Related papers: A Probabilistic $\ell_1$ Method for Clustering Hig…

The adoption of probabilistic models for the best individuals found so far is a powerful approach for evolutionary computation. Increasingly more complex models have been used by estimation of distribution algorithms (EDAs), which often…

Given an arbitrary set of high dimensional points in $\ell_1$, there are known negative results that preclude the possibility of always mapping them to a low dimensional $\ell_1$ space while preserving distances with small multiplicative…

The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…

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…

Clustering is one of the major tasks in data mining. In the last few years, Clustering of spatial data has received a lot of research attention. Spatial databases are components of many advanced information systems like geographic…

In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the…

We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high…

Clustering high-dimensional data is a critical challenge in machine learning due to the curse of dimensionality and the presence of noise. Traditional clustering algorithms often fail to capture the intrinsic structures in such data. This…

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…

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…

One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…

Existing clustering methods are based on a single granularity of information, such as the distance and density of each data. This most fine-grained based approach is usually inefficient and susceptible to noise. Inspired by adaptive process…

We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…

Big Data is a massive volume of both structured and unstructured data that is too large and it also difficult to process using traditional techniques. Clustering algorithms have developed as a powerful learning tool that can exactly analyze…

Kleinberg's axioms for distance based clustering proved to be contradictory. Various efforts have been made to overcome this problem. Here we make an attempt to handle the issue by embedding in high-dimensional space and granting wide gaps…

We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While feature selection is one of the most common approaches to reduce dimensionality in practice, most of the known…

In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…