Discriminative and Geometry-Preserving Adaptive Graph Embedding for dimensionality reduction.

Learning graph embeddings for high-dimensional data is an important technology for dimensionality reduction. The learning process is expected to preserve the discriminative and geometric information of high-dimensional data in a new low-dimensional subspace via either manual or automatic graph construction. Although both manual and automatic graph constructions can capture the geometry and discrimination of data to a certain degree, they working alone cannot fully explore the underlying data structure. To learn and preserve more discriminative and geometric information of the high-dimensional data in the low-dimensional subspace as much as possible, we develop a novel Discriminative and Geometry-Preserving Adaptive Graph Embedding (DGPAGE). It systematically integrates manual and adaptive graph constructions in one unified graph embedding framework, which is able to effectively inject the essential information of data involved in predefined graphs into the learning of an adaptive graph, in order to achieve both adaptability and specificity of data. Learning the adaptive graph jointly with the optimized projections, DGPAGE can generate an embedded subspace that has better pattern discrimination for image classification. Results derived from extensive experiments on image data sets have shown that DGPAGE outperforms the state-of-the-art graph-based dimensionality reduction methods. The ablation studies show that it is beneficial to have an integrated framework, like DGPAGE, that brings together the advantages of manual/adaptive graph construction.