Gobble Gobble: Random Graph Models for Large Empirical Networks and Blind Source Separation Techniques for Multiply Labeled Fluorescence Images

Sarah Rich
Sometimes in life things are complicated, and we just wish they were simpler! (Am I right, ladies?) A standard approach of theoreticians is to just pretend that they *are* simpler and keep going! We’ll consider this approach in the context of models for large empirical networks, like social networks and the Internet, and see where it succeeds and fails, how and why. We will use this open-ended exploration to motivate some of the questions the Speaker intends to pursue in her Master’s Thesis, and describe a bit about her successes and failings thus far!

Sumeet Kataria
Methods of blind source separation are used in many contexts to separate composite data sets according to their sources. Multiply labeled fluorescence microscopy images represent such sets, in which the sources are the individual labels. Their distributions are the quantities of interest and have to be extracted from the images. Non-negative matrix factorization (NMF) is the standard technique used to obtain the emission spectra of the identified components and images of their abundance. However, the solutions are not unique when spectra overlap strongly or when images are diffuse in their structure. To arrive at satisfactory results in such cases, we extend NMF with additional constraints to incorporate pre-existing knowledge about spectra and label distributions. We also use recent greedy coordinate descent algorithms to perform the decomposition – these methods are faster than the multiplicative update methods currently used. This speed-up is valuable in microscopy applications where the data sets have temporal, spectral and 3D-spatial information, and consequently are large. Our experiments suggest that these techniques can also be useful to obtain weak spectra in the presence of other strong spectra.