Entropy in Multivariate Analysis: Projection Pursuit
نویسنده
چکیده
Projection pursuit is an exploratory data-analytic method in multivariate (MV) analysis. It is similar to the well-known principal components analysis (PCA) in that it can be used to nd interesting structure within a MV data set. However, unlike PCA, which nds linear projections of maximum variance, projection pursuit nds linear projections of maximum non-normality, which sometimes is better at revealing structure within a MV data set. We describe how the negative Shannon entropy can be used for measuring non-normality. As a result we can view projection pursuit with the Shannon index as a method which nds the projection with the maximum entropy. We outline the constrained optimising projection pursuit algorithm and mention brie y the role of sphering a MV data set. Finally we illustrate the method as applied to the famous Lubischew beetle data and mention how it can be applied to multispectral images.
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