Principal components analysis (PCA) is one of a family of techniques for taking high-dimensional data, and using the dependencies between the variables to represent it in a more tractable, lower-dimensional form, without losing too much information. PCA is one of the simplest and most robust ways of doing such dimensionality reduction. It is also one of the best, and has been rediscovered many times in many fields, so it is also known as the Karhunen-Lo_eve transformation, the Hotelling transformation, the method of empirical orthogonal functions, and singular value decomposition.