Abstract
This chapter proposes a new discriminant analysis framework (NDA) for dimension reduction and recognition. In the NDA, the between-class and the within-class Laplacian scatter matrices are designed from sample to sample, respectively, to characterize the between-class separability and the within-class compactness. Then, a discriminant projection matrix is solved by simultaneously maximizing the between-class Laplacian scatter and minimizing the within-class Laplacian scatter. Benefiting from the linear separability of the kernelized mapping space and the dimension reduction of principal component analysis (PCA), an effective kernel PCA plus NDA method (KNDA) is proposed for rapid detection of gas mixture components. In this chapter, the NDA framework is derived with specific implementations. Experimental results demonstrate the superiority of the proposed KNDA method in multi-class recognition.
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