TY - GEN
T1 - Common component analysis for multiple covariance matrices
AU - Wang, Huahua
AU - Banerjee, Arindam
AU - Boley, Daniel L
PY - 2011
Y1 - 2011
N2 - We consider the problem of finding a suitable common low dimensional subspace for accurately representing a given set of covariance matrices. With one covariance matrix, this is principal component analysis (PCA). For multiple covariance matrices, we term the problem Common Component Analysis (CCA).While CCA can be posed as a tensor decomposition problem, standard approaches to tensor decompositions have two critical issues: (i) tensor decomposition methods are iterative and rely on the initialization; (ii) for a given level of approximation error, it is difficult to choose a suitable low dimensionality. In this paper, we present a detailed analysis of CCA that yields an effective initialization and iterative algorithms for the problem. The proposed methodology has provable approximation guarantees w.r.t. the global maximum and also allows one to choose the dimensionality for a given level of approximation error. We also establish conditions under which the methodology will achieve the global maximum. We illustrate the effectiveness of the proposed method through extensive experiments on synthetic data as well as on two real stock market datasets, where major financial events can be visualized in low dimensions.
AB - We consider the problem of finding a suitable common low dimensional subspace for accurately representing a given set of covariance matrices. With one covariance matrix, this is principal component analysis (PCA). For multiple covariance matrices, we term the problem Common Component Analysis (CCA).While CCA can be posed as a tensor decomposition problem, standard approaches to tensor decompositions have two critical issues: (i) tensor decomposition methods are iterative and rely on the initialization; (ii) for a given level of approximation error, it is difficult to choose a suitable low dimensionality. In this paper, we present a detailed analysis of CCA that yields an effective initialization and iterative algorithms for the problem. The proposed methodology has provable approximation guarantees w.r.t. the global maximum and also allows one to choose the dimensionality for a given level of approximation error. We also establish conditions under which the methodology will achieve the global maximum. We illustrate the effectiveness of the proposed method through extensive experiments on synthetic data as well as on two real stock market datasets, where major financial events can be visualized in low dimensions.
KW - Dimensionality reduction
KW - Parafac
KW - Pca
KW - Tensor decompositions
KW - Tucker
UR - http://www.scopus.com/inward/record.url?scp=80052650747&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80052650747&partnerID=8YFLogxK
U2 - 10.1145/2020408.2020565
DO - 10.1145/2020408.2020565
M3 - Conference contribution
AN - SCOPUS:80052650747
SN - 9781450308137
T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
SP - 956
EP - 964
BT - Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD'11
PB - Association for Computing Machinery
T2 - 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2011
Y2 - 21 August 2011 through 24 August 2011
ER -