Aðalhlutagreining

Aðalhlutagreining, often translated as Principal Component Analysis (PCA), is a statistical method used for dimensionality reduction. It aims to transform a dataset with many variables into a smaller set of variables, called principal components, while retaining as much of the original information or variance as possible. This technique is widely used in data science, machine learning, and pattern recognition to simplify complex datasets, improve the performance of algorithms, and facilitate visualization.

The core idea behind PCA is to find new variables, the principal components, that are linear combinations of the original variables. These components are orthogonal to each other, meaning they are uncorrelated. The first principal component captures the largest possible variance in the data, the second principal component captures the next largest variance that is orthogonal to the first, and so on. By selecting a subset of the principal components, one can represent the data in a lower-dimensional space without significant loss of information.

PCA is particularly useful when dealing with datasets where variables are highly correlated. By identifying the principal components, it effectively de-correlates the data. This process can help in identifying underlying patterns and structures that might be obscured by the large number of original variables. The number of principal components to retain is often determined by a threshold of explained variance or by visual inspection of a scree plot.