Numerical analysis for factorial data analysis. Part I: Numerical software — the package INDA for microcomputers

A large collection of factorial data analysis methods can be characterized by the following matrices: X , the k x n matrix of data, and A, B the symmetric positive definite matrices of size n, k which represent the chosen norms of ?ⁿ, ?^k, respectively. All methods amount to computing the largest eigenvalues of U = XAX^TB or the largest singular values of E = B^1/2XA^1/2 . In Part I of this paper we begin by a geometrical and probabilistic interpretation of the various methods, showing how U and E are defined in each case. We then define the computational kernel for factorial data analysis. We conclude by devising the numerical aspects of software implementation for this kernel on microcomputers and presenting the package INDA.