Complex Principal Component Analysis: Theory and Examples

Abstract

Complex principal component (CPC) analysis is shown to be a useful method for identifying traveling and standing waves in geophysical data sets. Combinations of simple progressive and standing oscillations are used to examine the properties of this technique. These examples illustrate that although CPC analysis allows for the identification of traveling waves, many of the drawbacks associated with conventional principal component analysis remain, and sometimes become worse; e.g. the interpretation of CPC solutions is more difficult since both amplitude and phase relationships must be considered. A method for linearly transforming complex principal components was devised in order to identify regional relationships within large geophysical data sets. The errors in CPC analysis resulting from limited sample sizes are discussed. Abstract Complex principal component (CPC) analysis is shown to be a useful method for identifying traveling and standing waves in geophysical data sets. Combinations of simple progressive and standing oscillations are used to examine the properties of this technique. These examples illustrate that although CPC analysis allows for the identification of traveling waves, many of the drawbacks associated with conventional principal component analysis remain, and sometimes become worse; e.g. the interpretation of CPC solutions is more difficult since both amplitude and phase relationships must be considered. A method for linearly transforming complex principal components was devised in order to identify regional relationships within large geophysical data sets. The errors in CPC analysis resulting from limited sample sizes are discussed.