Does the affinity matrix influence the performance of the Locality Preserving Projection algorithm?
Elias R. Silva, George D. C. Cavalcanti, Tsang Ing Ren · 2010
Classical feature extraction techniques, like PCA and LDA, do not deal properly with multimodal problems. Such techniques create projections that do not preserve the multimodal structure of the original data distribution. Locality Preserving Projection (LPP) is a feature extraction technique which looks for a transformation matrix that minimizes the changes into the structure of the data after the transformation. This local structure is captured by the affinity matrix. However, there many ways to calculate this affinity matrix. The main aim of this paper is to evaluate the influence of different affinity matrices over the LPP accuracy. The experiments showed that the correct choice of the affinity matrix can lead to a performance gain. Among the analyzed affinity matrices, Local Scaling and Nearest Neighbor reached the best results.