@article{10902/20607,
year = {2020},
url = {http://hdl.handle.net/10902/20607},
abstract = {This work presents a generalization of classical factor analysis (FA). Each of M channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the M multiple-input multipleoutput (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar.},
organization = {The work of D. Ramírez was supported in part by the Ministerio de Ciencia, Innovación y Universidades under Grant TEC2017-92552-EXP (aMBITION), in part by the Ministerio de Ciencia, Innovación y Universidades, jointly with the European Commission (ERDF), under Grant TEC2017-86921-C2-2-R (CAIMAN), and in part by The Comunidad de Madrid under Grant Y2018/TCS-4705 (PRACTICO-CM). The work of I. Santamaria and S. Van Vaerenbergh was supported by Ministerio de Ciencia, Innovación y Universidades and AEI/FEDER funds of the E.U. under Grant TEC2016-75067-C4-4-R (CARMEN). The work of L. L. Scharf was supported by National Science Foundation under Grant CCF-1712788.},
publisher = {Institute of Electrical and Electronics Engineers, Inc.},
publisher = {IEEE Transactions on Signal Processing, 2020, 68, 113-126},
title = {Multi-channel factor analysis with common and unique factors},
author = {Ramírez García, David and Santamaría Caballero, Luis Ignacio and Scharf, Louis L. and Vaerenbergh, Steven van},
}