Sparse local discriminant projections for discriminant knowledge extraction and classification

One of the major disadvantages of the linear dimensionality reduction algorithms, such as principle component analysis (PCA) and linear discriminant analysis (LDA), is that the projections are lack of physical interpretation. Moreover, which features or variables play an important role in feature extraction and classification in classical linear dimensionality reduction methods is still not investigated well. This paper proposes a novel supervised learning method called sparse local discriminant projections (SLDPs) for linear dimensionality reduction. Differed from the recent manifold-learning-based methods such as local preserving projections (LPPs), SLDP introduces a sparse constraint into the objective function and integrates the local geometry, discriminant information and within-class geometry to obtain the sparse projections. The sparse projections can be efficiently computed by the Elastic Net. The most important and interesting thing is that the sparse projections learned by SLDP have a direct physical interpretation and provide us the discriminant knowledge and insightful understanding for the extracted features. The experimental results show that SLDP can give reasonable semantic results and achieves competitive performance compared with some techniques such as PCA, LPP, neighbourhood preserving embedding (NPE) and the recently proposed unified sparse subspace learning (USSL).