TY - GEN
T1 - Sparse factor analysis via likelihood and ℓ1-regularization
AU - Ning, Lipeng
AU - Georgiou, Tryphon T.
PY - 2011
Y1 - 2011
N2 - In this note we consider the basic problem to identify linear relations in noise. We follow the viewpoint of factor analysis (FA) where the data is to be explained by a small number of independent factors and independent noise. Thereby an approximation of the sample covariance is sought which can be factored accordingly. An algorithm is proposed which weighs in an ℓ1-regularization term that induces sparsity of the linear model (factor) against a likelihood term that quantifies distance of the model to the sample covariance. The algorithm compares favorably against standard techniques of factor analysis. Their performance is compared first by simulation, where ground truth is available, and then on stock-market data where the proposed algorithm gives reasonable and sparser models.
AB - In this note we consider the basic problem to identify linear relations in noise. We follow the viewpoint of factor analysis (FA) where the data is to be explained by a small number of independent factors and independent noise. Thereby an approximation of the sample covariance is sought which can be factored accordingly. An algorithm is proposed which weighs in an ℓ1-regularization term that induces sparsity of the linear model (factor) against a likelihood term that quantifies distance of the model to the sample covariance. The algorithm compares favorably against standard techniques of factor analysis. Their performance is compared first by simulation, where ground truth is available, and then on stock-market data where the proposed algorithm gives reasonable and sparser models.
UR - http://www.scopus.com/inward/record.url?scp=84860693024&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84860693024&partnerID=8YFLogxK
U2 - 10.1109/CDC.2011.6161415
DO - 10.1109/CDC.2011.6161415
M3 - Conference contribution
AN - SCOPUS:84860693024
SN - 9781612848006
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5188
EP - 5192
BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Y2 - 12 December 2011 through 15 December 2011
ER -