Direct Discriminant Locality Preserving Projection With Hammerstein Polynomial Expansion

Discriminant locality preserving projection (DLPP) is a linear approach that encodes discriminant information into the objective of locality preserving projection and improves its classification ability. To enhance the nonlinear description ability of DLPP, we can optimize the objective function of DLPP in reproducing kernel Hilbert space to form a kernel-based discriminant locality preserving projection (KDLPP). However, KDLPP suffers the following problems: 1) larger computational burden; 2) no explicit mapping functions in KDLPP, which results in more computational burden when projecting a new sample into the low-dimensional subspace; and 3) KDLPP cannot obtain optimal discriminant vectors, which exceedingly optimize the objective of DLPP. To overcome the weaknesses of KDLPP, in this paper, a direct discriminant locality preserving projection with Hammerstein polynomial expansion (HPDDLPP) is proposed. The proposed HPDDLPP directly implements the objective of DLPP in high-dimensional second-order Hammerstein polynomial space without matrix inverse, which extracts the optimal discriminant vectors for DLPP without larger computational burden. Compared with some other related classical methods, experimental results for face and palmprint recognition problems indicate the effectiveness of the proposed HPDDLPP.