Classification with high-dimensional variables is a popular goal in many modern statistical studies. Fisher's linear discriminant analysis (LDA) is a common and effective tool for classifying entities into existing groups. It is well known that classification using Fisher's discriminant for high-dimensional data is as bad as random guessing because of the use of many noise features, which increases the misclassification rate. Recently, it is being acknowledged that complex biological mechanisms occur through multiple features working together, though individually these features may contribute to noise accumulation in the data. In view of these, it is important to perform classification with discriminant vectors that use a subset of important variables, while also utilizing prior biological relationships among features. We tackle this problem in this paper and propose methods that incorporate variable selection into the classification problem for the identification of important biomarkers. Furthermore, we incorporate into the LDA problem prior information on the relationships among variables using undirected graphs in order to identify functionally meaningful biomarkers. We compare our methods with existing sparse LDA approaches via simulation studies and real data analysis.
Bibliographical noteFunding Information:
We thank the Emory Predictive Health Institute Center for Health Discovery and Well Being for providing us with the gene expression and clinical data. Sandra Safo’s work was supported by NIH grant K12HD085850. Qi Long’s work was supported by NIH grants R03CA173770, R03CA183006, P30CA016520, and R01GM124111. The content of this paper is solely the responsibility of the authors and does not represent the views of the NIH.
- biological information, pathway analysis
- high-dimensional data
- linear discriminant analysis