Assessment of Linear Dependencies in Multivariate Data

Algorithm 633

“…A natural criterion for assessing the assignments is the sum of squares of the residuals, that 4, the square of the Frobenius norm of R, which is denoted by 7. From [5] the /3 that minimizes ? for a particular assignment of variables is given by b = w TlI+[w Tzl, ( The problem of determining the assignment of variables such that ?…”

“…As shown in [5], the computation of ? using the b given by (3.1) is expensive and can be accurately approximated for the assignments corresponding to small residuals by considering the space spanned by just V2 instead of the full [VI V2].…”

“…This relationship, along with the norm of R and other eigenvalue relationships as explained in Section 4 and in [5], provide the user with information concerning this particular choice of p2 and assignment of variables.…”

“…Recently, Kane et al [5] have developed a procedure called Linear Dependency Analysis (LDA), which assesses the existence of linear dependencies in a multivariate data matrix X. This paper describes the algorithm implementing the LDA procedure.…”

“…A brief description of some of the statistical and linear algebra theory behind the procedure is given below for notational purposes. Kane et al [5] should be consulted for additional details and discussion of the procedure's theoretical foundations.…”