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- W78110596 abstract "In this article we propose an algorithm for Principal Components Analysis when the variables are histogram type. This algorithm also works if the data table has variables of interval type and histogram type mixed. If all the variables are interval type it produces the same output as the one produced by the algorithm of the Centers Method propose in [5, Cazes, Chouakria, Diday and Schektman (1997)]. 1 The algorithm In this algorithm we use the idea proposed in [9, Diday (1998)]. We represent each histogram–individual by a succession of k interval–individuals (the first one included in the second one, the second one included in the third one and so on) where k is the maximum number of modalities taken by some variable in the input symbolic data table. Instead of representing the histograms in the factorial plane, we are going to represent the Empirical Distribution Function FY defined, in [3, Bock and Diday (2000)] associated with each histogram. In other words if we have an histogram variable Y on a set E = {a1, a2, . . .} of objects with domain Y represented by the mapping Y (a) = (U(a), πa), for a ∈ E, where πa is frequency distribution, then in the algorithm we will use the function F (x) = ∑ i / πi≤x πi instead of the histogram. Definition 1. Let X = (xij)i=1,2,...,m, j=1,2,...,n be a symbolic data table with variables type continuous, interval and histogram, and let be k = max{s, where s is the number of modalities of Y j , j = 1, 2, . . . , n} where Y j is a variable of histogram type1. We define the vector–succession of intervals associated with each cell of X as: 1 If all the variables are interval type then k = 1. 1. if xij = [a, b] then the vector–succession of intervals associated is: xij = " @default.
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- W78110596 title "Generalization of the Principal Components Analysis to Histogram Data" @default.
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