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Abstract:
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Many modern instruments deliver multi-dimensional signals, like spectra, images or frequency distributions. It often is of interest to use such data as regressors for classification or prediction, after "training" on complete observations. The problem is known as multivariate calibration (MVC), a very popular subject in the chemometric community. The result of MVC is a surface of regression coefficients. Classical methods, like principal component regression or partial least squares do not exploit the spatial characteristics of the data. We propose penalties to force neighboring regression coefficients to have similar values, using cross-validation is used to optimize the weight of the penalty. To make this scheme feasible in two or more dimensions, a tensor product basis of B-splines is introduced. Our penalized (generalized linear) regression framework allows non-normal responses.
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