päätekijäryhmästä

Päätekijäryhmä, known in English as principal component analysis (PCA), is a statistical method used for dimensionality reduction. It is a technique that transforms a set of possibly correlated variables into a set of linearly uncorrelated variables called principal components. The goal of PCA is to find a new set of variables that capture most of the variance in the original data with fewer dimensions.

The first principal component is the linear combination of the original variables that accounts for the largest possible variance in the data. The second principal component is the linear combination that accounts for the largest remaining variance, and it is orthogonal to the first principal component. This process continues for subsequent components, each accounting for progressively less variance and being orthogonal to all preceding components.

PCA is widely used in various fields, including machine learning, image processing, and bioinformatics. It is particularly useful when dealing with datasets that have a large number of features, as it can help to simplify the data, reduce noise, and improve the performance of machine learning algorithms. By reducing the number of variables, PCA can also help to visualize high-dimensional data in a lower-dimensional space, typically two or three dimensions.

The effectiveness of PCA depends on the assumption that the principal components are linear combinations of the original variables. It is also sensitive to the scaling of the original variables, so it is often recommended to standardize the data before applying PCA. The number of principal components to retain is typically determined by examining the proportion of variance explained by each component, often using a scree plot.