Abstract: In recent years, the use of vector variance as a
measure of multivariate variability has received much attention in
wide range of statistics. This paper deals with a more economic
measure of multivariate variability, defined as vector variance minus
all duplication elements. For high dimensional data, this will increase
the computational efficiency almost 50 % compared to the original
vector variance. Its sampling distribution will be investigated to make
its applications possible.
Abstract: This paper presents comparative study on recent
integer DCTs and a new method to construct a low sensitive structure
of integer DCT for colored input signals. The method refers to
sensitivity of multiplier coefficients to finite word length as an
indicator of how word length truncation effects on quality of output
signal. The sensitivity is also theoretically evaluated as a function of
auto-correlation and covariance matrix of input signal. The structure of
integer DCT algorithm is optimized by combination of lower sensitive
lifting structure types of IRT. It is evaluated by the sensitivity of
multiplier coefficients to finite word length expression in a function of
covariance matrix of input signal. Effectiveness of the optimum
combination of IRT in integer DCT algorithm is confirmed by quality
improvement comparing with existing case. As a result, the optimum
combination of IRT in each integer DCT algorithm evidently improves
output signal quality and it is still compatible with the existing one.