Part of the experience of giving a talk at Oberwolfach is documentation. First, they ask you to handwrite the abstract of your talk into a notebook of sorts for safekeeping. Later, they ask you to tex up an extended abstract for further documentation. This time, I gave a longer version of my SPIE talk (here are the slides). Since I posted my extended abstract on my blog last time, I figured I’d do it again:

This talk describes recent work on three different problems of interest in mathematical data science, namely, compressive classification, -means clustering, and deep learning. (Based on three papers: one, two, three.)

First, compressive classification is a problem that comes on the heels of compressive sensing. In compressive sensing, one exploits the underlying structure of a signal class in order to exactly reconstruct any signal from the class given very few linear measurements of the signal. However, many applications do not require an exact reconstruction of the image, but rather a classification of that image (for example, is this a picture of a cat, or of a dog?). As such, it makes intuitive sense that the classification task might succeed given far fewer measurements than are necessary for compressive sensing.

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