Related papers: $k$-means as a variational EM approximation of Gau…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
We consider a generalization of $k$-median and $k$-center, called the {\em ordered $k$-median} problem. In this problem, we are given a metric space $(\mathcal{D},\{c_{ij}\})$ with $n=|\mathcal{D}|$ points, and a non-increasing weight…
A theoretical model for polydisperse systems of hard spheres is said to be truncatable when the excess free energy depends on the size distribution through a finite number $K$ of moments. This Note proves an exact scaling relation for…
The K-Means clustering using LLoyd's algorithm is an iterative approach to partition the given dataset into K different clusters. The algorithm assigns each point to the cluster based on the following objective function \[\ \min…
The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…
This paper investigates the model degrees of freedom in k-means clustering. An extension of Stein's lemma provides an expression for the effective degrees of freedom in the k-means model. Approximating the degrees of freedom in practice…
Given a data set of size $n$ in $d'$-dimensional Euclidean space, the $k$-means problem asks for a set of $k$ points (called centers) so that the sum of the $\ell_2^2$-distances between points of a given data set of size $n$ and the set of…
In this work, we aim to solve a practical use-case of unsupervised clustering which has applications in predictive maintenance in the energy operations sector using quantum computers. Using only cloud access to quantum computers, we…
We contrast a minimalistic implementation of quantum k-means algorithm to classical k-means algorithm. With classical simulation results, we demonstrate a quantum performance, on and above par, with the classical k-means algorithm. We…
This paper presents an algorithm to solve the Soft k-Means problem globally. Unlike Fuzzy c-Means, Soft k-Means (SkM) has a matrix factorization-type objective and has been shown to have a close relation with the popular probability…
We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. This resolves the main…
We propose the Lasso Weighted $k$-means ($LW$-$k$-means) algorithm as a simple yet efficient sparse clustering procedure for high-dimensional data where the number of features ($p$) can be much larger compared to the number of observations…
Recently, due to an increasing interest for transparency in artificial intelligence, several methods of explainable machine learning have been developed with the simultaneous goal of accuracy and interpretability by humans. In this paper,…
Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to…
We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved…
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…
Clustering data is a popular feature in the field of unsupervised machine learning. Most algorithms aim to find the best method to extract consistent clusters of data, but very few of them intend to cluster data that share the same…
Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…