By Cook R. J., Kalbfleisch J. D.
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We now rely on computers at every stage of this transformation: structuring and exploring information, developing models, and communicating knowledge. In this book we teach a methodology that makes visualization central to the process of abstracting knowledge from information. Computers give us great power to represent information in pictures, but even more, they give us the power to interact with these pictures. If these are pictures of data, then interaction gives us the feeling of having our hands on the data itself and helps us to orient ourselves in the sea of information.
We snooped into the data. In reality, making pictures of data is not necessarily data snooping. If the purpose of an analysis is clear then making plots of the data is “just smart”, and we make many unexpected observations about the data, resulting in a richer and more informative analysis. We particularly like the quote by Crowder & Hand (1990): “The first thing to do with data is to look at them.... usually means tabulating and plotting the data in many different ways to ’see whats going on’.
Xnp Ap1 . . Xn1 A1d + . . + Xnp Apd n×d Here are several examples. If d = 1 and A = (1 0 . . 0) then variable, of the data, XA = [X11 X21 . . Xn1 ] . If A = ( √12 −1 √ 2 0 . . 0) then XA = (x11 − x12 ) (x21 − x22 ) (xn1 − xn2 ) √ √ √ ... 2 2 2 , which is a contrast of the first two variables in the data table. If d = 2 and 1 0 X11 X12 0 1 X21 X22 A = 0 0 then XA = . , .. .. . Xn1 Xn2 0 0 the first two columns of the data matrix. Generally the values in A can be any values between [−1, 1] with the constraints that the squared values for each column sum to 1 (normalized) and the inner product of two columns sums to 0 (orthogonal).