Graph Embedding and Extensions: A General Framework for Dimensionality Reduction

—Over the past few decades, a large family of algorithms—supervised or unsupervised; stemming from statistics or geometry theory—has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algori...

• Type: Journal
• Year: 2007
• Where: PAMI
• Authors: Shuicheng Yan, Dong Xu, Benyu Zhang, HongJiang Zhang, Qiang Yang, Stephen Lin
• Keywords: Algorithm, Dimensionality Reduction, Embedding, PAMI 2007