A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used.

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).

In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors in variables. As the previous mentioned papers, the algorithm mixes different tools from the inverse problem literature and the machine learning community. Coarsely, it is based on a two-step procedure: (1) a deconvolution step to deal with noisy inputs and (2) Newton's iterations as the popular k-means.

During the past decade, finite mixture modeling has become a well-established technique in data analysis and clustering. This paper focus on developing a variational inference framework to learn finite Beta-Liouville mixture models that have been proposed recently as an efficient way for proportional data clustering. In contrast to the conventional expectation maximization (EM) algorithm, commonly used for learning finite mixture models, the proposed algorithm has the advantages that it is more efficient from a computational point of view and by preventing over- and under-fitting problems. Moreover, the complexity of the mixture model (i.e. the number of components) can be determined automatically and simultaneously with the parameters estimation in a closed form as part of the Bayesian inference procedure. The merits of the proposed approach are shown using both artificial data sets and two interesting and challenging real applications namely dynamic textures clustering and facial expression recognition.

In past decade, more and more data are collected from multiple sources or represented by multiple views, where different views describe distinct perspectives of the data. Although each view could be individually used for finding patterns by clustering, the clustering performance could be more accurate by exploring the rich information among multiple views. Several multi-view clustering methods have been proposed to unsupervised integrate different views of data. However, they are graph based approaches, e.g. based on spectral clustering, such that they cannot handle the large-scale data. How to combine these heterogeneous features for unsupervised large-scale data clustering has become a challenging problem. In this paper, we propose a new robust large-scale multi-view clustering method to integrate heterogeneous representations of large-scale data. We evaluate the proposed new methods by six benchmark data sets and compared the performance with several commonly used clustering approaches as well as the baseline multi-view clustering methods. In all experimental results, our proposed methods consistently achieve superiors clustering performances.

Graph clustering has received growing attention in recent years as an important analytical technique, both due to the prevalence of graph data, and the usefulness of graph structures for exploiting intrinsic data characteristics.However, as graph data grows in scale, it becomes increasingly more challenging to identify clusters. In this paper we propose an efficient clustering algorithm for large-scale graph data using spectral methods. The key idea is to repeatedly generate a small number of "supernodes" connected to the regular nodes, in order to compress the original graph into a sparse bipartite graph. By clustering the bipartite graph using spectral methods, we are able to greatly improve efficiency without losing considerable clustering power. Extensive experiments show the effectiveness and efficiency of our approach.

Different solution approaches for combinatorial problems often exhibit incomparable performance that depends on the concrete problem instanceto be solved. Algorithm portfolios aim to combine the strengths of multiple algorithmic approaches by training a classifier that selects or schedules solvers dependent on the given instance. We devise a new classifier that selects solvers based on a cost-sensitive hierarchical clustering model. Experimental results on SAT and MaxSAT show that the new method outperforms the most effective portfolio builders to date.

Coalition formation is a fundamental approach to multi-agent coordination. In this paper we address the specific problem of coalition structure generation, and focus on providing good-enough solutions using a novel heuristic approach that is based on data clustering methods. In particular, we propose a hierarchical agglomerative clustering approach (C-Link), which uses a similarity criterion between coalitions based on the gain that the system achieves if two coalitions merge. We empirically evaluate C-Link on a synthetic benchmark data-set as well as in collective energy purchasing settings. Our results show that the C-link approach performs very well against an optimal benchmark based on Mixed-Integer Programming, achieving solutions which are in the worst case about 80% of the optimal (in the synthetic data-set), and 98% of the optimal (in the energy data-set). Thus we show that C-Link can return solutions for problems involving thousands of agents within minutes.

The level set tree approach of Hartigan (1975) provides a probabilistically based and highly interpretable encoding of the clustering behavior of a dataset. By representing the hierarchy of data modes as a dendrogram of the level sets of a density estimator, this approach offers many advantages for exploratory analysis and clustering, especially for complex and high-dimensional data. Several R packages exist for level set tree estimation, but their practical usefulness is limited by computational inefficiency, absence of interactive graphical capabilities and, from a theoretical perspective, reliance on asymptotic approximations. To make it easier for practitioners to capture the advantages of level set trees, we have written the Python package DeBaCl for DEnsity-BAsed CLustering. In this article we illustrate how DeBaCl's level set tree estimates can be used for difficult clustering tasks and interactive graphical data analysis. The package is intended to promote the practical use of level set trees through improvements in computational efficiency and a high degree of user customization. In addition, the flexible algorithms implemented in DeBaCl enjoy finite sample accuracy, as demonstrated in recent literature on density clustering. Finally, we show the level set tree framework can be easily extended to deal with functional data.

In this paper we investigate the problem of estimating the cluster tree for a density $f$ supported on or near a smooth $d$-dimensional manifold $M$ isometrically embedded in $\mathbb{R}^D$. We analyze a modified version of a $k$-nearest neighbor based algorithm recently proposed by Chaudhuri and Dasgupta. The main results of this paper show that under mild assumptions on $f$ and $M$, we obtain rates of convergence that depend on $d$ only but not on the ambient dimension $D$. We also show that similar (albeit non-algorithmic) results can be obtained for kernel density estimators. We sketch a construction of a sample complexity lower bound instance for a natural class of manifold oblivious clustering algorithms. We further briefly consider the known manifold case and show that in this case a spatially adaptive algorithm achieves better rates.