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$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…

The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…

We study graph clustering in the Stochastic Block Model (SBM) in the presence of both large clusters and small, unrecoverable clusters. Previous convex relaxation approaches achieving exact recovery do not allow any small clusters of size…

Clustering-based Approximate Nearest Neighbor Search (ANNS) organizes a set of points into partitions, and searches only a few of them to find the nearest neighbors of a query. Despite its popularity, there are virtually no analytical tools…

We consider the problem of feature detection in the presence of clutter in spatial point processes. Classification methods have been developed in previous studies. Among these, Byers and Raftery (1998) models the observed Kth nearest…

We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…

Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there…

We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…

Commonly-used clustering algorithms usually find ellipsoidal, spherical or other regular-structured clusters, but are more challenged when the underlying groups lack formal structure or definition. Syncytial clustering is the name that we…

Identification of clusters of co-expressed genes in transcriptomic data is a difficult task. Most algorithms used for this purpose can be classified into two broad categories: distance-based or model-based approaches. Distance-based…

Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a…

We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this…

For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least…

We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…

We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…

$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…

We present a sequential Bayesian learning method for tracking non-stationary signal-to-noise ratios in LDPC codes using probabilistic graphical models. We represent the LDPC code as a cluster graph using a general purpose cluster graph…

In this paper, a new cooperation structure for spectrum sensing in cognitive radio networks is proposed which outperforms the existing commonly-used ones in terms of energy efficiency. The efficiency is achieved in the proposed design by…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

Clustering by fast search and find of density peaks (DPC) (Since, 2014) has been proven to be a promising clustering approach that efficiently discovers the centers of clusters by finding the density peaks. The accuracy of DPC depends on…