GMFLLM: A general manifold framework unifying three classic models for dimensionality reduction

As one of the most important preprocess in pattern recognition, the dimensionality reduction is widely applied to the real-world tasks. In practice, there exist three corresponding well-known models, including the Locality Preserving Projection (LPP), the Linear Discriminant Analysis (LDA), and the Maximum Margin Criterion (MMC). Even though several previous works have revealed the partial relationship among the three, there are no further researches. In this paper, from the perspective of LPP, the complete connections among the three models are demonstrated, and then a new framework named GMFLLM is proposed to unify them. Further, since it is possible to utilize the proposed framework as an underlying platform to design more dimensionality reduction variants of LPP, fourteen new variants developed from GMFLLM are approached and investigated in the experiment. Moreover, the best of them, named as the Between-class concerned DLPP/MMC (BDLPP/MMC), is selected to compare with the other seven existing state-of-the-art methods on six image datasets. Results validate the effectiveness of BDLPP/MMC so as to show the generalization of GMFLLM.