@inproceedings{6c8d97cbaee8450b8ed32b51b93a099b,
title = "An order fitting rule for optimal subspace averaging",
abstract = "The problem of estimating a low-dimensional subspace from a collection of experimentally measured subspaces arises in many applications of statistical signal processing. In this paper we address this problem, and give a solution for the average subspace that minimizes an extrinsic mean-squared error, defined by the squared Frobenius norm between projection matrices. The solution automatically returns the dimension of the optimal average subspace, which is the novel result of the paper. The proposed order fitting rule is based on thresholding the eigenvalues of the average projection matrix, and thus it is free of penalty terms or other tuning parameters commonly used by other rank estimation techniques. Several numerical examples demonstrate the usefulness and applicability of the proposed criterion, showing how the dimension of the average subspace captures the variability of the measured subspaces.",
keywords = "Grassmann manifold, Subspace signal processing, extrinsic mean, flag manifold, order-fitting, subspace averaging",
author = "I. Santamaria and Scharf, {L. L.} and C. Peterson and M. Kirby and J. Francos",
note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 19th IEEE Statistical Signal Processing Workshop, SSP 2016 ; Conference date: 25-06-2016 Through 29-06-2016",
year = "2016",
month = aug,
day = "24",
doi = "10.1109/SSP.2016.7551843",
language = "English",
series = "IEEE Workshop on Statistical Signal Processing Proceedings",
publisher = "Institute of Electrical and Electronics Engineers",
booktitle = "2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016",
address = "United States",
}