15.2 Principal Component Analysis (PCA)
Principal Component Analysis (PCA) is a widely-used statistical technique that is employed to reduce the dimensionality of large datasets, making it easier to analyze them. PCA is particularly useful when dealing with datasets that have many variables, as it allows us to transform these variables into a smaller number of variables, called principal components, which are easier to manage and interpret.
PCA works by identifying the direction of maximum variance in the dataset and projecting the data onto that direction. The first principal component represents the direction with the most variance, and subsequent principal components represent directions that are orthogonal to the previous components and capture decreasing amounts of variance.
By reducing the number of variables in a dataset while still retaining as much information as possible, PCA can help uncover hidden patterns and relationships in the data. This can be particularly useful in...