A Note on Using Multiple Singular Value Decompositions to Cluster Complex Intracellular Calcium Ion Signals

Recently (Martinez et al. 2010),we compared calciumion signaling (Ca2+) between two exposures, where the data present as movies, or, more prosaically, time series of images. They described novel uses of singular value decompositions (SVD) and weighted versions of them (WSVD) to extract the signals from such movies, in a way that is semi-automatic and tuned closely to the actual data and their many complexities. These complexities include the following. First, the images themselves are of no interest: all interest focuses on the behavior of individual cells across time, and thus the cells need to be segmented in an automated manner. Second, the cells themselves have 100+ pixels, so that they form 100+ curves measured over time, so that data compression is required to extract the features of these curves. Third, some of the pixels in some of the cells are subject to image saturation due to bit depth limits, and this saturation needs to be accounted for if one is to normalize the images in a reasonably unbiased manner. Finally, theCa2+ signals have oscillations orwaves that vary with time and these signals need to be extracted. Thus, they showed how to use multiple weighted and standard singular value decompositions to detect, extract and clarify the Ca2+ signals. In this paper,we showhow this signal extraction lends itself to a cluster analysis of the cell behavior, which shows distinctly different patterns of behavior.