Characterizing L1-norm best-fit subspaces

J. Paul Brooks; José H. Dulá

doi:10.1117/12.2263690

5 May 2017 Characterizing L1-norm best-fit subspaces

J. Paul Brooks, José H. Dulá

Proceedings Volume 10211, Compressive Sensing VI: From Diverse Modalities to Big Data Analytics; 1021103 (2017) https://doi.org/10.1117/12.2263690
Event: SPIE Commercial + Scientific Sensing and Imaging, 2017, Anaheim, CA, United States

Abstract

Fitting affine objects to data is the basis of many tools and methodologies in statistics, machine learning, and signal processing. The L1 norm is often employed to produce subspaces exhibiting a robustness to outliers and faulty observations. The L1-norm best-fit subspace problem is directly formulated as a nonlinear, nonconvex, and nondifferentiable optimization problem. The case when the subspace is a hyperplane can be solved to global optimality efficiently by solving a series of linear programs. The problem of finding the best-fit line has recently been shown to be NP-hard. We present necessary conditions for optimality for the best-fit subspace problem, and use them to characterize properties of optimal solutions.

Conference Presentation

Citation Download Citation

J. Paul Brooks and José H. Dulá "Characterizing L1-norm best-fit subspaces", Proc. SPIE 10211, Compressive Sensing VI: From Diverse Modalities to Big Data Analytics, 1021103 (5 May 2017); https://doi.org/10.1117/12.2263690

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