Principal Component Analysis

Kernel principal component analysis (kernel PCA) [1] is an extension of principal component analysis (PCA) using techniques of kernel methods.

Principal Component Analysis (PCA)
The l1 direction corresponds to
the direction of largest variance of the data.
the eigenvector associated with the largest eigenvalue of the correlation matrix ( ).

Principal Component Analysis Constructing new features which are the principal components of a data set. The principal components are random variables of maximal variance constructed from linear combinations of the input features.

* Principal Component Analysis (PCA) is all about orthogonal projections.
* Multiple Linear Regression is fundamentally a problem in orthogonal projection.

Another data transformation that comes up is principal component analysis, one site with PCA software is the Carnegie-Mellon Statistics Library, see the file pca.c. I have never tried it.

Having the distance matrix, now you can use the distance matrix for various purposes and applications such as clustering (i.e. K means clustering) and data reduction (multidimensional scaling, Principal component analysis) and classification (LDA, ...

See also: Clustering, Classification, Variance, Distribution, Neural network