Päästandardijärjestelmät

Päästandardijärjestelmät, known in English as Principal Component Analysis (PCA), is a statistical technique widely used for dimensionality reduction in data analysis and machine learning. It is an unsupervised learning method that transforms a dataset with a large number of variables into a smaller set of uncorrelated variables, called principal components, while retaining most of the original information. The goal is to simplify complex data by identifying the directions of greatest variance.

The core idea behind PCA is to find a new set of orthogonal axes, the principal components, that capture the maximum variance in the data. The first principal component accounts for the largest possible variance, the second principal component accounts for the second largest variance among the remaining variance and is orthogonal to the first, and so on. This process allows for the identification of the most important underlying patterns and relationships within the data.

PCA is particularly useful when dealing with datasets that have many features, as it can help to reduce noise and computational complexity without significant loss of information. It is applied in various fields, including image compression, pattern recognition, bioinformatics, and finance, for tasks such as data visualization, feature extraction, and noise reduction. The selection of the number of principal components to retain is often based on the cumulative proportion of variance explained.