title: Structured feature selection using coordinate descent optimization.
abstract: BACKGROUND
  Existing feature selection methods typically do not consider prior knowledge in the form of structural relationships among features. In this study, the features are structured based on prior knowledge into groups. The problem addressed in this article is how to select one representative feature from each group such that the selected features are jointly discriminating the classes. The problem is formulated as a binary constrained optimization and the combinatorial optimization is relaxed as a convex-concave problem, which is then transformed into a sequence of convex optimization problems so that the problem can be solved by any standard optimization algorithm. Moreover, a block coordinate gradient descent optimization algorithm is proposed for high dimensional feature selection, which in our experiments was four times faster than using a standard optimization algorithm.
  
  
  RESULTS
  In order to test the effectiveness of the proposed formulation, we used microarray analysis as a case study, where genes with similar expressions or similar molecular functions were grouped together. In particular, the proposed block coordinate gradient descent feature selection method is evaluated on five benchmark microarray gene expression datasets and evidence is provided that the proposed method gives more accurate results than the state-of-the-art gene selection methods. Out of 25 experiments, the proposed method achieved the highest average AUC in 13 experiments while the other methods achieved higher average AUC in no more than 6 experiments.
  
  
  CONCLUSIONS
  A method is developed to select a feature from each group. When the features are grouped based on similarity in gene expression, we showed that the proposed algorithm is more accurate than state-of-the-art gene selection methods that are particularly developed to select highly discriminative and less redundant genes. In addition, the proposed method can exploit any grouping structure among features, while alternative methods are restricted to using similarity based grouping.
authors.affiliation: Center for Data Analytics and Biomedical Informatics, College of Science and Technology, Temple University, North 12th Street, Philadelphia, 19122, PA, USA. mohamed.ghalwash@temple.edu.|Mathematics Department, Faculty of Science, Ain Shams University, Cairo, 11331, Egypt. mohamed.ghalwash@temple.edu.
authors.forename: Mohamed F
authors.initials: MF
authors.lastname: Ghalwash
authors.affiliation: Center for Data Analytics and Biomedical Informatics, College of Science and Technology, Temple University, North 12th Street, Philadelphia, 19122, PA, USA.
authors.forename: Xi Hang
authors.initials: XH
authors.lastname: Cao
authors.affiliation: Center for Data Analytics and Biomedical Informatics, College of Science and Technology, Temple University, North 12th Street, Philadelphia, 19122, PA, USA.|Signals and Systems Department, School of Electrical Engineering, University of Belgrade, Belgrade, Serbia.
authors.forename: Ivan
authors.initials: I
authors.lastname: Stojkovic
authors.affiliation: Center for Data Analytics and Biomedical Informatics, College of Science and Technology, Temple University, North 12th Street, Philadelphia, 19122, PA, USA.
authors.forename: Zoran
authors.initials: Z
authors.lastname: Obradovic
mesh_terms: D000465:Algorithms; D016510:Corneal Neovascularization / Q000175:diagnosis / Q000235:genetics; D030541:Databases, Genetic; D005786:Gene Expression Regulation; D063990:Gene Ontology; D014644:Genetic Variation; D015658:HIV Infections / Q000175:diagnosis / Q000235:genetics; D006456:Hemoglobinuria / Q000175:diagnosis / Q000235:genetics; D006801:Humans; D008545:Melanoma / Q000175:diagnosis / Q000235:genetics; D046228:Microarray Analysis; D008962:Models, Theoretical; D009101:Multiple Myeloma / Q000175:diagnosis / Q000235:genetics; D018358:Neuroendocrine Tumors / Q000175:diagnosis / Q000235:genetics; D009506:Nevus / Q000175:diagnosis / Q000235:genetics; D013312:Stress, Physiological / Q000235:genetics; D014777:Virus Diseases / Q000175:diagnosis / Q000235:genetics
keywords: Block coordinate gradient descent; Gene expression; Microarray analysis; Prior knowledge; Structured feature selection