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Quantification of Differential Information Using Matrix Pencil and Its Applications

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Abstract

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.

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Data Availability

This is to declare that all the data used for the above research is open source and has been cited. This paper uses four datasets for different applications. The MNIST [6] and Google Speech Command Dataset [17] have been used for classification and multiclass signal representation-related applications. MPEG-7 Core Experiment CE-Shape-1 Test Set [8] has been used for transformation of one pattern to another and the dataset from Texas Data Repository [24] for activity detection.

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  1. Snigdha Bhagat and Shiv Dutt Joshi have contributed equally to this work.

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  1. Department of Electrical engineering, Indian Institute of Technology, Delhi, Delhi, 122009, India

    Snigdha Bhagat & Shiv Dutt Joshi

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  1. Snigdha Bhagat
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Bhagat, S., Joshi, S.D. Quantification of Differential Information Using Matrix Pencil and Its Applications. Circuits Syst Signal Process 42, 2169–2192 (2023). https://doi.org/10.1007/s00034-022-02198-x

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