Subscripts 1 and 2 in Equation (9) identify the populations to which the "meta-sample" means, standard deviations, and bias adjustments pertain.
Although the meta-sample size of ICS studies that considered credit was small (n = 2), access to credit was positively associated with ICS adoption.
As a low dimensional vector, the meta-sample a i retains almost all local features and the most important global features of the original high-dimensional sample x i.
After building all k k-1) /2 classifiers, we first determine if a testing sample x' is from class the ith or jth class by a local decision function where a' is the meta-sample of x'.
Then, maximizing the margin between two types of data is equivalent to the following problem: (3) where a t is the meta-sample calculated for the training sample x i.
It is easy to decompose each sample in the subspace spanned by all independent components Each statistically independent component is a basis in the subspace, i.e., where the mixing matrix and In other words, each sample can be represented as where the meta-sample a i is the i th row of the mixing matrix recording the coordinate values of the sample x i in the subspace.
With θ ∧ and S ∧ θ denoting the "meta-sample" mean and standard deviation of θ ∧ 1, θ ∧ 2,..., θ ∧ N r e p, we construct a confidence interval for θ via either (5) θ ∧ + or − C S ∧ θ / N r e p or, preferably, (6) θ ∧ + or − { B ∧ θ + C S ∧ θ / N r e p }, where B ∧ θ is a bias adjustment and C is a constant chosen so that the confidence interval has the desired coverage probability (typically 95%).
Moreover, the meta-samples obtained from MICA at τ=2 can clearly distinguish two types of samples.
Interestingly, two types of meta-samples demonstrate a " self-clustering" mechanism in that the meta-samples belonging to the same type show very close spatial proximities.
It is reasonable to believe an optimal level threshold will contribute to capturing important local and global features of the original data in the meta-samples.
Unlike the traditional SVM that builds a maximum margin hyperplane in the original high-dimensional space where n ~ 10 – 10, MICA-SVM separates biological samples by constructing the maximum margin hyperplane in the spanned subspace where using the meta-samples.
