A Beginner's Guide to Principal Component Analysis

In principal component analysis, a principal component is a new feature that is constructed from a linear combination of the original features in a dataset. The principal components are ordered such that the first principal component has the highest possible variance (i.e., the greatest amount of spread or dispersion in the data), and each subsequent component in turn has the highest variance possible under the constraint that it is orthogonal (i.e., uncorrelated) to the previous components. The idea behind PCA is to reduce the dimensionality of a dataset by projecting the data onto a lower-dimensional space, while still preserving as much of the variance in the data as possible. This is done by selecting a smaller number of principal components that capture the most important information in the data, and discarding the remaining, less important components. In this way, PCA can be used to identify patterns and relationships in high-dimensional data, and to visualize data in a lower-dimensional space for easier interpretation.