Quantization for classification accuracy in high-rate quantizers

Quantization of signals is required for many transmission, storage and compression applications. The original signal is quantized at the encoder side. At the decoder side, a replica of the original signal that should resemble the original signal in some sense is recovered. Present quantizers make an effort to reduce the distortion of the signal in the sense of reproduction fidelity. Consider scenarios in which signals are generated from multiple classes. The encoder focuses on the task of quantizing the data without any regards to the class of the signal. The quantized signal reaches the decoder where not only the recovery of the signal should take place but also a decision is to be made on the class of the signal based on the quantized version of the signal only. In this paper, we study the design of such scalar quantizer that is optimized for the task of classification at the decoder. We define the distortion to be the symmetric Kullback-Leibler (KL) divergence measure between the conditional probabilities of class given the signal before and after quantization. A high-rate analysis of the quantizer is presented and the optimum point density of the quantizer for minimizing the symmetric KL divergence is derived. The performance of this method on synthetically generated data is examined and observed to be superior in the task of classification of signals at the decoder.