Päätekijäerottelu

Päätekijäerottelu, or Principal Component Analysis (PCA), is a statistical technique used for dimensionality reduction. It transforms a dataset with many variables into a smaller set of new variables, called principal components, while retaining as much of the original data's variance as possible. These principal components are linear combinations of the original variables and are uncorrelated with each other.

The goal of PCA is to simplify complex datasets by identifying the most important underlying patterns. The first principal component captures the largest proportion of the variance in the data, the second component captures the next largest proportion of the remaining variance, and so on. By selecting a limited number of the top principal components, one can reduce the dimensionality of the data without significant loss of information.

PCA is widely used in various fields, including machine learning, image processing, and bioinformatics. It can be applied for data visualization, noise reduction, and as a preprocessing step for other machine learning algorithms. The effectiveness of PCA depends on the assumption that the data can be represented by a lower-dimensional subspace. It is sensitive to the scaling of the original variables, meaning that variables with larger ranges might dominate the principal components if not standardized beforehand.