Analyzing and Modeling Data and Knowledge: Proceedings of by T. Bausch, M. Schwaiger (auth.), Professor Dr. Martin

By T. Bausch, M. Schwaiger (auth.), Professor Dr. Martin Schader (eds.)

The quantity comprises revised types of papers awarded on the fifteenth Annual assembly of the "Gesellschaft f}r Klassifika- tion". Papers have been prepared within the following 3 components that have been the most streams of debate through the confe- rence: 1. information research, class 2. information Modeling, wisdom Processing, three. functions, targeted topics. New effects on constructing mathematical and statistical equipment permitting quantitative research of knowledge are suggested on. instruments for representing, modeling, storing and processing da- ta and information are mentioned. purposes in astro-phycics, archaelogy, biology, linguistics, and medication are offered.

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To get a graphical display of the projections you choose k = 2 or k = 3. Therefore the optimization problems are n :E Ti(ri - ri)T D;;-l(ri - ri) --+ min --+ min. ;=1 m :ECj(Cj - cifD;l(Ci - Cj) j=l The solutions are obtained by the concepts of "singular value decomposition" (or "basic structure") and "low rank matrix approximation". First the generalized singular value decomposition of the double centered correspondence matrix (P - reT) is calculated: P - reT = ADI'BT ATD;lA=BTD;;-lB=I and P,1~P,2~ with ••.

I". i, rn E"" 1-1 J2 nl rnf~k> JL~> ... ... Total: rl Ef';'l R, Clg~,,> C2g~". Cmg~k' in(R) = in(C) Cl E~lg~, C2 E~;lg~, Cm E~;lg~, Table 1: Decomposition of Inertia, Greenacre (1984), p. 91 The aim of correspondence analysis is to find the coordinates for an optimal k-dimensional subspace. These are the first k columns of F and G ("low rank matrix approximation"). The coordinate matrices are related in a very simple way by the so-called "transition formulas": F=RGD-,.. 1 G= CFD-,..

Structural Analysis in Input-Output Tables W. Hauke Institut fiir Statistik und Mathematische Wirtschaftstheorie, Universitat Augsburg Memminger Str. 14,8900 Augsburg, GERMANY Abstract: The technology matrix as the basis of input-output tables shows the delivery structure among the different sectors in the economy. The columns of this matrix describe the input structures and the rows the output structures of the sectors. In this paper these data are analyzed with correspondence analysis to expose structures and uncover structural changes.

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