Download e-book for iPad: Data Analysis (Digital Signal and Image Processing) by Gérard Govaert

By Gérard Govaert

The 1st a part of this booklet is dedicated to tools looking suitable dimensions of knowledge. The variables therefore bought supply an artificial description which frequently leads to a graphical illustration of the information. After a common presentation of the discriminating research, the second one half is dedicated to clustering equipment which represent one other process, usually complementary to the tools defined within the first half, to synthesize and to research the information. The e-book concludes by way of analyzing the hyperlinks current among facts mining and knowledge research.

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Example text

3). Regarding the cloud of individuals in PCA (Chapter 1), we seek a sequence of axes having a maximum projected inertia, each being orthogonal to those already found. For the analysis of the rows cloud, we are led to the singular values decomposition of X DI XDJ , where DI is the diagonal matrix of the row weights (fi. j ) [ESC 08, p. 111]. As in PCA, the eigenvectors are the unit vectors of the directions (in RI ) maximizing the NI inertia; the eigenvalues are the inertias of the NI projection on these directions.

The strong values on the first diagonal express the good recognition of tastes, which are excellent for sweet. The negative values relative to sweet (−1, which is the minimum) expresses the absence of confusion between this taste and the others. 25) at the intersection of sour and bitter tastes expresses a confusion between these two tastes. The transformation of the data correctly translates our direct analysis of the table. 25 (c) discrepancy from independence fij fi. 000 (b) independence model fi.

This theoretical situation corresponds to the table having n ˜ ij (theoretical frequency) or f˜ij (theoretical probability) as the general term: n ˜ ij = ni. j n f˜ij = fi. j . This ‘theoretical’ table constitutes the independence model. It has the same margins as the observed table: ni. = n ˜ i. j . ˜ ij ), then (on the If the data table satisfies the relation of independence (nij = n one hand) all the row profiles and (on the other hand) all the column profiles are equal to the corresponding average profile: fij /fi.

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