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.