Principal Curves and Surfaces
Linear Principal Components. A linear model formulation. The Principal Curve and Surface models. Theory for principal curves and surfaces. Algorithmic details. Estimation of curves and surfaces. Gold assay pairs. Generalized linear principal components.
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The construction of lower-dimensional manifolds from high-dimensional data is an important task in data mining, machine learning and statistics. The authors consider principal manifolds as a regularized, non-linear empirical quantization error functional.
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