Related papers: Simplicial clustering using the $\alpha$--transfor…
We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on $k$-means clustering and…
Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…
In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a classification problem, this transformation induces complete separation among the associated Gaussian…
"Clustering" the significance and application of this technique is spread over various fields. Clustering is an unsupervised process in data mining, that is why the proper evaluation of the results and measuring the compactness and…
Data clustering is a technique for clustering set of objects into known number of groups. Several approaches are widely applied to data clustering so that objects within the clusters are similar and objects in different clusters are far…
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of,…
High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…
We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…
The clustering algorithms that view each object data as a single sample drawn from a certain distribution, Gaussian distribution, for example, has been a hot topic for decades. Many clustering algorithms: such as k-means and spectral…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…
We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…
In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
Estimating the number of clusters (K) is a critical and often difficult task in cluster analysis. Many methods have been proposed to estimate K, including some top performers using resampling approach. When performing cluster analysis in…
We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The…
We present a technique for clustering categorical data by generating many dissimilarity matrices and averaging over them. We begin by demonstrating our technique on low dimensional categorical data and comparing it to several other…
The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…
The incremental K-means clustering algorithm has already been proposed and analysed in paper [Chakraborty and Nagwani, 2011]. It is a very innovative approach which is applicable in periodically incremental environment and dealing with a…
Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses.…
Clustering of data points is a fundamental tool in data analysis. We consider points $X$ in a relaxed metric space, where the triangle inequality holds within a constant factor. The {\em cost} of clustering $X$ by $Q$ is $V(Q)=\sum_{x\in X}…