Related papers: Strong Consistency of Sparse K-means Clustering
This paper presents a comparative analysis of different optimization techniques for the K-means algorithm in the context of big data. K-means is a widely used clustering algorithm, but it can suffer from scalability issues when dealing with…
Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space…
We present a new clustering algorithm called k-means-u* which in many cases is able to significantly improve the clusterings found by k-means++, the current de-facto standard for clustering in Euclidean spaces. First we introduce the…
Manifold clustering, with its exceptional ability to capture complex data structures, holds a pivotal position in cluster analysis. However, existing methods often focus only on finding the optimal combination between K-means and manifold…
In this paper, we consider nonparametric clustering of $M$ independent and identically distributed (i.i.d.) data sequences generated from {\em unknown} distributions. The distributions of the $M$ data sequences belong to $K$ underlying…
The K-subspaces (KSS) method is a generalization of the K-means method for subspace clustering. In this work, we present local convergence analysis and a recovery guarantee for KSS, assuming data are generated by the semi-random union of…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…
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…
We study the problem of clustering $T$ trajectories of length $H$, each generated by one of K unknown ergodic Markov chains over a finite state space of size $S$. We derive an instance-dependent, high-probability lower bound on the…
We define the notion of a well-clusterable data set combining the point of view of the objective of $k$-means clustering algorithm (minimising the centric spread of data elements) and common sense (clusters shall be separated by gaps). We…
Clustering high-dimensional data is a critical challenge in machine learning due to the curse of dimensionality and the presence of noise. Traditional clustering algorithms often fail to capture the intrinsic structures in such data. This…
Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to…
Clustering can be defined as the process of assembling objects into a number of groups whose elements are similar to each other in some manner. As a technique that is used in many domains, such as face clustering, plant categorization,…
Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…
A recent literature in econometrics models unobserved cross-sectional heterogeneity in panel data by assigning each cross-sectional unit a one-dimensional, discrete latent type. Such models have been shown to allow estimation and inference…
We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high…
Most of the research on clustering ensemble focuses on designing practical consistency learning algorithms.To solve the problems that the quality of base clusters varies and the low-quality base clusters have an impact on the performance of…
In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…
In this paper, we give a conditional lower bound of $n^{\Omega(k)}$ on running time for the classic k-median and k-means clustering objectives (where n is the size of the input), even in low-dimensional Euclidean space of dimension four,…