Related papers: Subspace Clustering with Missing and Corrupted Dat…

This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…

Motivated by DNA-based storage, we study the noisy shuffling channel, which can be seen as the concatenation of a standard noisy channel (such as the BSC) and a shuffling channel, which breaks the data block into small pieces and shuffles…

There is an extensive set of methods to determine sparse sources from mixtures where the mixing coefficients are unknown. Each method involves plotting N sets of mixed data against each other in N-dimensional space. In the approach adopted…

This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise…

The measurement of the abundance of galaxy clusters in the Universe is a sensitive probe of cosmology, which depends on both the expansion history of the Universe and the growth of structure. Density fluctuations across the finite survey…

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces…

We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the model $X_i = z_i \theta +…

Missing datasets, in which some objects have missing values in certain dimensions, are prevalent in the Real-world. Existing clustering algorithms for missing datasets first impute the missing values and then perform clustering. However,…

We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data,…

A new submodule clustering method via sparse and low-rank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic…

In this paper, we propose a simple algorithm to cluster nonnegative data lying in disjoint subspaces. We analyze its performance in relation to a certain measure of correlation between said subspaces. We use our clustering algorithm to…

We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

Subspace clustering algorithms are used for understanding the cluster structure that explains the dataset well. These methods are extensively used for data-exploration tasks in various areas of Natural Sciences. However, most of these…

Source coding is the canonical problem of data compression in information theory. In a locally encodable source coding, each compressed bit depends on only few bits of the input. In this paper, we show that a recently popular model of…

Clustering is considered a non-supervised learning setting, in which the goal is to partition a collection of data points into disjoint clusters. Often a bound $k$ on the number of clusters is given or assumed by the practitioner. Many…

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…