R: Data Analysis and Visualization

Data dimension reduction

Reduction of dimensionality is often necessary in the analysis of complex multivariate datasets, which is always in high-dimensional format. So, for example, problems modeled by the number of variables present, the data mining tasks on the multidimensional analysis of qualitative data. There are also many methods for data dimension reduction for qualitative data.

The goal of dimensionality reduction is to replace large matrix by two or more other matrices whose sizes are much smaller than the original, but from which the original can be approximately reconstructed, usually by taking their product with loss of minor information.

Eigenvalues and Eigenvectors

An eigenvector for a matrix is defined as when the matrix (A in the ...