{"id":168073,"date":"2015-05-01T00:00:00","date_gmt":"2015-05-01T00:00:00","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/understanding-and-evaluating-sparse-linear-discriminant-analysis\/"},"modified":"2018-10-16T20:06:42","modified_gmt":"2018-10-17T03:06:42","slug":"understanding-and-evaluating-sparse-linear-discriminant-analysis","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/understanding-and-evaluating-sparse-linear-discriminant-analysis\/","title":{"rendered":"Understanding and Evaluating Sparse Linear Discriminant Analysis"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Linear discriminant analysis (LDA)<br \/>\nrepresents a simple yet powerful technique for partitioning a p-dimensional<br \/>\nfeature vector into one of K classes based on a linear projection learned from<br \/>\nN labeled observations.  However, it is well-established<br \/>\nthat in the high-dimensional setting (p > N) the underlying projection<br \/>\nestimator degenerates. Moreover, any linear discriminate function involving a<br \/>\nlarge number of features may be difficult to interpret. To ameliorate these<br \/>\nissues, two general categories of sparse LDA modifications have been proposed,<br \/>\nboth to reduce the number of active features and to stabilize the resulting<br \/>\nprojections. The first, based on optimal scoring, is more straightforward to<br \/>\nimplement and analyze but has been heavily criticized for its ambiguous<br \/>\nconnection with the original LDA formulation. In contrast, a second strategy<br \/>\napplies sparse penalty functions directly to the original LDA objective but<br \/>\nrequires additional heuristic trade-off parameters, has unknown global and<br \/>\nlocal minima properties, and requires a greedy sequential optimization<br \/>\nprocedure.  In all cases the choice of<br \/>\nsparse regularizer can be important, but no rigorous guidelines have been<br \/>\nprovided regarding which penalty might be preferable. Against this backdrop, we<br \/>\nwinnow down the broad space of candidate sparse LDA algorithms and promote a<br \/>\nspecific selection based on optimal scoring coupled with a particular, complementary<br \/>\nsparse regularizer. This overall process ultimately progresses our<br \/>\nunderstanding of sparse LDA in general, while leading to targeted modifications<br \/>\nof existing algorithms that produce superior results in practice on three high-dimensional<br \/>\ngene data sets.<\/p>\n<p><\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Linear discriminant analysis (LDA) represents a simple yet powerful technique for partitioning a p-dimensional feature vector into one of K classes based on a linear projection learned from N labeled observations. However, it is well-established that in the high-dimensional setting (p > N) the underlying projection estimator degenerates. Moreover, any linear discriminate function involving a [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Artificial Intelligence and Statistics (AISTATS)","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Yi Wu, Jeong-Min 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