Related papers: Improved Combinatorial Approximations for Weighted…

We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…

An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise…

We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…

The classic pivot based clustering algorithm of Ailon, Charikar and Chawla [JACM'08] is factor 3, but all concrete examples showing that it is no better than 3 are based on some very good clusters, e.g., a complete graph minus a matching.…

In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…

In the correlation clustering problem for complete signed graphs, the input is a complete signed graph with edges weighted as $+1$ (denote recommendation to put this pair in the same cluster) or $-1$ (recommending to put this pair of…

In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled)…

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…

We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

We present a massively parallel algorithm, with near-linear memory per machine, that computes a $(2+\varepsilon)$-approximation of minimum-weight vertex cover in $O(\log\log d)$ rounds, where $d$ is the average degree of the input graph.…

Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…

This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows…

We consider max-weighted matching with costs for learning the weights, modeled as a "Pandora's Box" on each endpoint of an edge. Each vertex has an initially-unknown value for being matched to a neighbor, and an algorithm must pay some cost…

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

Graph clustering problems typically aim to partition the graph nodes such that two nodes belong to the same partition set if and only if they are similar. Correlation Clustering is a graph clustering formulation which: (1) takes as input a…

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…

Many algorithms for approximate nearest neighbor search in high-dimensional spaces partition the data into clusters. At query time, in order to avoid exhaustive search, an index selects the few (or a single) clusters nearest to the query…

Correlation Clustering is a fundamental clustering problem, and there has been a line of work on improving the approximation ratio for this problem in recent years. A key algorithmic component in these works is the cluster LP. Chromatic…