  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.
