On the convergence of row-modification algorithm for matrix projections

Authors:
Xiaomi Hu;Jürgen Hansohm;Linda Hoffmann;Ye Emma Zohner
Affiliations:
Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260-0033, USA;University of the Federal Armed Forces, Munich, Germany;Wichita State University, Wichita, KS, USA;Wichita State University, Wichita, KS, USA
Venue:
Journal of Multivariate Analysis
Year:
2012

Citing 2
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Multivariate isotonic regression under tree semi-order restrictions and test in multivariate normal distribution

ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part II

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Abstract

This paper proposes an algorithm for matrix minimum-distance projection, with respect to a metric induced from an inner product that is the sum of inner products of column vectors, onto the collection of all matrices with their rows restricted in closed convex sets. This algorithm produces a sequence of matrices by modifying a matrix row by row, over and over again. It is shown that the sequence is convergent, and it converges to the desired projection. The implementation of the algorithm for multivariate isotonic regressions and numerical examples are also presented in the paper.