Extraction of Components with Structured Variance

We present a method for exploratory data analysis of large spatiotemporal data sets such as global longtime climate measurements, extending our previous work on semiblind source separation of climate data. The method seeks fast changing components whose variances exhibit slow behavior with specific temporal structure. The algorithm is developed in the framework of denoising source separation. It finds sources iteratively and alternates between estimating the variance structure of extracted sources and using the structure to find new source estimates. The performance of the algorithm is first demonstrated on a simple example of a semiblind source separation problem with artificially generated signals. Then, the proposed technique is applied to the global surface temperature measurements coming from the NCEP/NCAR re-analysis project. Fast changing temperature components whose variances have prominent annual and decadal structures are extracted. The extracted annual components reflect higher temperature variability over the continents during winters. The components with slower changing variances might correspond to some interesting weather phenomena characterized by slowly changing temperature variability in specific regions.