Data Analysis (Digital Signal and Image Processing), 1st by Gérard Govaert

By Gérard Govaert

The 1st a part of this publication is dedicated to tools looking proper dimensions of information. The variables therefore got offer an artificial description which regularly leads to a graphical illustration of the information. After a basic presentation of the discriminating research, the second one half is dedicated to clustering tools which represent one other technique, usually complementary to the equipment defined within the first half, to synthesize and to research the knowledge. The e-book concludes through interpreting the hyperlinks present among facts mining and information research.

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Since we have the formulae allowing principal components computations, we simply have to compute linear combinations of these supplementary points characteristics. Categories Test values Coordinates Label Frequency 1 2 3 4 5 1 2 3 4 5 1. 19 2 . 03 3 . 10. 5. 1. Introduction Online statistical process control is essentially based on control charts for measurements, drawing the evolution of a product or process characteristics. A control chart is a tool which allows a shift of a location (mean) or a dispersion (standard deviation, range) parameter regarding fixed standard or nominal values to be detected through successive small samples (xi , i = 1, 2, .

We seek associations and oppositions of categories that express most of this relationship. As in PCA, duality relations relate the analysis of the clouds NI and NJ . Denoting the coordinate of the column j on the rank s axis as Gs (j): – inertias of clouds NI and NJ in projection on their principal rank s axis are equal: 2 2 λs = fi. j [Gs (j)] ; i j – the coordinates of the rows and the columns on the rank s axes are related by the transition or barycentric (or quasi-barycentric) formulae: 1 Fs (i) = √ λs 1 Gs (j) = √ λs fij 1 Gs (j) = √ fi.

No. 3. (a) Raw data and (b) associated contingency table The complete disjunctive table (CDT, also known as indicator matrix) crosses the individuals and the categories. Its columns are the indicators of the categories. It presents a remarkable property that has important effects on the analysis: j∈q yij = 1 ∀q. The sum of the columns belonging to the same variable is constant and all its terms are equal to 1. 9. Three presentations of the data in MCA: (a) raw data, where ziq is the label (or number) of the category of the variable q possessed by i, n is the number of individuals and Q is the number of variables; (b) complete disjunctive table (CDT), where yij = 1 if i possesses the category j (of q) and 0 if not, nj is the number of individuals possessing the category j, Jq is the number of categories of the variable q and J1 = 3; and (c) Burt table (BT), where nkj is the number of individuals possessing both the category j (of q) and the category k (of t).

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