Vector quantization for classification in a simple network

Summary form only given. We design a generalized Gauss mixture vector quantizer (GMVQ) with an encoder at each sensor and a decoder at the common receiver, minimizing the expected quadratic discriminant analysis (QDA) distortion between the original data and the Gauss mixture component, to which it is assigned by the decoder. Each encoder first predicts the index assignment of the other encoder based on its own noisy version of the data. We denote the predicted index of the other encoder by j^p. Then, the encoder assigns its own noisy version to the index i such that the Gauss mixture component associated with the index pair (i, j^p) at the decoder is the one minimizing the expected QDA distortion. The decoder, upon receiving an index from each encoder, maps the received index pair to the mixture component, minimizing the expected distortion. The quantizer is trained using the Lloyd algorithm, by iteratively updating the encoders and the decoder. Each encoder is updated by predicting the index assignments of the other encoder followed by assigning each noisy input vector to the index, minimizing the expected QDA distortion. The decoder is updated by mapping each index pair to the optimum Gauss mixture component followed by the update of the parameters of each Gauss mixture component. We have implemented our algorithm on three different data sets: a mixture of Gaussians, a mixture of Laplacians and a a set of aerial images. For each data set, we observed that the classification performance achieved by our algorithm is very close to the theoretically optimal (Bayes) performance.