Quantification and localization of features in time-frequency plane

Many feature extraction techniques in literature have studied data representation, but most techniques do not explicitly investigate the feature localization aspect. This is one of the first works in which signals have been transformed to matrices using positive time-frequency transform, and matrix decomposition and representation techniques such as PCA, ICA, and NMF have been applied on these matrices to study the feature representation and localization issues. To estimate each techniquespsila localization, we propose a localization measurement method. We also construct a non stationary synthetic signal which resembles major characteristics of real world signals, and then apply the feature extraction techniques on a simple time-frequency distribution (TFD) of this signal. The localization results show that matrix factorization 1-D deconvolution (NMF1D) offers the most localized features with 99.6% localization. In addition, we demonstrate that under different number of basis components and noisy conditions, NMF1D offers the most robust localization.