Sparse factor analysis via likelihood and ℓ1-regularization

Lipeng Ning; Tryphon T. Georgiou

doi:10.1109/CDC.2011.6161415

Sparse factor analysis via likelihood and ℓ₁-regularization

Lipeng Ning, Tryphon T. Georgiou

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

13 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5188-5192
Number of pages	5
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6161415
State	Published - 2011
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: Dec 12 2011 → Dec 15 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 12/15/11

Publisher link

10.1109/CDC.2011.6161415

Find It

Find It at U of M Libraries

Cite this

Ning, L., & Georgiou, T. T. (2011). Sparse factor analysis via likelihood and ℓ₁-regularization. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 5188-5192). [6161415] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6161415

Sparse factor analysis via likelihood and ℓ₁-regularization. / Ning, Lipeng; Georgiou, Tryphon T.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 5188-5192 6161415 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ning, L & Georgiou, TT 2011, Sparse factor analysis via likelihood and ℓ₁-regularization. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161415, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5188-5192, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161415

@inproceedings{a2967a94fe384109b109a4040ae38792,

title = "Sparse factor analysis via likelihood and ℓ1-regularization",

abstract = "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.",

author = "Lipeng Ning and Georgiou, {Tryphon T.}",

year = "2011",

doi = "10.1109/CDC.2011.6161415",

language = "English (US)",

isbn = "9781612848006",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "5188--5192",

booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

}

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 -