Dimension Reduction Methods

One characteristic of computational statistics is the processing of enormous amounts of data. It is now possible to analyze large amounts of high-dimensional data through the use of high-performance contemporary computers. In general, however, several problems occur when the number of dimensions becomes high.

[1]  David B. Cooper,et al.  Describing Complicated Objects by Implicit Polynomials , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  P. Hall.  On Polynomial-Based Projection Indices for Exploratory Projection Pursuit , 1989 .

[3]  Gabriel Taubin,et al.  Distance approximations for rasterizing implicit curves , 1994, TOGS.

[4]  M. Mizuta.  Algebraic curve fitting for multidimensional data with exact squares distance , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[5]  M. Mizuta.  A Derivation of the Algebraic Curve for Multi-dimensional Data using the Least-squares Distance , 1992 .

[6]  John W. Tukey,et al.  A Projection Pursuit Algorithm for Exploratory Data Analysis , 1974, IEEE Transactions on Computers.

[7]  G. Nason.  Three‐Dimensional Projection Pursuit , 1995 .

[8]  GENERALIZED PRINCIPAL COMPONENTS ANALYSIS INVARIANT UNDER ROTATIONS OF A COORDINATE SYSTEM , 1984 .

[9]  Ker-Chau Li,et al.  Sliced Inverse Regression for Dimension Reduction , 1991 .

[10]  Robin Sibson,et al.  What is projection pursuit , 1987 .

[11]  T. Hastie,et al.  Principal Curves , 2007 .

[12]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Ronald S. Landis.  Data Analytic Methods , 2013 .

[14]  David J. Kriegman,et al.  Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  M. Mizuta.  Rasterizing Algebraic Curves and Surfaces in the Space with Exact Distances , 1997, ICONIP.

[16]  J. Friedman.  Exploratory Projection Pursuit , 1987 .