Estimating Sparse Sources from Data Mixtures using Maxima in Phase Space Plots

In Blind Source Separation (BSS), one estimates sources from data mixtures where the mixing coefficients are unknown. In the particular case of Sparse Component Analysis (SCA), each underlying source exists for only a finite amount of time when other sources are negligible. In this paper, one approach to SCA is presented where the data are represented using phase space analysis and one estimates the main source from the maximum in the phase plot. Deflation is used to estimate the other sources. The proposed method is tested on simulated data and experimental ECG data taken from an expectant mother. It is shown that, in most cases, the performance of the proposed method is comparable to that of Principal Component Analysis (PCA) and FastICA for clean data. In the case of noisy data, PCA is found to be more robust for higher noise levels. For situations where the sources have coincident peaks, the method breaks down as expected, as the maximum in the phase plot does not correspond to an individual source.

Comparison of Clustering Methods for Extraction of Uncorrelated Sparse Sources from Data Mixtures

There is an extensive set of methods to determine sparse sources from mixtures where the mixing coefficients are unknown. Each method involves plotting N sets of mixed data against each other in N-dimensional space. In the approach adopted in this paper, N dimensional normalised vectors are produced by joining data points that are adjacent in time. A novel clustering approach is adopted: the two vectors, not necessarily adjacent in time, which are closest to each other are identified and one of these vectors is taken as the principal direction corresponding to one of the sources. It is shown, using a deflation approach, that it is possible to estimate individual sources to within a multiplicative constant. This novel method is compared with two related methods and the standard FastICA algorithm. This new method has comparable performances to three other methods when applied to examples of purely sparse, semi-sparse and non-sparse sources and also when applied to fetal ECG data.