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Abstract:
If globally high dimensional data has locally only low
dimensional distributions, it is advantageous to perform a local
dimensionality reduction before further processing the data. In
this paper we examine several techniques for local dimensionality
reduction in the context of locally weighted linear regression. As
possible candidates, we derive local versions of factor analysis
regression, principal component regression, principal component
regression on joint distributions, and partial least squares
regression. After outlining the statistical basis of these methods,
we perform Monte Carlo simulations to evaluate their robustness
with respect to violations of their statistical assumptions. One
surprising outcome is that locally weighted partial least squares
regression offers the best average results, thus outperforming even
factor analysis, the theoretically most appealing of our candidate
techniques.
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