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

Labeling the Features Not the Samples: Efficient Video Classification with Minimal Supervision

Feature selection is essential for effective visual recognition. We propose an efficient joint classifier learning and feature selection method that discovers sparse, compact representations of input features from a vast sea of candidates, with an almost unsupervised formulation. Our method requires only the following knowledge, which we call the \emph{feature sign}---whether or not a particular feature has on average stronger values over positive samples than over negatives. We show how this can be estimated using as few as a single labeled training sample per class. Then, using these feature signs, we extend an initial supervised learning problem into an (almost) unsupervised clustering formulation that can incorporate new data without requiring ground truth labels. Our method works both as a feature selection mechanism and as a fully competitive classifier. It has important properties, low computational cost and excellent accuracy, especially in difficult cases of very limited training data. We experiment on large-scale recognition in video and show superior speed and performance to established feature selection approaches such as AdaBoost, Lasso, greedy forward-backward selection, and powerful classifiers such as SVM.Comment: arXiv admin note: text overlap with arXiv:1411.771

Multiclass latent locally linear support vector machines

Kernelized Support Vector Machines (SVM) have gained the status of off-the-shelf classifiers, able to deliver state of the art performance on almost any problem. Still, their practical use is constrained by their computational and memory complexity, which grows super-linearly with the number of training samples. In order to retain the low training and testing complexity of linear classifiers and the exibility of non linear ones, a growing, promising alternative is represented by methods that learn non-linear classifiers through local combinations of linear ones. In this paper we propose a new multi class local classifier, based on a latent SVM formulation. The proposed classifier makes use of a set of linear models that are linearly combined using sample and class specific weights. Thanks to the latent formulation, the combination coefficients are modeled as latent variables. We allow soft combinations and we provide a closed-form solution for their estimation, resulting in an efficient prediction rule. This novel formulation allows to learn in a principled way the sample specific weights and the linear classifiers, in a unique optimization problem, using a CCCP optimization procedure. Extensive experiments on ten standard UCI machine learning datasets, one large binary dataset, three character and digit recognition databases, and a visual place categorization dataset show the power of the proposed approach