Local structured feature learning with dynamic maximum entropy graph

Highlights：

• Proposed model adaptively selects k neighbors for each data point by imposing L0-norm constraint on similarity matrix. Thus, the graph constructed in our method is k-connected which is more sensitive to local structure of data than full-connected graph in above methods.

• Proposed model learns the similarity matrix and the transformation matrix simultaneously such that the kNN graph is dynamically updated. In such way, the neighborships of each sample can be found in the optimal subspace rather than in original space. Additionally, we impose a maximum entropy regularization on similarity matrix so that the trivial solution can be avoided naturally.

• An efficient iterative optimization algorithm is presented to solve proposed problem with L0-norm constraint, and a strict proof of convergence is provided as well. Experiments conducted on synthetic and several real-world data sets demonstrate the superiority of proposed DMEG compared to related state-of-the-art methods on classification task.

摘要

•We derive a more discriminative LDA which generates the whitening transformation, and it can minimize the scatter within same samples while keeping the scatter of total samples unchanged simultaneously.•Proposed model adaptively selects k neighbors for each data point by imposing L0-norm constraint on similarity matrix. Thus, the graph constructed in our method is k-connected which is more sensitive to local structure of data than full-connected graph in above methods.•Proposed model learns the similarity matrix and the transformation matrix simultaneously such that the kNN graph is dynamically updated. In such way, the neighborships of each sample can be found in the optimal subspace rather than in original space. Additionally, we impose a maximum entropy regularization on similarity matrix so that the trivial solution can be avoided naturally.•An efficient iterative optimization algorithm is presented to solve proposed problem with L0-norm constraint, and a strict proof of convergence is provided as well. Experiments conducted on synthetic and several real-world data sets demonstrate the superiority of proposed DMEG compared to related state-of-the-art methods on classification task.