Multidimensional nonlinear embedding models for image scene dimensionality reduction and visualization

Wadzanai D Lunga, Purdue University

Abstract

Many pattern recognition applications rely on building decision making models based on meaningful and often hidden patterns of real world objects represented as points in a high dimensional feature space. Such a space presents great opportunities, as well as computational modeling hurdles that include the curse of dimensionality. Assumptions are often made, and more challenges encountered in easing the difficulty of analyzing and interpreting such data. The first step could be to assume that regular data information resides on a lower dimensional manifold. An immediate challenge is how to design mapping models such that the nonlinear relationships in observations are captured by Euclidean or non-Euclidean manifolds. Furthermore, can there be a general nonlinear embedding framework whose platform has functional properties for building new solutions to the problem of dimensionality reduction? To address these challenges, this thesis embarks on three fronts to provide and develop efficient nonlinear dimensionality algorithms by exploiting the regularity details within image scenes. First, it presents a non-Euclidean spherical stochastic neighbor embedding technique for the purposes of mapping data whose similarity spectrum suggests a nonzero negative eigenfraction. Secondly, the study presents a general framework based on the dynamic equations described by gradient potential fields. The framework incorporates a force field intuition to seek a minimum energy configuration state of a neighborhood graph. Thirdly, the platform is applied to propose novel unsupervised multidimensional artificial field embedding techniques that rely on the intuitive superposition of pair-dependent quadratic distance attraction and inverse-distance repulsion functions. The proposed models provide capabilities that preserve the local topology of data and establish significant discriminatory boundaries between different structures. Experimental investigations for visualization, gradient field trajectories, and semisupervised classification on remote sensing and computer vision images demonstrate the superiority of the proposed models over current state-of-art methods.

Degree

Ph.D.

Advisors

Ersoy, Purdue University.

Subject Area

Computer Engineering|Electrical engineering|Computer science

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