Modern data acquisition routinely produces massive amounts of high dimensional data with complex statistical dependency structures. Latent variable graphical models provide a succinct representation of such complex dependency structures by relating the observed variables to a set of latent ones. By defining a joint distribution over observed and latent variables, the marginal distribution of the observed variables can be obtained by integrating out the latent ones. This allows complex distributions over observed variables (e.g., clique models) to be expressed in terms of more tractable joint models (e.g., tree models) over the augmented variable space. Probabilistic graphical models with latent variables have been deployed successfully to a diverse range of problems such as in document analysis (Blei et al., 2002), social network modeling (Hoff et al., 2002), speech recognition (Rabiner and Juang, 1986) and bioinformatics (Clark, 1990). In this paper, we focus on latent variable models where the latent structures are trees (we call it a "latent tree" for short).

ABSTRACT This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller variation compared to the original data and can be evaluated in a simple proposed unimodality test. Compared with the existing unimodality tests, Sigtest is more accurate in detecting the overlapped clusters and has a much less computational complexity. Simulation results demonstrate the efficiency of this statistic test for both real and synthetic data sets.

This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM, and provides a hard clustering with convergence guarantees similar to those of the k-means algorithm. Empirical results from a synthetic test with moving Gaussian clusters and a test with real ADS-B aircraft trajectory data demonstrate that the algorithm requires orders of magnitude less computational time than contemporary probabilistic and hard clustering algorithms, while providing higher accuracy on the examined datasets.

While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings are not well-understood. In this paper, we provide precise information theoretic bounds on the clustering accuracy and sample complexity of learning a mixture of two isotropic Gaussians in high dimensions under small mean separation. If there is a sparse subset of relevant dimensions that determine the mean separation, then the sample complexity only depends on the number of relevant dimensions and mean separation, and can be achieved by a simple computationally efficient procedure. Our results provide the first step of a theoretical basis for recent methods that combine feature selection and clustering.

Research on distributed machine learning algorithms has focused primarily on one of two extremes---algorithms that obey strict concurrency constraints or algorithms that obey few or no such constraints. We consider an intermediate alternative in which algorithms optimistically assume that conflicts are unlikely and if conflicts do arise a conflict-resolution protocol is invoked. We view this optimistic concurrency control'' paradigm as particularly appropriate for large-scale machine learning algorithms, particularly in the unsupervised setting. We demonstrate our approach in three problem areas: clustering, feature learning and online facility location. We evaluate our methods via large-scale experiments in a cluster computing environment. "

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. and Amini et al. proposed variations on the algorithm that artificially inflate the node degrees for improved statistical performance. The current paper extends the previous theoretical results to the more canonical spectral clustering algorithm in a way that removes any assumption on the minimum degree and provides guidance on the choice of tuning parameter. Moreover, our results show how the star shape" in the eigenvectors--which are consistently observed in empirical networks--can be explained by the Degree-Corrected Stochastic Blockmodel and the Extended Planted Partition model, two statistical model that allow for highly heterogeneous degrees. Throughout, the paper characterizes and justifies several of the variations of the spectral clustering algorithm in terms of these models. "

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 study a $k$-nearest neighbor based algorithm recently proposed by Chaudhuri and Dasgupta. 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 provide a sample complexity lower bound for a natural class of clustering algorithms that use $D$-dimensional neighborhoods.

Determinantal Point Process (DPP) has gained much popularity for modeling sets of diverse items. The gist of DPP is that the probability of choosing a particular set of items is proportional to the determinant of a positive definite matrix that defines thesimilarity of those items. However, computing the determinant requires time cubic in the number of items, and is hence impractical for large sets. In this paper, we address this problem by constructing a rapidly mixing Markov chain, from which we can acquire a sample from the given DPP in sub-cubic time. In addition, weshow that this framework can be extended to sampling from cardinalityconstrained DPPs.As an application, we show how our sampling algorithm can be used to provide a fast heuristic for determining the number of clusters, resulting in better clustering. There are some crucial errors in the proofs of the theorem which invalidate the theoretical claims of this paper. Please consult the appendix for more details.

This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following a classic approach in clustering by [13], we reduce the problem of finding a clustering with low cost to the problem of finding a coreset of small size. We provide a distributed method for constructing a global coreset which improves over the previous methods by reducing the communication complexity, and which works over general communication topologies. Experimental results on large scale data sets show that this approach outperforms other coreset-based distributed clustering algorithms.

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclass total variation clustering that does not rely on recursion. The results greatly outperform previous total variation algorithms and compare well with state-of-the-art NMF approaches.