From Event: SPIE Commercial + Scientific Sensing and Imaging, 2017
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.
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 (Presented at SPIE Commercial + Scientific Sensing and Imaging: April 12, 2017; Published: 5 May 2017); https://doi.org/10.1117/12.2263690.
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