, of the same data set. The criterion, called variation of information (VI), measures the amount of information lost and gained in changing from clustering \({\cal C}\) to clustering \({\cal C}'\). The criterion makes no assumptions about how the clusterings were generated and applies to both soft and hard clusterings. The basic properties of VI are presented and discussed from the point of view of comparing clusterings. In particular, the VI is positive, symmetric and obeys the triangle inequality. Thus, surprisingly enough, it is a true metric on the space of clusterings.

Comparing Clusterings by the Variation of Information

We present a new view of image segmentation by pairwise similarities. We interpret the similarities as edge flows in a Markov random walk and study the eigenvalues and eigenvectors of the walk's transition matrix. This interpretation shows that spectral methods for clustering and segmentation have a probabilistic foundation. In particular, we prove that the Normalized Cut method arises naturally from our framework. Finally, the framework provides a principled method for learning the similarity function as a combination of features.

/pdf/learning-segmentation-by-random-walks-3zc62igh7x.pdf

Marina Meila

Papers

Comparing clusterings---an information based distance

Learning with mixtures of trees

A Random Walks View of Spectral Segmentation.

Comparing Clusterings by the Variation of Information

Learning Segmentation by Random Walks