Overlearning in marginal distribution-based ICA: analysis and solutions

The present paper is written as a word of caution, with users of independent component analysis (ICA) in mind, to overlearning phenomena that are often observed.\\ We consider two types of overlearning, typical to high-order statistics based ICA. These algorithms can be seen to maximise the negentropy of the source estimates. The first kind of overlearning results in the generation of spike-like signals, if there are not enough samples in the data or there is a considerable amount of noise present. It is argued that, if the data has power spectrum characterised by $1/f$ curve, we face a more severe problem, which cannot be solved inside the strict ICA model. This overlearning is better characterised by bumps instead of spikes. Both overlearning types are demonstrated in the case of artificial signals as well as magnetoencephalograms (MEG). Several methods are suggested to circumvent both types, either by making the estimation of the ICA model more robust or by including further modelling of the data

Proper Inner Product with Mean Displacement for Gaussian Noise Invariant ICA

Independent Component Analysis (ICA) is a classical method for Blind Source Separation (BSS). In this paper, we are interested in ICA in the presence of noise, i.e., the noisy ICA problem. Pseudo-Euclidean Gradient Iteration (PEGI) is a recent cumulant-based method that defines a pseudo Euclidean inner product to replace a quasi-whitening step in Gaussian noise invariant ICA. However, PEGI has two major limitations: 1) the pseudo Euclidean inner product is improper because it violates the positive definiteness of inner product; 2) the inner product matrix is orthogonal by design but it has gross errors or imperfections due to sample-based estimation. This paper proposes a new cumulant-based ICA method named as PIMD to address these two problems. We first define a Proper Inner product (PI) with proved positive definiteness and then relax the centering preprocessing step to a mean displacement (MD) step. Both PI and MD aim to improve the orthogonality of inner product matrix and the recovery of independent components (ICs) in sample-based estimation. We adopt a gradient iteration step to find the ICs for PIMD. Experiments on both synthetic and real data show the respective effectiveness of PI and MD as well as the superiority of PIMD over competing ICA methods. Moreover, MD can improve the performance of other ICA methods as well

Blind Beamforming on a Randomly Distributed Sensor Array System

We consider a digital signal handling sensor array system, in light of haphazardly dispersed sensor node, for observation and source localization applications. In most array handling system, the sensor array geometry is settled and known and the steering array vector/complex data is utilized as a part of beam- formation. In this system, the array adjustment may be illogical because of obscure situation and introduction of the sensors with obscure frequency/spatial responses.In this project work a blind beamforming method is used by utilizing just the deliberate sensor information, to shape either an example information or a sample correlation matrix. The greatest power accumulation measure is utilized to acquire array weights from the predominant eigenvector connected with the largest eigenvalue of a matrix eigenvalue issue. A productive blind beamforming time delay appraisal of the predominant source is proposed. Source localization in light of a least squares (LS) technique for time delay estimation is additionally given. Results taking into account investigation, simulation, and measured acoustical sensor information demonstrate the viability of this beamforming system for sign upgrade and spacetime filtering