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Topological Data Analysis (TDA) is a topic which has recently seen many applications. The goal of this special session is to highlight the bridge between signal processing, machine learning and techniques in topological data analysis. In this way, we hope to encourage more engineers to start exploring TDA and its applications. This paper briefly introduces the standard techniques used in this area, delineates the common theme connecting the works presented in this session, and concludes with a brief summary of each of the papers presented.

We consider the problem of selecting optimal sensor placements. The proposed approach is based on the sampling theorem of graph signals. We choose sensors that maximize the graph cut-off frequency, i.e., the most informative sensors for predicting the values on unselected sensors. We study the existing methods in the context of graph signal processing and clarify the relationship between these methods and the proposed approach. The effectiveness of our approach is verified through numerical experiments, showing advantages in prediction error and execution time.

SmartRoadSense is a collaborative project aimed at monitoring road surface conditions exploiting the sensors, i.e., accelerometers and GPS, commonly embedded in most mobile devices. Given a smartphone connected to the cabin of a car travelling on a road, the SmartRoadSense app analyzes the accelerometer signals and extracts a roughness index (based on a linear predictive coding analysis) characterizing the quality of the road.

We consider the problem of solving a quadratic potential game with single quadratic constraints, under no monotonicity condition of the game, nor convexity in any of the player's problem. We show existence of Nash equilibria (NE) in the game, and propose a framework to calculate Pareto efficient solutions. Regarding the corresponding non-convex potential function, we show that strong duality holds with its corresponding dual problem, give existence results of solutions and present conditions for global optimality. Finally, we propose a centralized method to solve the potential problem, and a distributed version for compact constraints. We also present simulations showing convergence behavior of the proposed distributed algorithm.

In the 1960s, Marshall McLuhan published the book entitled, The Extensions of Man focusing primarily on television, an electronic media as being the outward extension of human nervous system, which from contemporary interpretation marks the previous stage of Big Data.

Ph.D. Thesis by Donald McCuan (advisor Andrew Knyazev), Department of Mathematical and Statistical Sciences, University of Colorado Denver, 2012, originally posted at http://math.ucdenver.edu/theses/McCuan_PhdThesis.pdf (1126)

Presentation at LANL and UC Davis, 2009. Originally posted at http://math.ucdenver.edu/~aknyazev/research/conf/

We develop novel algorithms and software on parallel computers for data clustering of large datasets. We are interested in applying our approach, e.g., for analysis of large datasets of microarrays or tiling arrays in molecular biology and for segmentation of high resolution images.