N face images are given for training; then, through the basic face representation process, they are represented as a D -dimensional vector (called the

base vector) while forming an N-by-D matrix, where D is defined by the code number of the local encoder and the grid density (e.g., D = 256 codes x 120 patches = 30,720).

The problem discussed above will be referred to as the BVD problem (

Base Vector Discontinuity problem).

The dimensionality is decided by the number of

base vectors. The dimensionality of the

base vector is called the rank of the generated lattice.

It is obvious from (40) that we have IPI [greater than or equal to] 0 and that IPI equals zero if and only if p is a rescaled canonical

base vector that only one element of vector is not zero.

In the mutation operator of most DE variants, a mutant vector can be treated as the lead individual to explore the search space and generated by adding a difference vector to a

base vector. We have observed, however, that these two vectors (i.e., base and difference vectors) in most of DE are usually selected randomly, which does not fully utilize the useful population information to guide the search.

Three other parents are used to generate each trial vector; the

base vector and two difference vectors.

Since both the frequency and time domain models are based upon functionally similar matrix coefficient, characteristic polynomials, the UMPA (m, n, v) terminology can be used for models in both domains to reflect the order of the denominator polynomial (m), the order of the numerator polynomial (n), and the order of the

base vector (v) involved in the basic UMPA formulation.

For the sake of convenient description, the solution which is selected to plus a perturbed value is called as the

base vector. [x.sub.r1] (the

base vector) is perturbed by adding to it the product of the control parameter and the difference of [x.sub.r2] between [x.sub.r3].

In this case (4) admits one-dimensional Lie algebra spanned by the

base vectorThe imaginary 3D

base vector i of the quaternionic number space is the imaginary base number of the complex number space.

Moreall, A Structural /Statistical feature

base vector for handwritten character recognition, Pattern Recognition Letters, 19, pp.