The use of covariance matrices in dimension reduction for space-time data

Ian Jolliffe
University of Exeter

Space-time data are high dimensional, but the dimensionality of the data can usually be reduced substantially without losing much information. Techniques for achieving an 'optimal' dimension reduction are often based on covariance or correlation matrices. The best-known and most widely used technique of this type is known as principal component analysis (PCA) by statisticians and empirical orthogonal function (EOF) analysis by atmospheric scientists. Much of the talk will be concerned with PCA, some of the decisions associated with its use, and some extensions and modifications to the technique. Its use and interpretation in geosciences will be emphasised.

However, in PCA the objective is to retain as much variance as possible in the reduced number of dimensions, and in some situations other objectives may be associated with the dimension reduction. Other dimension reduction techniques, that have different objectives but are still based on covariance or correlation matrices, will be briefly discussed.

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