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Consider a collection of sample points <math>\{x_1,x_2,\cdots,x_n\}</math> where <math> x_i \in R^m</math>. We divide the methods in two categories: | Consider a collection of sample points <math>\{x_1,x_2,\cdots,x_n\}</math> where <math> x_i \in R^m</math>. We divide the methods in two categories: | ||
| − | * Outer Characteristics of the point cloud: These methods require the spectral analysis of a positive definite kernel of dimension m. | + | * '''Outer Characteristics of the point cloud:''' These methods require the spectral analysis of a positive definite kernel of dimension m, the extrinsic dimensionality of the data. |
| − | * Inner characteristics of the point cloud: These methods require the spectral analysis of a positive definite kernel of dimension n, the number of samples in the sample cloud. | + | * '''Inner characteristics of the point cloud:''' These methods require the spectral analysis of a positive definite kernel of dimension n, the number of samples in the sample cloud. |
Revision as of 23:42, 17 April 2008
Consider a collection of sample points $ \{x_1,x_2,\cdots,x_n\} $ where $ x_i \in R^m $. We divide the methods in two categories:
- Outer Characteristics of the point cloud: These methods require the spectral analysis of a positive definite kernel of dimension m, the extrinsic dimensionality of the data.
- Inner characteristics of the point cloud: These methods require the spectral analysis of a positive definite kernel of dimension n, the number of samples in the sample cloud.
Outer Characteristics of the point cloud Methods
- PCA: Principal Component Analysis
- Fisher Discriminant Analysis
Inner characteristics of the point cloud Methods
- MDS
