A comprehensive methodology for classification-oriented non-supervised analysis through the use of spectral techniques is presented here. This methodology includes a non-supervised clustering stage developed under the multiway criterion of normalized partitions. This technique is preferred because it does not require an additional clustering algorithm. Additionally, it results in a suitable partition, since it considers the information obtained from a solution of one’s own. Besides, adequate affinity measurements are applied, and the number of clusters is automatically estimated in order to reduce processing time and improve algorithm convergence. Experimental results are obtained on an image database. The quality of the cluster is measured by means of segmentation results. Also, a non-supervised performance measurement was introduced.
Spectral clustering has represented a good alternative in digital signal processing and pattern recognition; however a decision concerning the affinity functions among data is still an issue. In this work it is presented an extended version of a traditional multiclass spectral clustering method which employs prior information about the classified data into the affinity matrixes aiming to maintain the background relation that might be lost in the traditional manner, that is using a scaled exponential affinity matrix constrained by weighting the data according to some prior knowledge and via k-way normalized cuts clustering, results in a semi-supervised methodology of traditional spectral clustering. Test was performed over toy data classification and image segmentation and evaluated with and unsupervised performance measures (group coherence, fisher criteria and silhouette).
In this paper we propose a kernel spectral clustering-based technique to catch the different regimes experienced by a time-varying system. Our method is based on a multtiple kernel learning approach, which is a linear combination of kernels. The calculation of the linear combination coefficients is done by determining a ranking vector that quantifies the overall dynamical behavior of the analyzed data sequence over-time. This vector can be calculated from the eigenvectors provided by the the solution of the kernel spectral clustering problem. We apply the proposed technique to a trial from the Graphics Lab Motion Capture Database from Carnegie Mellon University, as well as to a synthetic example, namely three moving Gaussian clouds. For comparison purposes, some conventional spectral clustering techniques are also considered, namely, kernel k- means and min-cuts. Also, standard k-means. The normalized mutual information and adjusted random index metrics are used to quantify the clustering performance. Results show the usefulness of proposed technique to track dynamic data, even being able to detect hidden objects.
Normalized-cut clustering (NCC) is a benchmark graph-based approach for unsupervised data analysis. Since its traditional formulation is a quadratic form subject to orthogonality conditions, it is often solved within an eigenvector-based framework. Nonetheless, in some cases the calculation of eigenvectors is prohibitive or unfeasible due to the involved computational cost – for instance, when dealing with high dimensional data. In this work, we present an overview of recent developments on approaches to solve the NCC problem with no requiring the calculation of eigenvectors. Particularly, heuristic-search and quadratic-formulation-based approaches are studied. Such approaches are elegantly deduced and explained, as well as simple ways to implement them are provided.
The analysis of dynamic or time-varying data has emerged as an issue of great interest taking increasingly an important place in scientific community, especially in automation, pattern recognition and machine learning. There exists a broad range of important applications such as video analysis, motion identification, segmentation of human motion and airplane tracking, among others. Spectral matrix analysis is one of the approaches to address this issue. Spectral techniques, mainly those based on kernels, have proved to be a suitable tool in several aspects of interest in pattern recognition and machine learning even when data are time-varying, such as the estimation of the number of clusters, clustering and classification. Most of spectral clustering approaches have been designed for analyzing static data, discarding the temporal information, i.e. the evolutionary behavior along time. Some works have been developed to deal with the time varying effect. Nonetheless, an approach able to accurately track and cluster time-varying data in real time applications remains an open issue. This thesis describes the design of a kernel-based dynamic spectral clustering using a primaldual approach so as to carry out the grouping task involving the dynamic information, that is to say, the changes of data frames along time. To this end, a dynamic kernel framework aimed to extend a clustering primal formulation to dynamic data analysis is introduced. Such framework is founded on a multiple kernel learning (MKL) approach. Proposed clustering approach, named dynamic kernel spectral clustering (DKSC) uses a linear combination of kernels matrices as a MKL model. Kernel matrices are computed from an input frame sequence represented by data matrices. Then, a cumulative kernel is obtained, being the model coefficients or weighting factors obtained by ranking each sample contained in the frame. Such ranking corresponds to a novel tracking approach that takes advantages of the spectral decomposition of a generalized kernel matrix. Finally, to get the resultant cluster assignments, data are clustered using the cumulative kernel matrix. Experiments are done over real databases (human motion and moon covered by clouds) as well as artificial data (moving-Gaussian clouds). As a main result, proposed spectral clustering method for dynamic data proved to be able for grouping underlying events and movements and detecting hidden objects as well. The proposed approach may represent a contribution to the pattern recognition field, mainly, for solving problems involving dynamic information aimed to either tracking or clustering of data.