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

Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space. However, so far, the emphasis has been on batch techniques. It is only recently, that online techniques have been considered in the context of adaptive signal processing tasks. Moreover, these efforts have only been focussed on real valued data sequences. To the best of our knowledge, no adaptive kernel-based strategy has been developed, so far, for complex valued signals. Furthermore, although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications that deal with complex signals, with Communications being a typical example. In this paper, we present a general framework to attack the problem of adaptive filtering of complex signals, using either real reproducing kernels, taking advantage of a technique called \textit{complexification} of real RKHSs, or complex reproducing kernels, highlighting the use of the complex gaussian kernel. In order to derive gradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool of Wirtinger's Calculus, which has recently attracted attention in the signal processing community. To this end, in this paper, the notion of Wirtinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS offers significant performance improvements over several linear and nonlinear algorithms, when dealing with nonlinearities.Comment: 15 pages (double column), preprint of article accepted in IEEE Trans. Sig. Pro

Challenges and opportunities in machine learning for geometry

Over the past few decades, the mathematical community has accumulated a significant amount of pure mathematical data, which has been analyzed through supervised, semi-supervised, and unsupervised machine learning techniques with remarkable results, e.g., artificial neural networks, support vector machines, and principal component analysis. Therefore, we consider as disruptive the use of machine learning algorithms to study mathematical structures, enabling the formulation of conjectures via numerical algorithms. In this paper, we review the latest applications of machine learning in the field of geometry. Artificial intelligence can help in mathematical problem solving, and we predict a blossoming of machine learning applications during the next years in the field of geometry. As a contribution, we propose a new method for extracting geometric information from the point cloud and reconstruct a 2D or a 3D model, based on the novel concept of generalized asymptotes.Agencia Estatal de Investigació

Dimensionality Reduction, Classification and Reconstruction Problems in Statistical Learning Approaches

Statistical learning theory explores ways of estimating functional dependency from a given collection of data. The specific sub-area of supervised statistical learning covers important models like Perceptron, Support Vector Machines (SVM) and Linear Discriminant Analysis (LDA). In this paper we review the theory of such models and compare their separating hypersurfaces for extracting group-differences between samples. Classification and reconstruction are the main goals of this comparison. We show recent advances in this topic of research illustrating their application on face and medical image databases.Statistical learning theory explores ways of estimating functional dependency from a given collection of data. The specific sub-area of supervised statistical learning covers important models like Perceptron, Support Vector Machines (SVM) and Linear Discriminant Analysis (LDA). In this paper we review the theory of such models and compare their separating hypersurfaces for extracting group-differences between samples. Classification and reconstruction are the main goals of this comparison. We show recent advances in this topic of research illustrating their application on face and medical image databases

Misogyny Detection in Social Media on the Twitter Platform

The thesis is devoted to the problem of misogyny detection in social media. In the work we analyse the difference between all offensive language and misogyny language in social media, and review the best existing approaches to detect offensive and misogynistic language, which are based on classical machine learning and neural networks. We also review recent shared tasks aimed to detect misogyny in social media, several of which we have participated in. We propose an approach to the detection and classification of misogyny in texts, based on the construction of an ensemble of models of classical machine learning: Logistic Regression, Naive Bayes, Support Vectors Machines. Also, at the preprocessing stage we used some linguistic features, and novel approaches which allow us to improve the quality of classification. We tested the model on the real datasets both English and multilingual corpora. The results we achieved with our model are highly competitive in this area and demonstrate the capability for future improvement