K-means clustering algorithm is a method of cluster analysis which aims to partition n observations into clusters in which each observation belongs to the cluster with the nearest mean. It is one of the simplest unconfirmed learning algorithms that solve the well known clustering problem. It is similar to the hope maximization algorithm for mixtures of Gaussians in that they both attempt to fin...

In clique tree clustering, inference consists of propagation in a clique tree compiled from a Bayesian network. In this paper, we develop an analytical approach to characterizing clique tree growth as a function of increasing Bayesian network connectedness, speci cally: (i) the expected number of moral edges in their moral graphs or (ii) the ratio of the number of non-root nodes to the number o...

Finding the “right” number of clusters, Ic, for a data set is a difficult, and often ill-posed, problem. In a probabilistic clustering context, likelihood-ratios, penalized likelihoods, and Bayesian techniques are among the more popular techniques. In this paper a new cross-validated likelihood criterion is investigated for determining cluster structure. A practical clustering algorithm based o...

We present an online video segmentation algorithm based on a novel nonparametric Bayesian clustering method called Bayesian Split-Merge Clustering (BSMC). BSMC can efficiently cluster dynamically changing data through split and merge processes at each time step, where the decision for splitting and merging is made by approximate posterior distributions over partitions with Dirichlet Process (DP...

This article presents and analyzes algorithms that systematically generate random Bayesian networks of varying difficulty levels, with respect to inference using tree clustering. The results are relevant to research on efficient Bayesian network inference, such as computing a most probable explanation or belief updating, since they allow controlled experimentation to determine the impact of imp...

The problem of inferring a clustering of a data set has been the subject of much research in Bayesian analysis, and there currently exists a solid mathematical foundation for Bayesian approaches to clustering. In particular, the class of probability distributions over partitions of a data set has been characterized in a number of ways, including via exchangeable partition probability functions ...

Recently, semi-supervised spectral clustering algorithms have been developing rapidly, which are proposed to improve the clustering performance. In this paper, we first review the current existing spectral clustering algorithms in an unified-framework and give a straightforward explanation about the spectral clustering algorithm. Then, we present a semi-supervised method to improve the clusteri...

Bayesian hierarchical clustering (BHC) is an agglomerative clustering method, where a probabilistic model is defined and its marginal likelihoods are evaluated to decide which clusters to merge. While BHC provides a few advantages over traditional distance-based agglomerative clustering algorithms, successive evaluation of marginal likelihoods and careful hyperparameter tuning are cumbersome an...

We consider the problem of multiband image clustering and segmentation. We propose a new methodology for doing this, called modelbased cluster trees. This is grounded in model-based clustering, which bases inference on finite mixture models estimated by maximum likelihood using the EM algorithm, and automatically chooses the number of clusters by Bayesian model selection, approximated using BIC...

1. Bayesian Statistical Method The Bayesian Motif Clustering (BMC) algorithm proposed in the main article is based on an explicit statistical model that describes the relationship between the observed motifs and the putative regulons (clusters) and a Markov chain Monte Carlo computational method. We describe first the general Bayesian inference procedure and then its detailed implementation for...