The Geomblog

(Via Lance) Partha Niyogi just passed away.

I first met Partha at SoCG 2007 in Gyeongju, where he gave an invited presentation on geometric perspectives in machine learning. We also spent a very pleasant day playing hookey from the conference, wandering around the nearby tourist spots, and talking about geometry and machine learning. He was a brilliant researcher with an impatience and drive that led him to do some truly excellent work.

Anyone who's ever dabbled in machine learning knows about the strong connections between ML and geometry, dating back to the very notion of VC dimension. But while the connections between the areas are manifest and plentiful, there haven't been many people who could successfully navigate both realms. Partha was one of those unusual people, who coupled deep mathematical insight with a strong vision for problems in ML. Most recently, he organized a wonderful summer school in machine learning and geometry, whose syllabus is worth perusing to get a sense of the depth of this interaction.

In many circles, he's most known for his work in manifold learning, where in collaboration with Misha Belkin, Steve Smale and others, he laid out a series of rigorous results on the problem of how to "learn" a low dimensional manifold given access to samples of points from it. The work on Laplacian Eigenmaps is a key marker in this area, and has had tremendous influence in the realm of "non-Euclidean" data analysis. Among his other recent contributions in theory-land are a neat result from FOCS 2006 with Belkin and Narayanan on sampling the surface of a convex polytope using heat flow and the Laplace operator.

It's a great loss.

Via Michael Trick comes the news that David Gale has died. To us CS folks, he's probably best known for the Gale-Shapely stable marriage algorithm (that has controlled the lives of thousands of medical interns since - talk about impact !), and the Gale Transform in projective geometry.

Apart from all of that, he was also a tremendously influential economist and expert in optimization. His obituary has much more.