Related papers: Statistical Properties of Convex Clustering
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…
The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that…
The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to…
In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…
In many applications of X-ray computed tomography, an unsupervised segmentation of the reconstructed 3D volumes forms an important step in the image processing chain for further investigation of the digitized object. Therefore, the goal is…
Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…
Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and…
Vibration-based condition monitoring systems are receiving increasing attention due to their ability to accurately identify different conditions by capturing dynamic features over a broad frequency range. However, there is little research…
We analyze online \cite{BottouBengio} and mini-batch \cite{Sculley} $k$-means variants. Both scale up the widely used $k$-means algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
In this paper a novel possibilistic c-means clustering algorithm, called Adaptive Possibilistic c-means, is presented. Its main feature is that {\it all} its parameters, after their initialization, are properly adapted during its execution.…
We propose a novel methodology for feature screening in clustering massive datasets, in which both the number of features and the number of observations can potentially be very large. Taking advantage of a fusion penalization based convex…
We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local…
Cognitive diagnosis models (CDMs) are a popular tool for assessing students' mastery of sets of skills. Given a set of $K$ skills tested on an assessment, students are classified into one of $2^K$ latent skill set profiles that represent…
This paper builds the clustering model of measures of market microstructure features which are popular in predicting stock returns. In a 10-second time-frequency, we study the clustering structure of different measures to find out the best…
There are many cluster analysis methods that can produce quite different clusterings on the same dataset. Cluster validation is about the evaluation of the quality of a clustering; "relative cluster validation" is about using such criteria…