A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved

Asymmetric Spectral clustering

This report presents the mathematical foundation of the asymmetric spectral clustering approach given in the thesis of S.E. Atev (University of Wisconsin, 2011). This method, implemented in a companion R package AsymmetricClustering, is based on a Riemannian conjugate gradient algorithm to find a minimization problem based on an optimization problem involving unitary matrix

Segmentation of Dynamic PET Images with Kinetic Spectral Clustering

International audienceSegmentation is often required for the analysis of dynamic positron emission tomography (PET) images. However, noise and low spatial resolution make it a difficult task and several supervised and unsupervised methods have been proposed in the literature to perform the segmentation based on semi-automatic clustering of the time activity curves of voxels. In this paper we propose a new method based on spectral clustering that does not require any prior information on the shape of clusters in the space in which they are identified. In our approach, the p-dimensional data, where p is the number of time frames, is first mapped into a high dimensional space and then clustering is performed in a low-dimensional space of the Laplacian matrix. An estimation of the bounds for the scale parameter involved in the spectral clustering is derived. The method is assessed using dynamic brain PET images simulated with GATE and results on real images are presented. We demonstrate the usefulness of the method and its superior performance over three other clustering methods from the literature. The proposed approach appears as a promising pre-processing tool before parametric map calculation or ROI-based quantification tasks

Graph construction with condition-based weights for spectral clustering of hierarchical datasets

Most of the unsupervised machine learning algorithms focus on clustering the data based on similarity metrics, while ignoring other attributes, or perhaps other type of connections between the data points. In case of hierarchical datasets, groups of points (point-sets) can be defined according to the hierarchy system. Our goal was to develop such spectral clustering approach that preserves the structure of the dataset throughout the clustering procedure. The main contribution of this paper is a set of conditions for weighted graph construction used in spectral clustering. Following the requirements – given by the set of conditions – ensures that the hierarchical formation of the dataset remains unchanged, and therefore the clustering of data points imply the clustering of point-sets as well. The proposed spectral clustering algorithm was tested on three datasets, the results were compared to baseline methods and it can be concluded the algorithm with the proposed conditions always preserves the hierarchy structure