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Bengisu Ozbay PhD Dissertation Defense
April 17, 2024 @ 12:00 pm - 2:00 pm
Name:
Bengisu Ozbay
Title:
Fast Semi-Algebraic Clustering for Efficient System Identification and
Geometric Scene Understanding
Date:
4/17/2024
Time:
12:00:00 PM
Location:(EV) 102
Committee Members:
Prof. Mario Sznaier (Advisor)
Prof. Octavia Camps
Prof. Taskin Padir
Prof. Rifat Sipahi
Abstract:
As the demand for data-driven techniques in machine learning and computer vision continues to rise, the reliance on unsupervised learning methods becomes increasingly prevalent. Piecewise linear or affine models offer versatile solutions across various domains, including system identification and computer vision tasks.
This dissertation introduces an efficient methodology that relies solely on singular value decomposition of matrices, maintaining a fixed size independent of the total number of data points. Remarkably, this method only requires execution a number of times equivalent to the number of clusters. Through singular value decomposition (SVD) of the empirical moments matrix containing the data, we demonstrate the feasibility of identifying the polynomials representing hyperplanes. Central to this approach is the utilization of polynomials and Christoffel functions, facilitating the partitioning of data into distinct clusters, each with its own set of parameters extracted using application-specific techniques.
The dissertation explores various challenges, including semi-algebraic clustering, identification of switching auto-regressive models with exogenous inputs (SARX), affine linear subspace clustering, two-view motion segmentation, identification of Wiener systems, and switched nonlinear system identification using block-oriented models. The proposed semi-algebraic clustering framework identifies reliable subsets from data, sequentially segments data using Christoffel polynomials, and extends the approach beyond linear affine arrangements to address challenges involving quadratic surfaces in two-view motion segmentation and higher order algebraic varieties in switched-Wiener system identification.