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Spatially adaptive binary classifier using B-splines and total variation penalty. (English) Zbl 1434.62111
For classifier problems the computation of decision boundaries is considered, where for a theoretical analysis, the problem is restricted to a two-dimensional predictor space, hence, the computation of a decision curve \(g\). Based on certain training data, and using a spline approximation, the problem is reduced to the solution of a parameter optimization problem for the coefficients of the spline approximation. Here, the objective function is defined by the mean hinge loss with respect to given training data and an additive weighted norm term depending of the vector of spline-coefficients. The resulting optimization problem is numerically solved by a coordinate decent algorithm. Theoretical properties of the method are discussed, and numerical studies are given.
62H30 Classification and discrimination; cluster analysis (statistical aspects)
65D07 Numerical computation using splines
62C25 Compound decision problems in statistical decision theory
Full Text: DOI
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