Particle swarm diagonalization of fourth order cumulants tensor for estimation of least dependent components

Least dependent components estimation is the main goal in many independent component analysis (ICA) techniques, such as ICA-JADE [1] and MILCA [2]. Extraction of information theoretically independent source vectors from signal mixtures matrix is the target of these techniques. An important chemical application of such techniques is in unsupervised clustering. In ICA-JADE, the applied criteria for showing independence of components are elements of fourth order cumulants tensor (FCT), which is a crucial subject in higher order statistics (HOC). Variance and covariance are the second order cumulants, and kurtosis is a sort of fourth order cumulant. Diagonalized FCT for a set of profiles shows their information based independence. Particle swarm optimization (PSO) belongs to the strong family of global optimization techniques, inspired by the social behavior of animals [3]. In PSO a swarm of particles flow in parameters space through pathways which are driven by their own and neighbors best performances. The proposed method is based on orthogonal rotation of whitened data (orthonormal and uncorrelated) or non-whitened data into the least dependent profiles. The angles of rotations in all possible direction of space are optimized by PSO to obtain super-diagonalized FCT. The method was successfully applied for clustering of ink samples using NIR spectra. The main advantage of the proposed PSO technique is flexibility in using different objective functions in place or in addition to FCT.