On the training distortion of vector quantizers

The in-training-set performance of a vector quantizer as a function of its training set size is investigated. For squared error distortion and independent training data, worst case type upper bounds are derived on the minimum training distortion achieved by an empirically optimal quantizer. These bounds show that the training distortion can underestimate the minimum distortion of a truly optimal quantizer by as much as a constant times n/sup -1/2/, where n is the size of the training data. Earlier results provide lower bounds of the same order.