Multi-channel factor analysis with common and unique factors

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...

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Detalles Bibliográficos
Autores: Ramírez García, David, Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436, Scharf, Louis L., Vaerenbergh, Steven van|||0000-0003-3091-0171
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/20607
Acceso en línea:http://hdl.handle.net/10902/20607
Access Level:acceso abierto
Palabra clave:Block minorization-maximization (BMM) algorithms
Expectation-maximization (EM) algorithms
Maximum likelihood (ML) estimation
Multi-channel factor analysis (MFA)
Multiple-input multiple-output (MIMO) channels
Passive radar
Descripción
Sumario: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.