Related papers: Consistency of Lloyd's Algorithm Under Perturbatio…
High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant…
The seminal paper by Mazumdar and Saha \cite{MS17a} introduced an extensive line of work on clustering with noisy queries. Yet, despite significant progress on the problem, the proposed methods depend crucially on knowing the exact…
We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal…
Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…
We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of $O(n\log{n})$-bit input per node can be solved in roughly $n$ rounds, where $n$ is the size…
Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…
Clustering scientific publications can reveal underlying research structures within bibliographic databases. Graph-based clustering methods, such as spectral, Louvain, and Leiden algorithms, are frequently utilized due to their capacity to…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Subspace clustering becomes inherently difficult near intersections, where points from different subspaces are barely separated. Most existing theoretical results address this issue by imposing separation or sampling assumptions that limit…
We establish the pointwise convergence of the iterative Lloyd algorithm, also known as $k$-means algorithm, when the quadratic quantization error of the starting grid (with size $N\ge 2$) is lower than the minimal quantization error with…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…
Due to the massive size of modern network data, local algorithms that run in sublinear time for analyzing the cluster structure of the graph are receiving growing interest. Two typical examples are local graph clustering algorithms that…
We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…
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…
Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier…
We propose a new analysis framework for clustering $M$ items into an unknown number of $K$ distinct groups using noisy and actively collected responses. At each time step, an agent is allowed to query pairs of items and observe bandit…