In this work we introduce a concept of complexity for undirected graphs in terms the spectral analysis Laplacian operator defined by incidence matrix graph. Precisely, compute norm vector eigenvalues both graph and its complement take their product. Doing so, obtain quantity that satisfies two basic properties are expected measure complexity. First,complexity fully connected disconnected vanish...

One well-known problem with diphone concatenation is the occurrence of audible discontinuities at diphone boundaries, which are most prominent in vowels and semi-vowels. Significant formant jumps at certain boundaries suggest that the problem is of a spectral nature. We have examined this hypothesis by correlating the results of a listening experiment with spectral distances measured across dip...

\eVe look at spectral clustering as optimization. \eVe show that near some special points called perfect, spectral clustering optimizes simultaneously two criteria: a dissimilarity measure that we call the rrmltiway normalized c'ut (lvfNC'I1t) and a cluster coherence measure that we call the gap. The immediate implication from the user's p.o.v is that spectral clustering will optimize any trade...

In this study we compared several different spectral distortion measures including the Itakura-Saito (IS), the log likelihood ratio (LLR), the likelihood ratio (LR), the cepstral (CEP), and two perceptually based distortion measures, the weighted likelihood ratio (WLR) and the weighted slope metric (WSM) distortion measures, in terms of their effects on the performance of a standard dynamic tim...

Necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half-line Schrödinger operator with square integrable potential.