By Gisella Facchinetti (auth.), Jerzy Sołdek, Jerzy Pejaś (eds.)
Advanced computing device Systems is a set of 40 chosen papers offered to the 8th foreign convention on computers, October 2001 in Mielno, Poland. those papers offer a complete precis of perform and learn development in info applied sciences:
- Recognition, safety and security concentrates at the widely-known difficulties of data platforms security.
- Methods of synthetic Intelligence provides tools and algorithms that are the fundamentals for the purposes of synthetic intelligence environments.
- Intelligent brokers and allotted actions contains laboratory study on multiagent clever platforms in addition to upon their purposes in looking details, negotiating and assisting decision.
- Distributed Productions Networks and Modeling complicated structures current creation techniques in disbursed shared digital setting, digital answer of integer optimization difficulties, and a queuing method of functionality optimization within the allotted creation network.
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Additional info for Advanced Computer Systems: Eighth International Conference, ACS ‘2001 Mielno, Poland October 17–19, 2001 Proceedings
In the paper we propose two methods (called Plug-in and Procrustes) which taking into account the interdependencies between the variables provided in a robust covariance matrix S· - permit to reconstruct the data matrix in such a way, that its covariance matrix is exactly equal to the given robust covariance matrix S· . We call this process backprojection through the robust covariance matrix. The proposed method of backprojection is shown on four benchmark data sets. Key words: Outliers, Robust covariance matrix, QR-factorization, Visualization of multivariate data 1.
Both of them use the following two basic paradigms from numerical algebra: Paradigm on Cholesky factorization of the matrix S·. For a nonsingular Gramian matrix S' there exists an unique upper triangular matrix R' of order p, with all diagonal elements positive, such that S* =(II n)(R*) T R* . g. , p. 141). Paradigm on QR factorization of the matrix X * . Suppose that the sought matrix X· satisfies (1). Then the matrix X' has to have the following QR factorization (for the definition and the computation of the QR factorization see, for example, Golub and Van Loan , pp.
P) are the singular values of C. It is well known that (10) is the minimizer of (8). If C has full rank then the minimizer of (8) is unique. We now apply the concept of the orthogonal Procrustes problem to chose an orthogonal matrix Q in (3). For this purpose we consider the following problem: Find Q* EOn' for which the following minimum is attained: (11) It is the Procrustes problem (8) with A =X T , B =[(R*) T, 0] and QT instead of Q, because Frobenius norms of a matrix and its transpose are the same.