相关论文: A notion of stability for k-means clustering

We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the…

K-means is an effective clustering technique used to separate similar data into groups based on initial centroids of clusters. In this paper, Normalization based K-means clustering algorithm(N-K means) is proposed. Proposed N-K means…

We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…

We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…

The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic system for distance based clustering algorithms that…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a…

Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful…

We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

Clustering is widely used for unsupervised structure discovery, yet it offers limited insight into how reliable each individual assignment is. Diagnostics, such as convergence behavior or objective values, may reflect global quality, but…

We study the classic $k$-median and $k$-means clustering objectives in the beyond-worst-case scenario. We consider three well-studied notions of structured data that aim at characterizing real-world inputs: Distribution Stability…

Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a…

We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based…

There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…

We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain…

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…

The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…