An Analog Programmable Multidimensional Radial Basis Function Based Classifier

Abstract

A compact analog programmable multidimensional radial basis function (RBF)-based classifier is demonstrated. The probability distribution of each feature in the templates is modeled by a Gaussian function that is approximately realized by the bell-shaped transfer characteristics of a proposed floating-gate circuit, which we term a floating-gate bump circuit. The maximum likelihood, the mean, and the variance of the distribution are stored in floating-gate transistors and are independently programmable. By cascading these floating-gate bump circuits, the overall transfer characteristics approximate a multivariate Gaussian function with a diagonal covariance matrix. An array of these circuits constitute a compact multidimensional RBF-based classifier that can easily implement a Gaussian mixture model. When followed by a winner-take-all circuit, the RBF-based classifier forms an analog vector quantizer. We use receiver operating characteristic curves and equal error rate to evaluate the performance of our RBF-based classifier as well as a resultant analog vector quantizer. We show that the classifier performance is comparable to that of digital counterparts. The proposed approach can be at least two orders of magnitude more power efficient than the digital microprocessors at the same task.Index Terms-Analog classifier, bump circuit, floating-gate transistor, Gaussian-like analog circuit, radial basis function (RBF), vector quantizer. I. MOTIVATIONS FOR ANALOG RBF CLASSIFIERM ULTIVARIATE Gaussian response functions can be used as building blocks in many applications including radial basis function (RBF)-based classifiers, Gaussian mixture modeling of data, and vector quantizers. This paper discusses the development of an analog Gaussian response function having a diagonal covariance matrix and demonstrates its application to vector quantization.When followed by a winner-take-all (WTA) stage, a RBFbased classifier forms a multidimensional analog vector quantizer. A vector quantizer compares distances or similarities between an input vector and the stored templates. It classifies the input data to the most representative template. Vector quantization is a typical pattern recognition and data compression technique. Crucial issues of the vector quantizer implementation concern the storage efficiency and the computational cost of searching the best-matching template. In the past decade, efficient digital [2], [3] and analog [4]-[6] hardware vector quantizers have been developed. In general, the analog vector quantizers have been shown to be more power efficient than their digital counterparts. However, in a previous design [4], the Manuscript Fig. 1. Analog RBF-based classifier in an analog front-end for speech recognition. The front-end of our current speech recognition system includes a bandpass-filter bank based analog Cepstrum generator, an analog RBF-based classifier, and a continuous-time HMM. Putting the DSP stages behind the analog front-end makes the entire system more efficient. computational efficiency is parti...

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