Bayesian Inference via Low-Dimensional Manifolds for Attributed Data Points
Rebekah L Farrar · OhioLink ETD Center (Ohio Library and Information Network) · 2013
An important problem in many disciplines is the extraction of information from extremely large datasets, sometimes with billions of dimensions.This problem is compounded by the many applications that incorporate multiple sensor modalities to create a layered sensing scheme within a single scene.However, the intrinsic dimensionality of the data that needs to be extracted is often much less than the dimensionality of the data itself.Therefore, inference schemes that exploit the structure of the data can be designed around reducing the dimensionality of the data set.Dimensionality reduction has many applications, including pattern recognition, image analysis, and data compression.Unfortunately, the common techniques, such as Principal Component Analysis (PCA), are limited by the absence of an associated probability density.There would be several advantages to the addition of a probability density.First, it would enable Bayesian inference methods.Second, classification tasks would benefit from the added information gained by posterior probabilities.In sensing applications, the training data may be accompanied by one or more labels that define a nonlinear data manifold.For instance, with optical data, it may be the case that the angle of the object relative to the viewing direction is known.This creates an intrinsic pose angle parameter that the high-dimensional data is labeled with.We propose a method to exploit this measured intrinsic variable when performing dimension reduction and inference.Data are modeled as jointly Gaussian in the projected space, iii conditioned on pose angle, the measured intrinsic variable.An example application is demonstrated using simulated X-band radar scattering from civilian vehicles.I would like to extend thanks to my advisers, Dr. Lee Potter and Dr. Emre Ertin.Without their careful explanations and sage advice this thesis would not have been possible.They have been my greatest supporters and encouragers throughout this entire process.I would also like to thank the Department of Electrical and Computer Engineering at the Ohio State University as well as IUCRC.Without their financial support, completing a master's degree would have been immeasurably more challenging.I would like to especially thank Dr. Lee