Component-based variation reduction method

PCA is a method based on the Karhunen-Loeve transformation (KL transformation) of the data points in the feature space. In KL transformation, the data points in the feature space are rotated such that the new coordinates of the sample points become the linear combination of the original coordinates. And the first principal component is chosen to be the direction with largest variation of the distribution of sample points. After the KL transformation and the neglect of the components with minor variation of coordinates of sample points, we can make dimension reduction without significant loss of the information about the distribution of sample points in the feature space. Up to now PCA is probably the most widespread multivariate statistical technique used in chemometrics. Within the chemical community the first major application of PCA was reported in 1970s, and form the foundation of many modem chemometric methods. Conventional approaches are univariate in which only one independent variable is used per sample, but this misses much information for the multivariate problem of SAR, in which many descriptors are available on a number of candidate compounds. PCA is one of several multivariate methods that allow us to explore patterns in multivariate data, answering questions about similarity and classification of samples on the basis of projection based on principal components. 

---