How many clusters? An information theoretic perspective

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scal...

A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the behavior of this method from a theoretical point of view. However, the results are very technical and difficult to interpret for non-experts. In this paper we give a high-level overview about the existing literature on clustering stability...

A combinatorial cost function for hierarchical clustering was introduced by Dasgupta \cite{dasgupta2016cost}. It has been generalized by Cohen-Addad et al. \cite{cohen2019hierarchical} to a general form named admissible function. In this paper, we investigate hierarchical clustering from the \emph{information-theoretic} perspective and formulate a new objective function. We also establish the relationship between these two perspectives. In algorithmic aspect, we get rid of th...

A major challenge when using k-means clustering often is how to choose the parameter k, the number of clusters. In this letter, we want to point out that it is very easy to draw poor conclusions from a common heuristic, the "elbow method". Better alternatives have been known in literature for a long time, and we want to draw attention to some of these easy to use options, that often perform better. This letter is a call to stop using the elbow method altogether, because it se...

We consider the problem of estimating the number of clusters ($k$) in a dataset. We propose a non-parametric approach to the problem that is based on maximizing a statistic constructed from similarity graphs. This graph-based statistic is a robust summary measure of the similarity information among observations and is applicable even if the number of dimensions or number of clusters is possibly large. The approach is straightforward to implement, computationally fast, and can...

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple $k$-means algorithm. $k$-means attempts to find an {\it optimal clustering} that minimizes the sum-of-square...

Currently, data-driven discovery in biological sciences resides in finding segmentation strategies in multivariate data that produce sensible descriptions of the data. Clustering is but one of several approaches and sometimes falls short because of difficulties in assessing reasonable cutoffs, the number of clusters that need to be formed or that an approach fails to preserve topological properties of the original system in its clustered form. In this work, we show how a simp...

Existing clustering algorithms such as K-means often need to preset parameters such as the number of categories K, and such parameters may lead to the failure to output objective and consistent clustering results. This paper introduces a clustering method based on the information theory, by which clusters in the clustering result have maximum average information entropy (called entropy payload in this paper). This method can bring the following benefits: firstly, this method ...

This technical report provides the supplementary material for a paper entitled "Information based clustering", to appear shortly in Proceedings of the National Academy of Sciences (USA). In Section I we present in detail the iterative clustering algorithm used in our experiments and in Section II we describe the validation scheme used to determine the statistical significance of our results. Then in subsequent sections we provide all the experimental results for three very di...

The information bottleneck (IB) approach to clustering takes a joint distribution $P\!\left(X,Y\right)$ and maps the data $X$ to cluster labels $T$ which retain maximal information about $Y$ (Tishby et al., 1999). This objective results in an algorithm that clusters data points based upon the similarity of their conditional distributions $P\!\left(Y\mid X\right)$. This is in contrast to classic "geometric clustering'' algorithms such as $k$-means and gaussian mixture models (...