An Interpretable Compression and Classification System: Theory and Applications

Abstract: This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear property, the extracted and reduced features can be inversed to original data, like a linear transform such as Fourier transform, so that one can quantify and visualize the contribution of individual features towards the original data. Also, the reduced features and reversibility naturally endure the proposed system ability of data compression. This system can significantly compress data with a small percent deviation between the compressed and the original data. At the same time, when the compressed data is used for classification, it still achieves high testing accuracy. Furthermore, we observe that the extracted features of the proposed system can be approximated to uncorrelated Gaussian random variables. Hence, classical theory in estimation and detection can be applied for classification. This motivates us to propose using a MAP (maximum a posteriori) based classification method. As a result, the extracted features and the corresponding performance have statistical meaning and mathematically interpretable. Simulation results show that the proposed classification system not only enjoys significant reduced training and testing time but also high testing accuracy compared to the conventional schemes.