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6. Dimension Reduction Methods
Masahiro Mizuta
Subsections
6.1 Introduction
6.2 Linear Reduction of High-dimensional Data
6.2.1 Principal Component Analysis
6.2.1.1 Proportion and Accumulated Proportion
6.2.2 Projection Pursuit
6.2.2.1 Algorithm
6.2.2.2 Projection Indexes
6.2.2.3 Relative Projection Pursuit
6.3 Nonlinear Reduction of High-dimensional Data
6.3.1 Generalized Principal Component Analysis
6.3.2 Algebraic Curve and Surface Fitting
6.3.2.1 Algebraic Curve and Surface
6.3.2.2 Approximate Distance
6.3.2.3 Exact Distance
6.3.2.4 Algebraic Surface Fitting
6.3.2.5 Bounded and Stably Bounded Algebraic Curve and Surface
6.3.2.6 Parameterization
6.3.2.7 Examples
6.3.3 Principal Curves
6.3.3.1 Definition of Principal Curve
6.4 Linear Reduction of Explanatory Variables
6.4.1 Sliced Inverse Regression
6.4.2 Sliced Inverse Regression Model
6.4.3 SIR Model and Non-Normality
6.4.4 SIRpp Algorithm
6.4.5 Numerical Examples
6.5 Concluding Remarks