Local structured feature learning with dynamic maximum entropy graph

Abstract In recent years, Linear Discriminant Analysis (LDA) has seen huge adoption in data mining applications. Due to its globality, it is incompetent to handle multimodal data. Besides, most of LDA’s variants learn the projection matrix based on the pre-defined similarity matrix, which is easily affected by noisy and irrelevant features. To address above two issues, a novel local structured feature learning with Dynamic Maximum Entropy Graph (DMEG) method is developed which firstly develops a more discriminative LDA with whitening constraint that can minimize the within-class scatter while keeping the total samples scatter unchanged simultaneously. Second, for exploring the local structure of data, the l0-norm constraint is imposed on similarity matrix to ensure the k connectivity on graph. More importantly, proposed model learns the similarity and projection matrix simultaneously to ensure that the neighborships can be found in the optimal subspace where the noise have been removed already. Moreover, a maximum entropy regularization is employed to reinforce the discriminability of graph and avoid the trivial solution. Last but not least, an efficient iterative optimization algorithm is provided to optimize proposed model with a NP-hard constraint. Extensive experiments conducted on synthetic and several real-world data sets demonstrate the efficiency in classification task and robustness to noise of proposed method.