Quantification of Differential Information Using Matrix Pencil and Its Applications

Appropriate signal representation is the fundamental issue of concern in all signal processing-based applications. For instance, in the context of signal compression one would require the signal representation to be such that most of the information is confined in the smallest subspace with least number of coefficients. In classification scenario, the representation has to be such that it accentuates differential information amongst classes. In the context of applications dealing with signal decomposition or denoising, one would require the representation such that it separates the input into its independent components so that individual components, i.e. the signal and noise lie in separate spaces. In this paper, we propose signal representation scheme that can be regarded as generalised KLT for multi-class scenario. We introduce an approach that would find the differential information between two classes rather than modelling individual classes separately. These classes are viewed on a common frame of reference in which one class would have a constant variance, unlike the other class which would have unequal variance along its basis vectors which would capture the differential information of one class over the other. This, when mathematically formulated, leads to the solution of the Matrix Pencil equation. This is borne out by illustrative examples on the classification of the MNIST (Deng in IEEE Signal Process Mag 29(6):141–142, 2012) and Google Speech Command Dataset (Pete in Software Engineer, G.B.T. Google Speech Command Dataset. https://ai.googleblog.com/2017/08/launching-speech-commands-dataset.html, 2017). Its applicability for biomedical data like brain state transition detection has also been explored and recorded.