A Road to Classification in High Dimensional Space: The Regularized Optimal Affine Discriminant

• DOI: 10.1111/j.1467-9868.2012.01029.x
• Publication Date: 2012-04-12T20:17:57Z
• Authors: Jianqing Fan; Yang Feng; Xin Tong
• Keywords: Independence; Regularization

For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due diverging spectra and noise accumulation. Therefore, researchers proposed independence rules circumvent spectra, sparse mitigate issue of However, in biological applications, there are often a group correlated genes responsible for clinical outcomes, use covariance information can significantly reduce misclassification rates. In theory extent such error rate reductions unveiled by comparing rates rule. To materialize gain based on finite samples, Regularized Optimal Affine Discriminant (ROAD) proposed. ROAD selects an increasing number features as regularization relaxes. Further benefits be achieved when screening method employed narrow feature pool before hitting ROAD. An efficient Constrained Coordinate Descent algorithm (CCD) also developed solve associated optimization problems. Sampling properties oracle type established. Simulation studies real data analysis support our theoretical demonstrate advantages new classification procedure under variety correlation structures. A delicate result continuous piecewise linear solution path problem at population level justifies interpolation CCD algorithm.