Empirical orthogonal functions

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A set of empirical orthogonal functions is a set of basis functions which specify a transform on a set of empirical signals, which result in a set of signals that, phenomenologically speaking, are statistically independant; i.e. have maximum variance. Thus, information is evenly distributed amongst the signals, as well as the equally measurable values of the signal, resulting in maximum information entropy, and robustness to noise.

When one discusses empirical orthogonal functions, they are concerned with how to extract these functions from a given system, with regard to a given set of information. They are also concerned with, therefore, what the empirical orthogonal functions that pertain to a given thing-in-the-world are, in relation to another given thing-in-the-world.

Related topics:

• Source separation
• Blind signal separation
• Nonlinear dimensionality reduction
• Transform coding