Latent Variable Inference in Dynamical Systems Using Empirical Intrinsic Geometry

SpeakerDr. Ronen Talmon
Organization Technion - Israel Institute of Technology
LocationEB II 1230
DateAugust 29, 2014 12:50 PM

Abstract:

In this talk, we will present a data-driven method for building the canonical geometry of signal samples, which is independent of the coordinate system of the signal. This canonical geometry enables us to discover intrinsic latent variables, i.e., hidden variables which are invariant to the instrumental/measurement modalities and to ambient noise. We exploit the dynamics of the signal to explore the local tangent planes of the low-dimensional manifold of the signal. This information is used to define a Riemannian distance metric, which in turn is used to construct a Laplace operator. Such a construction is equivalent to an inverse problem, which is formulated as a nonlinear differential equation and is solved empirically through the eigenvectors of the Laplace operator. We will show that applying our method to simulation and real data allows for accurate recovery of latent intrinsic variables. Furthermore, the recovered latent variables have a true physical meaning. In particular, for biomedical signals, which are often difficult to analyze since they tend to be very noisy and highly dependent on the instrumental modality (e.g., the type of sensors used for the signal acquisition), we will show that the intrinsic variables give rise to a better understanding of the human body and brain.

Bio:

Ronen Talmon is an Assistant Professor of electrical engineering at the Technion - Israel Institute of Technology, Haifa, Israel. He received the B.A. degree (Cum Laude) in mathematics and computer science from the Open University in 2005, and the Ph.D. degree in electrical engineering from the Technion in 2011. From 2000 to 2005, he was a software developer and researcher at a technological unit of the Israeli Defense Forces. From 2005 to 2011, he was a Teaching Assistant at the Department of Electrical Engineering, Technion. From 2011 to 2013, he was a Gibbs Assistant Professor at the Mathematics Department, Yale University, New Haven, CT. In 2013, he joined the Department of Electrical Engineering of the Technion. His research interests are statistical signal processing, analysis and modeling of signals, speech enhancement, biomedical signal processing, applied harmonic analysis, and diffusion geometry. Dr. Talmon is the recipient of the Irwin and Joan Jacobs Fellowship, the Andrew and Erna Fince Viterbi Fellowship, and the Horev Fellowship.

  August 2014
Sun Mon Tues Wed Thu Fri Sat
     12
3456789
10111213141516
17181920212223
24252627282930
31