The Convergence Characteristics of The Time-Averaged Distortion in Vector Quantization: Part II. Applications to Testing Trained Codebooks

벡터 앙자화에서 시간 평균 왜곡치의 수렴 특성: II. 훈련된 부호책의 감사 기법

When codebooks designed by a clustering algorithm using training sets, a time-averaged distortion, which is called the inside-training-set- distortion (ITSD), is usually calculated in each iteration of the algorithm, since the input probability function is unknown in general. The algorithm stops if the ITSD no more significantly decreases. Then, in order to test the trained codebook, the outside-training-set-distortion (OTSD) is to be calculated by a time-averaged approximation using the test set. Hence codebooks that yield small values of the OTSD are regarded as good codebooks. In other words, the calculation of the OTSD is a criterion to testing a trained codebook. But, such an argument is not always true if some conditions are not satisfied. Moreover, in order to obtain an approximation of the OTSD using the test set, it is known that a large test set is requared in general. But, large test set causes heavy calculation com0plexity. In this paper, from the analyses in [16], it has been revealed that the enough size of the test set is only the same as that of the codebook when codebook size is large. Then a simple method to testing trained codebooks is addressed. Experimental results on synthetic data and real images supporting the analysis are also provided and discussed.