Horn's Curve Estimation Through Multi-Dimensional Interpolation
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH GRADUATE SCHOOL OF ENGINEERING AND MANAGEMENT
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A well-known multivariate data reduction method is principal components analysis PCA. PCA transforms the variables under study into a set of components that are used to summarize the variation among the variables. The benefit is the dimension of the data may be reduced by the descriptive power of the components, permitting tractable analysis on large and messy datasets. Integral to successful PCA is determining when to stop extracting components - the matter is not a trivial one. A component extraction stopping rule that consistently produces reliable estimates of principal components is Horns test. The drawback of the test is it requires a large amount of random data to evaluate the hidden component structure. Leveraging the flexibility and power of the MATLAB software package, a lookup table interpolates nearest neighbor searches of pre-processed mean eigenvalue data to provide real-time results for datasets up to 1,000 variables on 7,000 samples. The methodology is extended to a linear regression second-order model producing Horns curve, significantly reducing the required size of the lookup table with no loss of resolution into the dimensionality estimate.
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