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In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…

Machine Learning · Statistics 2009-09-15 Ery Arias-Castro

A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…

Methodology · Statistics 2022-02-15 Soumita Modak

The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a…

Machine Learning · Statistics 2017-03-16 Dinh Phung , Ba-Ngu Bo

Clustering is a technique for the analysis of datasets obtained by empirical studies in several disciplines with a major application for biomedical research. Essentially, clustering algorithms are executed by machines aiming at finding…

Quantitative Methods · Quantitative Biology 2024-09-30 Diego Ulisse Pizzagalli , Santiago Fernandez Gonzalez , Rolf Krause

Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii)…

Methodology · Statistics 2015-12-23 Yen-Chi Chen , Christopher R. Genovese , Larry Wasserman

A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the…

Machine Learning · Computer Science 2022-10-18 Soumita Modak

Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…

Statistics Theory · Mathematics 2016-08-16 Charles Bouveyron , Stéphane Girard , Cordelia Schmid

Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…

Machine Learning · Computer Science 2018-03-06 Sohil Atul Shah , Vladlen Koltun

Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…

Databases · Computer Science 2012-03-20 Saptarsi Goswami , Amlan Chakrabarti

Urban structure detection is a basic task in urban geography. Clustering is a core technology to detect the patterns of urban spatial structure, urban functional region, and so on. In big data era, diverse urban sensing datasets recording…

Social and Information Networks · Computer Science 2017-07-13 Xin Lin , Haifeng Li , Yan Zhang , Lei Gao , Ling Zhao , Min Deng

We propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure. Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact…

Statistics Theory · Mathematics 2022-09-09 Bo Zhang , Guangming Pan , Qiwei Yao , Wang Zhou

Clustering is a widely used technique in data mining applications for discovering patterns in underlying data. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes.…

Artificial Intelligence · Computer Science 2007-05-23 Zengyou He , Xiaofei Xu , Shengchun Deng

Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…

Machine Learning · Computer Science 2014-08-26 Sibei Yang , Liangde Tao , Bingchen Gong

Clustering of motion trajectories is highly relevant for human-robot interactions as it allows the anticipation of human motions, fast reaction to those, as well as the recognition of explicit gestures. Further, it allows automated analysis…

Robotics · Computer Science 2024-04-29 Christoph Zelch , Jan Peters , Oskar von Stryk

It is often of interest to perform clustering on longitudinal data, yet it is difficult to formulate an intuitive model for which estimation is computationally feasible. We propose a model-based clustering method for clustering objects that…

Methodology · Statistics 2020-05-19 Daniel K. Sewell , Yuguo Chen , William Bernhard , Tracy Sulkin

Cluster analysis which focuses on the grouping and categorization of similar elements is widely used in various fields of research. Inspired by the phenomenon of atomic fission, a novel density-based clustering algorithm is proposed in this…

Machine Learning · Computer Science 2020-04-28 Shizhan Lu

In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…

Computer Vision and Pattern Recognition · Computer Science 2022-07-22 William F. Basener , Alexey Castrodad , David Messinger , Jennifer Mahle , Paul Prue

High-dimensional clustering often relies on geometric or local-similarity structure, but the dominant separation between groups may not always be location-based. Differences in dispersion can create asymmetric local-neighborhood patterns:…

Methodology · Statistics 2026-05-15 Hao Chen , Xiancheng Lin

Clustering is a common technique for statistical data analysis, Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another, but are very…

Machine Learning · Computer Science 2012-03-12 T Soni Madhulatha

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…

Computer Vision and Pattern Recognition · Computer Science 2023-03-09 Thomas Lang