A simple short proof of the Johnson-Lindenstrauss lemma (concerning nearly isometric embeddings of finite point sets in lower-dimensional spaces) is given. This result is applied to show that if G is a graph on n vertices and with smallest eigenvalue i then its sphericity sph(G) is less than cA2 log n. It is also proved that if G or its complement is a forest then sph(G) < c log n holds. Q 19%8...

This article deals with the problem of testing the hypothesis that q p-variate normal distributions are independent and that their covariance matrices are equal. The exact null distribution of the likelihood ratio statistic when q = 2 is obtained using inverse Mellin transform and the definition of Meijer’s G-function. Results for p = 2, 3, 4 and 5 are given in computable series forms.

Three simple speaker verification techniques based on vector quantization, sphericity models and dynamic time warping, respectively, are developed and tested using the same experimental protocol. Two types of feature vectors, the linear prediction derived cepstral coefficients and the melfrequency cepstral coefficients are considered. The efficiency of the combination of the type of acoustic an...

Parametric analysis of variance (ANOVA) is frequently used to analyse experimental data, yet for the results to be considered as accurate, certain assumptions must be respected: the normality of the distribution of the sampled data, the homogeneity of variance among the groups being compared (i.e., homoscedasticity), and, in certain cases, sphericity. The present work focuses on the methods for...

The transmission of stress is analysed for static periodic arrays of rigid grains, with perfect and zero friction. For minimal coordination number (which is sensitive to friction , sphericity and dimensionality), the stress distribution is soluble without reference to the corresponding displacement fields. In non-degenerate cases, the constitutive equations are found to be simple linear in the ...

This paper considers improving the power of tests for the identity and sphericity hypotheses regarding high dimensional covariance matrices. The power improvement is achieved by employing the banding estimator for the covariance matrices, which leads to significant reduction in the variance of the test statistics in high dimension. Theoretical justification and simulation experiments are provid...