Related papers: Clustering Mixtures with Almost Optimal Separation…
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…
We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors facilitating…
Motivated by many applications, we study clustering with a faulty oracle. In this problem, there are $n$ items belonging to $k$ unknown clusters, and the algorithm is allowed to ask the oracle whether two items belong to the same cluster or…
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…
We present a new algorithm for clustering points in R^n. The key property of the algorithm is that it is affine-invariant, i.e., it produces the same partition for any affine transformation of the input. It has strong guarantees when the…
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…
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its…
Clustering is a pivotal challenge in unsupervised machine learning and is often investigated through the lens of mixture models. The optimal error rate for recovering cluster labels in Gaussian and sub-Gaussian mixture models involves ad…
Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…
Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…
We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
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…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
Among ensemble clustering methods, Evidence Accumulation Clustering is one of the simplest technics. In this approach, a co-association (CA) matrix representing the co-clustering frequency is built and then clustered to extract consensus…
Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…
Though mostly used as a clustering algorithm, k-means are originally designed as a quantization algorithm. Namely, it aims at providing a compression of a probability distribution with k points. Building upon [21, 33], we try to investigate…
Given an integer $k\geq1$ and a set $P$ of $n$ points in $\REAL^d$, the classic $k$-PCA (Principle Component Analysis) approximates the affine \emph{$k$-subspace mean} of $P$, which is the $k$-dimensional affine linear subspace that…
We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to…