Summarizing complexity in high dimensions

High-dimensional, multispectral data on complex physical systems are increasingly common. As the amount of information in data sets increases, the difficulty of effectively utilizing it also increases. For such data, summary information is required for understanding and modeling the underlying dynamics. It is here proposed to use an extension of computational mechanics [C. R. Shalizi and J. P. Crutchfield, J. Stat. Phys. 104, 817 (2001)] to arbitrary spatiotemporal and spectral dimension, for providing such summary information. An example of the use of these tools to identify state evolution in the brain, an archetypal, complex biophysical system, serves as an illustration.