Editing Dimensionality reduction (section)

===Principal component analysis (PCA)===
{{Main|Principal component analysis}}

The main linear technique for dimensionality reduction, principal component analysis, performs a linear mapping of the data to a lower-dimensional space in such a way that the variance of the data in the low-dimensional representation is maximized. In practice, the [[covariance]] (and sometimes the [[correlation and dependence|correlation]]) [[matrix (mathematics)|matrix]] of the data is constructed and the [[eigenvalues and eigenvectors|eigenvectors]] on this matrix are computed. The eigenvectors that correspond to the largest eigenvalues (the principal components) can now be used to reconstruct a large fraction of the variance of the original data. Moreover, the first few eigenvectors can often be interpreted in terms of the large-scale physical behavior of the system, because they often contribute the vast majority of the system's energy, especially in low-dimensional systems. Still, this must be proved on a case-by-case basis as not all systems exhibit this behavior. The original space (with dimension of the number of points) has been reduced (with data loss, but hopefully retaining the most important variance) to the space spanned by a few eigenvectors. {{Citation needed|date=September 2017}}