Geometry in Signal Processing and Machine Learning ( Report on a Workshop Sponsored by the National Science Foundation )

The purpose of the Estes Park Workshop was to assemble mathematicians, statisticians, and engineers to explore problems in signal processing and machine learning, within the purview of CISE, that would be illuminated by a geometric view and be solved by methods of Riemannian, differential, symplectic, and algebraic geometry. The workshop was the latest in a sequence of workshops convened by Dr. John Cozzens of NSF:

[1]  Stephen D. Howard,et al.  An exact Bayesian detector for multistatic passive radar , 2016, 2016 50th Asilomar Conference on Signals, Systems and Computers.

[2]  Louis L. Scharf,et al.  An order fitting rule for optimal subspace averaging , 2016, 2016 IEEE Statistical Signal Processing Workshop (SSP).

[3]  Joseph M. Francos,et al.  Universal Manifold Embedding for Geometrically Deformed Functions , 2016, IEEE Transactions on Information Theory.

[4]  Shun-ichi Amari,et al.  Information Geometry and Its Applications , 2016 .

[5]  Thomas A. Palka.  Bounds and algorithms for subspace estimation on Riemannian quotient submanifolds , 2016 .

[6]  Bruce A. Draper,et al.  Finding the Subspace Mean or Median to Fit Your Need , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[7]  Stephen D. Howard,et al.  Passive radar detection using multiple transmitters , 2013, 2013 Asilomar Conference on Signals, Systems and Computers.

[8]  William Moran,et al.  Bayesian recursive estimation on the rotation group , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[9]  Peter Schwander,et al.  The symmetries of image formation by scattering. II. Applications. , 2011, Optics express.

[10]  Peter Schwander,et al.  The symmetries of image formation by scattering. I. Theoretical framework. , 2010, Optics express.

[11]  Rama Chellappa,et al.  Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Louis L. Scharf,et al.  Detection of Spatially Correlated Gaussian Time Series , 2010, IEEE Transactions on Signal Processing.

[13]  Joseph M. Francos,et al.  Parametric Estimation of Affine Transformations: An Exact Linear Solution , 2009, Journal of Mathematical Imaging and Vision.

[14]  Mikhail Belkin,et al.  Towards a theoretical foundation for Laplacian-based manifold methods , 2005, J. Comput. Syst. Sci..

[15]  Jingdong Chen,et al.  Microphone Array Signal Processing , 2008 .

[16]  Louis L. Scharf,et al.  Intrinsic Quadratic Performance Bounds on Manifolds , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[17]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[18]  Ann B. Lee,et al.  Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[19]  S.T. Smith,et al.  Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds , 2005, IEEE Transactions on Signal Processing.

[20]  Yi Ma.  A Differential Geometric Approach to Multiple View Geometry in Spaces of Constant Curvature , 2004, International Journal of Computer Vision.

[21]  P. Absil,et al.  Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation , 2004 .

[22]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[23]  A. Leshem,et al.  Multichannel detection of Gaussian signals with uncalibrated receivers , 2001, IEEE Signal Processing Letters.

[24]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[25]  Trevor F. Cox,et al.  Metric multidimensional scaling , 2000 .

[26]  F. Solis.  Geometry of Local Adaptive Galerkin Bases , 2000 .

[27]  I. Hassan.  Embedded , 2005, The Cyber Security Handbook.

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[32]  R. Wijsman.  Invariant measures on groups and their use in statistics , 1990 .

[33]  Robert A. Wijsman.  Proper Action in Steps, with Application to Density Ratios of Maximal Invariants , 1985 .

[34]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

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