Boosting simple projections for multi-class dimensionality reduction

This paper presents a novel method for dimensionality reduction and for multi-class classification tasks. This method iteratively selects a series of simple but effective 1D subspaces, and then combines the corresponding 1D projections by Adaboost.M2. Its major advantages are: (1) it does not impose specific assumptions on data distribution; (2) it minimizes Bayes error estimation in low-dimensional space; (3) it simplifies existing subspace-based methods to eigenvalue decomposition problem; and (4) each of the 1D subspaces (with associated nearest neighbor classifier) has different emphasis - measured by weighted training error. Experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed method.