Related papers: Asymptotics for The $k$-means
Utilizing the sample size of a dataset, the random cluster model is employed in order to derive an estimate of the mean number of K-Means clusters to form during classification of a dataset.
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…
Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…
We study beyond worst case analysis for the $k$-means problem where the goal is to model typical instances of $k$-means arising in practice. Existing theoretical approaches provide guarantees under certain assumptions on the optimal…
There has been considerable work on improving popular clustering algorithm `K-means' in terms of mean squared error (MSE) and speed, both. However, most of the k-means variants tend to compute distance of each data point to each cluster…
Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…
There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results…
K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed…
Determining the number of clusters present in a dataset is an important problem in cluster analysis. Conventional clustering techniques generally assume this parameter to be provided up front. %user supplied. %Recently, robustness of any…
K-means is one of the most widely used algorithms for clustering in Data Mining applications, which attempts to minimize the sum of the square of the Euclidean distance of the points in the clusters from the respective means of the…
K-means clustering is widely used in psychological and psychometric research to identify profiles, subgroups, and potential typologies, yet its classical formulation does not test whether such groups exist as latent psychological…
We present a $k$-means-based clustering algorithm, which optimizes the mean square error, for given cluster sizes. A straightforward application is balanced clustering, where the sizes of each cluster are equal. In the $k$-means assignment…
This paper introduces a unified approach to cluster refinement and anomaly detection in datasets. We propose a novel algorithm that iteratively reduces the intra-cluster variance of N clusters until a global minimum is reached, yielding…
For some or all of the data instances a number of independent-world clustering issues suffer from incomplete data characterization due to losing or absent attributes. Typical clustering approaches cannot be applied directly to such data…
$k-$means Clustering requires as input the exact value of $k$, the number of clusters. Two challenges are open: (i) Is there a data-determined definition of $k$ which is provably correct and (ii) Is there a polynomial time algorithm to find…
The classical k-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of k-means to missing data, namely k-POD, uses only the observed…
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…
This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called $k$-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate…
Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning…
Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…