Data Reduction of Body Surface Potential Maps by Means of Orthogonal Expansions

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Abstract
The electrical activity of the heart is reflected at the body surface by a potential distnbution which continuously changes in time throughout the cardiac cycle. Sampled versions of the potential data can be considered either as vectors or as matrices. From this conception, two different methods for data reduction can be developed within the frame of the Karhunen-Loeve expansion: a one-step method which implies an expansion into one set of eigenvectors, and a two-step method implying an expansion into two sets of eigenvectors. The set of eigen-vectors for the one-step method and the two sets of eigenvectors (space and time) for the two-step method were derived from the recorded body surface potentials of 136 subjects, used for the representation of the data of this group of subjects (design set), and also applied to a group of 135 subjects (test set). The rms error of the representation using 36 eigenvectors following the one-step method was 47 AV for the design set and 73 AV for the test set. When the two-step method was applied using six eigenvectors in space and six eigenvectors in time (also having 36 coefficients), the error was found to-be 77 , uV for the design set and 80 , uV for the test set. It is concluded that the one-step method is to be preferred for the representation of body surface potential data within a given group.