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.