Related papers: Distribution free optimality intervals for cluster…
Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
Inference in clustering is paramount to uncovering inherent group structure in data. Clustering methods which assess statistical significance have recently drawn attention owing to their importance for the identification of patterns in high…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
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…
We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly…
Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…
K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…
In this paper, a novel method to perform model-based clustering of time series is proposed. The procedure relies on two iterative steps: (i) K global forecasting models are fitted via pooling by considering the series pertaining to each…
We propose a new method for clustering based on the local minimization of the \gamma-divergence, which we call the spontaneous clustering. The greatest advantage of the proposed method is that it automatically detects the number of clusters…
We address general-shaped clustering problems under very weak parametric assumptions with a two-step hybrid robust clustering algorithm based on trimmed k-means and hierarchical agglomeration. The algorithm has low computational complexity…
The purpose of this paper is to improve the traditional K-means algorithm. In the traditional K mean clustering algorithm, the initial clustering centers are generated randomly in the data set. It is easy to fall into the local minimum…
Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…
This note introduces a novel clustering preserving transformation of cluster sets obtained from $k$-means algorithm. This transformation may be used to generate new labeled data{}sets from existent ones. It is more flexible that Kleinberg…
We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…
This paper deals with the clustering of univariate observations: given a set of observations coming from $K$ possible clusters, one has to estimate the cluster means. We propose an algorithm based on the minimization of the "KP" criterion…
This paper proposes a novel, nonparametric, interpoint distance-based measure to investigate whether there exist any groups in a set of given data, and if so then, how many groups are prevailing in total. It is a cluster accuracy index…
We study the canonical fair clustering problem where each cluster is constrained to have close to population-level representation of each group. Despite significant attention, the salient issue of having incomplete knowledge about the group…
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…
The paper presents a formula for the reclassification of multidimensional data points (columns of real numbers, "objects", "vectors", etc.). This formula describes the change in the total squared error caused by reclassification of data…