That is either a sloppiness in writing or reliance on the relationship
between eigen decomposition and SVD.
SSM - square symmetric matrix
AM - arbitrary matrix
In ED, SSM = Q E Q'
In SVD, AM = P D Q'
SSM = AM' AM
= Q D P' P D Q' = Q D D Q'
= Q E Q', if E = D D
I haven't checked that above, but it is pretty close to accurate. You
may need to throw in a division by n.
David Chang wrote:
>Hi, thank you for reading this message. I have the following problems in
>getting the "correct" CRIMCOORD transformation of categorical variables
>in QUEST decision tree algorithm. Your help will be greatly appreciated.
>
>Q1: In Loh & Shih's paper (Split Selection Models for Classification
>Trees, Statistica Sinica, 1997, vol 7, p815-840), they mentioned about
>the mapping from categorical variable to ordered variable via CRIMCOORD.
>But, their explanation, in particular, step 5 of algorithm 2 is not
>clear. For example, they wrote "Perform a singular value decomposition
>of the matrix GFU and let a (vector) be the eigenvector (of what?)
>associated with the largest eigenvalue" in step 5. Does this mean
>a(vector) is the eigenvector of transpose(GFU)*GFU?
>
>Q2.
>I tried to verify the data sets in Table 1. Data set I-III are OK. But,
>the result for data set IV seems to be incorrect. Could any one of you
>help me verify that?
>
>Thank you very much for your help !!
>
>David
>
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