<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Lester Mackey</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Deflation Methods for Sparse PCA</style></title><secondary-title><style face="normal" font="default" size="100%">Neural Information Processing Systems (NIPS'08)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">12/2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://books.nips.cc/papers/files/nips21/NIPS2008_0197.pdf</style></url></web-urls></urls><pub-location><style face="normal" font="default" size="100%">Vancouver, Canada</style></pub-location><pages><style face="normal" font="default" size="100%">1-8</style></pages><abstract><style face="normal" font="default" size="100%">In analogy to the PCA setting, the sparse PCA problem is often solved by iter- 
atively alternating between two subtasks: cardinality-constrained rank-one vari- 
ance maximization and matrix deﬂation. While the former has received a great 
deal of attention in the literature, the latter is seldom analyzed and is typically 
borrowed without justiﬁcation from the PCA context. In this work, we demon- 
strate that the standard PCA deﬂation procedure is seldom appropriate for the 
sparse PCA setting. To rectify the situation, we ﬁrst develop several deﬂation al- 
ternatives better suited to the cardinality-constrained context. We then reformulate 
the sparse PCA optimization problem to explicitly reﬂect the maximum additional 
variance objective on each round. The result is a generalized deﬂation procedure 
that typically outperforms more standard techniques on real-world datasets. 

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