Identifying patterns in multicomponent signals by extended cross correlation

The analysis of current problems in physical chemistry often requires the identification of patterns that encode the composition, structure, and dynamics of a system. Overlapped patterns, unexpected patterns, and patterns whose forms are initially unknown are especially difficult to identify and to extract. We have developed two new techniques for pattern recognition and extraction designed for these situations. These techniques, extended cross correlation (XCC) and extended auto correlation (XAC), identify and extract multiple patterns from experimental data even when the number of derived patterns exceeds the number of experiments. The XCC, which is the focus of this paper, allows the rapid identification and extraction of patterns that are repeated in multiple experimental records. The related XAC technique permits the identification of complex patterns that are parameterized in a multidimensional way, even when the patterns are obscured by the presence of interfering data. The XCC and XAC provide straightforward methods for extracting the features which comprise a pattern, and can be applied in a model-free way. This paper provides a formal description of multidimensional forms of the XCC technique, and illustrates use of the XCC on large data sets with multiple patterns. (C) 1997 American Institute of Physics. [S0021-9606(97)02044-8].