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IEEE DSP Workshop 2011


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IEEE DSP Workshop 2011

  1. 1. QUANTIZATION FOR CLASSIFICATION ACCURACY IN HIGH-RATE QUANTIZERS Behzad M. Dogahe Manohar N. Murthi Department of Electrical and Computer Engineering IEEE DSP Workshop, January 2011
  2. 2. Outline • Motivation • Background • Problem Statement and Solution • Simulations • Concluding Remarks
  3. 3. Motivation • Quantization of signals is required for many applications • The original signal is quantized at the encoder and at the decoder side a replica 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 quantization 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
  4. 4. Motivation • Goal: Design of a quantizer that is optimized for the task of classification at the decoder • Application Scenarios:  Want to have good sound fidelity (good voice/audio quality) but also want to be able to perform speaker recognition  Sensor network where the sensors have low complexity, simple quantizers, but the decoder/sensor sink node does more sophisticated processing (so the raw signal value is needed, but we also want to be able to classify the sensed signal)
  5. 5. Background Quantizerx )(ˆ xQx  x xˆ x )(xp x )(x x xˆ x )(xp x )(x In high-rate theory point density function represents the density of codebook points in any region for a quantizer. The design of a quantizer is equivalent to design of the optimal point density function. )(xp : Probability Density Function
  6. 6. Background • Design of Quantizer involves minimizing: where is Distortion Measure • Examples of Distortion Measure:  MSE  Log Spectral Distortion • High-Rate Theory: 2 ˆ)ˆ,( xxxxd  Optimization Problem
  7. 7. Background • Following the steps in [Gardner and Rao] point density function will be derived as (n is the dimension of x) W.R. Gardner and B.D. Rao, “Theoretical analysis of the high-rate vector quantization of lpc parameters,” Speech and Audio Processing, IEEE Transactions on, vol. 3, no. 5, pp. 367 –381, sep 1995.
  8. 8. Problem Statement • We are looking for a point density function that is representative of a quantizer that performs well in the classification task • We have to select a distortion measure that is well defined for classification purposes • We chose the symmetric Kullback-Leibler divergence measure between probability of class given the signal before and after quantization
  9. 9. Problem Statement & Solution We assume a generative model for classifier. Hence and are known a priori. Trade-off Distortion Measure:
  10. 10. Simulations • Signal is from two classes with known conditional PDFs • Dashed lines represent the decision boundaries • Point density function dedicates codebook points to the boundaries
  11. 11. Simulations • only dedicates codebook points where the signal is concentrated • By introducing tradeoff between MSE and classification, codebook points move to the classification boundaries
  12. 12. Simulations 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 KL Tradeoff (a = 0.2)Tradeoff (a = 0.8) MSE 10 Bits 8 Bits 6 Bits Classification Error (%) • The higher the bit rate of quantizer the better classification accuracy • As we move from MSE to KL, the classification accuracy improves
  13. 13. Simulations -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 KL Tradeoff (a = 0.2) Tradeoff (a = 0.8) MSE 10 Bits 8 Bits 6 Bits Distortion (dB) • Pure KL performs poorly as far as the distortion of the signal • However, introducing the slightest tradeoff with MSE improves distortion significantly
  14. 14. Concluding Remarks • A solution for quantization of signals for the purpose of obtaining a more accurate classification at the decoder was proposed • High-rate theory for quantizer design was employed • An optimal point density function was derived • The performance of this method on synthetically generated data was examined and observed to be superior in the task of classification of signals at the decoder • The tradeoff between the reproduction fidelity and classification accuracy was studied as well • In our future work, we will study the practical vector quantizer design based on the high-rate theory