Pääakselimenetelmä

Pääakselimenetelmä, often translated as Principal Component Analysis (PCA), is a statistical technique used for dimensionality reduction. It aims to simplify a complex dataset by transforming its original variables into a new set of uncorrelated variables called principal components. These components are ordered in such a way that the first few capture the most variance in the data, while the later ones capture progressively less. This allows for a more efficient representation of the data by retaining most of the important information in a smaller number of dimensions.

The process of PCA involves calculating the covariance matrix of the original data. Eigenvectors and eigenvalues are then computed from this covariance matrix. The eigenvectors represent the directions of maximum variance in the data, which become the principal components. The corresponding eigenvalues indicate the magnitude of variance along these directions. By selecting the eigenvectors associated with the largest eigenvalues, one can construct a lower-dimensional subspace that best represents the original data.

PCA is widely applied in various fields, including machine learning, image processing, and bioinformatics. It is often used as a pre-processing step to improve the performance of other algorithms by reducing noise and computational complexity. For example, in image compression, PCA can be used to represent images with fewer components, thereby reducing storage space without significant loss of visual quality. Similarly, in pattern recognition, it helps to identify the most discriminative features in a dataset.