10:30 AM on Thursday, June 20, 2013
Location: Virginia Tech Research Center, 900 N. Glebe Rd., Arlington, VA
Invited Speaker: Gustavo K. Rohde, Ph.D., Assoc Prof of BME and ECE, Carnegie Mellon University
Numerous applications in modern science and technology require pattern recognition to be performed in signal and image databases. The predominant scenario in these applications is that the dimension of available signals is usually much larger than the number of data samples available. In dealing with sparsely populated high-dimensional ambient spaces, the assumption of appropriate underlying generative models can significantly facilitate useful outcomes such as high detection and classification rates, as well as visualization and interpretation of the observed phenomena. While the field of harmonic analysis has provided numerous tools (e.g. Fourier & wavelet transforms, etc.) enabling the development of digital sensors and communication networks, mathematical approaches to mining "structural" information in signal and image databases have been limited. Existing tools (numerical feature extraction, textons, PCA transforms, data-driven manifold learning, etc.) can be effective in many cases. However, they operate without utilizing any underlying generative model for the variation of structure (appearance) in a given database. Hence their adoption in any given application is limited to trial and error while interpretation, visualization, as well as generative (analytical) modeling of appearance is often difficult.
In thinking about the variation in a signal/image database, for example, one can directly observe that these can be explained by deformations of the underlying coordinate space, as well as intensity changes (morphing). Inspired by the continuity equation, I will describe a framework for the analysis of positive semi definite signals that utilizes the theory of optimal transport as an underlying mathematical model for explaining observed appearance variations. Based on a linearized version of the optimal transport metric, we have developed a new, nonlinear, computationally efficient, data embedding method (transform) which can allow one to measure meaningful distances between samples (signals or images). As opposed to alternative methods, the distance we propose is a true mathematical distance (no information loss) on signal/image space, while its computation does not depend on other samples in the database. Furthermore, the framework also allows for direct and automated generative modeling, thus enabling meaningful visualization and understanding of appearance variations. We demonstrate the application of the framework to the analysis of biomedical images. Specifically, we show that the framework has the potential to obtain higher discrimination accuracies in comparison to existing approaches in cancer detection problems from cell phenotypes. Furthermore, we show the approach can be useful in extracting interpretable biological information explaining differences between sub cellular structures in cancer detection and other problems.