Eigenspectrum regularisation reverse neighbourhood discriminative learning

Linear discriminant analysis is a classical method for solving problems of dimensional reduction and pattern classification. Although it has been extensively developed, however, it still suffers from various common problems, such as the Small Sample Size (SSS) and the multimodal problem. Neighbourhood linear discriminant analysis (nLDA) was recently proposed to solve the problem of multimodal class caused by the contravention of independently and identically distributed samples. However, due to the existence of many small-scale practical applications, nLDA still has to face the SSS problem, which leads to instability and poor generalisation caused by the singularity of the within-neighbourhood scatter matrix. The authors exploit the eigenspectrum regularisation techniques to circumvent the singularity of the within-neighbourhood scatter matrix of nLDA, which is called Eigenspectrum Regularisation Reverse Neighbourhood Discriminative Learning (ERRNDL). The algorithm of nLDA is reformulated as a framework by searching two projection matrices. Three eigenspectrum regularisation models are introduced to our framework to evaluate the performance. Experiments are conducted on the University of California, Irvine machine learning repository and six image classification datasets. The proposed ERRNDL-based methods achieve considerable performance.