Baraniuk, Richard G2016-02-052016-02-052015-052015-04-21May 2015Patel, Raajen. "oASIS: Adaptive Column Sampling for Kernel Matrix Approximation." (2015) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/88435">https://hdl.handle.net/1911/88435</a>.https://hdl.handle.net/1911/88435Kernel or similarity matrices are essential for many state-of-the-art approaches to classification, clustering, and dimensionality reduction. For large datasets, the cost of forming and factoring such kernel matrices becomes intractable. To address this challenge, we introduce a new adaptive sampling algorithm called Accelerated Sequential Incoherence Selection (oASIS) that samples columns without explicitly computing the entire kernel matrix. We provide conditions under which oASIS is guaranteed to exactly recover the kernel matrix with an optimal number of columns selected. Numerical experiments on both synthetic and real-world datasets demonstrate that oASIS achieves performance comparable to state-of-the-art adaptive sampling methods at a fraction of the computational cost. The low runtime complexity of oASIS and its low memory footprint enable the solution of large problems that are simply intractable using other adaptive methods.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Machine LearningMatrix ApproximationKernel MethodsThesis2016-02-05