Inference and Evaluation of the Multinomial Mixture Model for Text Clustering

In this article, we investigate the use of a probabilistic model for unsupervised clustering in text collections. Unsupervised clustering has become a basic module for many intelligent text processing applications, such as information retrieval, text classification or information extraction. The model considered in this contribution consists of a mixture of multinomial distributions over the word counts, each component corresponding to a different theme. We present and contrast various estimation procedures, which apply both in supervised and unsupervised contexts. In supervised learning, this work suggests a criterion for evaluating the posterior odds of new documents which is more statistically sound than the "naive Bayes" approach. In an unsupervised context, we propose measures to set up a systematic evaluation framework and start with examining the Expectation-Maximization (EM) algorithm as the basic tool for inference. We discuss the importance of initialization and the influence of other features such as the smoothing strategy or the size of the vocabulary, thereby illustrating the difficulties incurred by the high dimensionality of the parameter space. We also propose a heuristic algorithm based on iterative EM with vocabulary reduction to solve this problem. Using the fact that the latent variables can be analytically integrated out, we finally show that Gibbs sampling algorithm is tractable and compares favorably to the basic expectation maximization approach

A Survey on Soft Subspace Clustering

Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been extensively studied and well accepted by the scientific community, SSC algorithms are relatively new but gaining more attention in recent years due to better adaptability. In the paper, a comprehensive survey on existing SSC algorithms and the recent development are presented. The SSC algorithms are classified systematically into three main categories, namely, conventional SSC (CSSC), independent SSC (ISSC) and extended SSC (XSSC). The characteristics of these algorithms are highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201

Enrichment Procedures for Soft Clusters: A Statistical Test and its Applications

Clusters, typically mined by modeling locality of attribute spaces, are often evaluated for their ability to demonstrate ‘enrichment’ of categorical features. A cluster enrichment procedure evaluates the membership of a cluster for significant representation in pre-defined categories of interest. While classical enrichment procedures assume a hard clustering definition, in this paper we introduce a new statistical test that computes enrichments for soft clusters. We demonstrate an application of this test in refining and evaluating soft clusters for classification of remotely sensed images

A Short Survey on Data Clustering Algorithms

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial analysis. Formally speaking, given a set of data instances, a clustering algorithm is expected to divide the set of data instances into the subsets which maximize the intra-subset similarity and inter-subset dissimilarity, where a similarity measure is defined beforehand. In this work, the state-of-the-arts clustering algorithms are reviewed from design concept to methodology; Different clustering paradigms are discussed. Advanced clustering algorithms are also discussed. After that, the existing clustering evaluation metrics are reviewed. A summary with future insights is provided at the end

Variable selection for model-based clustering using the integrated complete-data likelihood

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty. However, the calibration of the penalty term can suffer from criticisms. Model selection methods are an efficient alternative, yet they require a difficult optimization of an information criterion which involves combinatorial problems. First, most of these optimization algorithms are based on a suboptimal procedure (e.g. stepwise method). Second, the algorithms are often greedy because they need multiple calls of EM algorithms. Here we propose to use a new information criterion based on the integrated complete-data likelihood. It does not require any estimate and its maximization is simple and computationally efficient. The original contribution of our approach is to perform the model selection without requiring any parameter estimation. Then, parameter inference is needed only for the unique selected model. This approach is used for the variable selection of a Gaussian mixture model with conditional independence assumption. The numerical experiments on simulated and benchmark datasets show that the proposed method often outperforms two classical approaches for variable selection.Comment: submitted to Statistics and Computin