By Gérard Govaert
The 1st a part of this e-book is dedicated to tools looking suitable dimensions of knowledge. The variables hence received supply a man-made description which regularly leads to a graphical illustration of the knowledge. After a normal presentation of the discriminating research, the second one half is dedicated to clustering equipment which represent one other technique, frequently complementary to the tools defined within the first half, to synthesize and to investigate the knowledge. The publication concludes by means of analyzing the hyperlinks present among info mining and information research.
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Additional info for Data Analysis (Digital Signal and Image Processing)
J f . j 2 . It quantiﬁes to which extent the two rows i and deviate from the independence model in the same way. Symmetrically, the weights of the rows induce the metric in RJ . The distance between the columns j and h is: d2 (j, h) = fi. j fij fih − fi. j fi. h 2 . This use of the weights of the points of a cloud as a metric in the other space is natural. We attach the same importance to a row as an element of a cloud, on the one 30 Data Analysis hand, and as a dimension on the other hand. It induces a set of relations between the clouds NI and Nj referred to as ‘duality’ .
J j i 2 2 = Inertia(NJ ) = Φ2 = 1 2 χ . n Analyzing the dispersion of the clouds NI and NJ therefore consists of studying the discrepancy between the data and the independence model. 6. 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.
0 (d) decomposition of χ2 n (fij −fi. j )2 fi. 2. Data and independence model Correspondence Analysis 37 Let us note that, regarding the discrepancy with the independence model, the recognition of the bitterness is slightly more remarkable than that of the sourness, whereas direct inspection of the table suggests a (slightly) better recognition for sour. Even if surprising, this contradiction is apparent. The calculation of the discrepancy with the independence model takes into account the two margins of the data table, which shows that perceptions identiﬁed as sour are more frequent than those identiﬁed as bitter (12 against 8).
Data Analysis (Digital Signal and Image Processing) by Gérard Govaert