We present an extension of convex-hull nonnegative matrix factorization (CH-NMF) which was recently proposed as a large scale variant of convex non-negative matrix factorization (CNMF) or Archetypal Analysis (AA). CH-NMF factorizes a non-negative data matrix V into two non-negative matrix factors V ≈ WH such that the columns of W are convex combinations of certain data points so that they are r...

As a novel clustering algorithm, spectral clustering is applied in machine learning extensively. Spectral clustering is built upon spectral graph theory, and has the ability to process the clustering of non-convex sample spaces. Most of the existing spectral clustering algorithms are based on k-means algorithm, and k-means algorithm uses the iterative optimization method to find the optimal sol...

We study the convex relaxation of clustering and hamming embedding, focusing on the asymmetric case (co-clustering and asymmetric hamming embedding), understanding their relationship to LSH as studied by [7] and to the max-norm ball, and the differences between their symmetric and asymmetric versions.

The Graph-based Convex Clustering (GCC) method has gained increasing attention recently. The GCC method adopts a fused regularizer to learn the cluster centers and obtains a geometric clusterpath by varying the regularization parameter. One major limitation is that solving the GCC model is computationally expensive. In this paper, we develop efficient graph reduction techniques for the GCC mode...

Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a signifi...

Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a signifi...

This paper considers the problem of clustering a partially observed unweighted graph—i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint clusters so that there is relatively dense (observed) connectivity within cluster...

ℓ 1-graph [19, 4], a sparse graph built by reconstructing each datum with all the other data using sparse representation , has been demonstrated to be effective in clustering high dimensional data and recovering independent subspaces from which the data are drawn. It is well known that ℓ 1-norm used in ℓ 1-graph is a convex relaxation of ℓ 0-norm for enforcing the sparsity. In order to handle g...

Robbins’s visionary 1951 paper can be seen as an exercise in binary classification, but also as a precursor to the outpouring of recent work on high-dimensional data analysis and multiple testing. It can also be seen as the birth of empirical Bayes methods. Our objective in the present note is to use this problem and several variants of it to provide a glimpse into the evolution of empirical Ba...

In this paper, we propose clustering methods for use on data described as tropically convex. Our approach is similar to used in the Euclidean space, where identify groupings of observations using tropical analogs K-means and hierarchical space. We provide results from computational experiments generic simulated well an application phylogeny ultrametrics, demonstrating efficacy these methods.