Related papers: Quantizing Multiple Sources to a Common Cluster Ce…
It is often of interest to perform clustering on longitudinal data, yet it is difficult to formulate an intuitive model for which estimation is computationally feasible. We propose a model-based clustering method for clustering objects that…
In a two-stage cluster sampling procedure, $n$ random populations are drawn independently from independent populations and a sub-sample of observations is taken in each of them. The estimator of the general mean of the observed variables is…
We consider the problem of model-based clustering in the presence of many correlated, mixed continuous and discrete variables, some of which may have missing values. Discrete variables are treated with a latent continuous variable approach…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
Several methods have been proposed to estimate the number of clusters in a dataset; the basic ideal behind all of them has been to study an index that measures inter-cluster separation and intra-cluster cohesion over a range of cluster…
While an important topic in practice, the estimation of the number of non-noise components in blind source separation has received little attention in the literature. Recently, two bootstrap-based techniques for estimating the dimension…
Given a set of points $P \subset \mathbb{R}^d$, the $k$-means clustering problem is to find a set of $k$ {\em centers} $C = \{c_1,...,c_k\}, c_i \in \mathbb{R}^d,$ such that the objective function $\sum_{x \in P} d(x,C)^2$, where $d(x,C)$…
In multi-view clustering, different views may have different confidence levels when learning a consensus representation. Existing methods usually address this by assigning distinctive weights to different views. However, due to noisy nature…
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…
Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., $\textit{deep constrained clustering}$ (DCC) -- has proven effective for incorporating weak supervision into massive data…
A celebrated result of Pollard proves asymptotic consistency for $k$-means clustering when the population distribution has finite variance. In this work, we point out that the population-level $k$-means clustering problem is, in fact,…
We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two…
The widely applied density peak clustering (DPC) algorithm makes an intuitive cluster formation assumption that cluster centers are often surrounded by data points with lower local density and far away from other data points with higher…
We present LSD-C, a novel method to identify clusters in an unlabeled dataset. Our algorithm first establishes pairwise connections in the feature space between the samples of the minibatch based on a similarity metric. Then it regroups in…
A unified metric is given for the evaluation of object tracking systems. The metric is inspired by KL-divergence or relative entropy, which is commonly used to evaluate clustering techniques. Since tracking problems are fundamentally…
We address the problem of validating the ouput of clustering algorithms. Given data $\mathcal{D}$ and a partition $\mathcal{C}$ of these data into $K$ clusters, when can we say that the clusters obtained are correct or meaningful for the…
In this paper, the decades-old clustering method k-means is revisited. The original distortion minimization model of k-means is addressed by a pure stochastic minimization procedure. In each step of the iteration, one sample is tentatively…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…