Adaptive Flexible Optimal Graph for Unsupervised Dimensionality Reduction

Graph-based dimensionality reduction methods are widely used in classification and clustering tasks due to their superior performance. The key to the performance of these methods is how to construct the graph. Although some existing methods can obtain an adaptive graph and a projection matrix simultaneously by combining manifold learning and graph construction in a unified framework, the linear constraint used in manifold learning is too hard. To solve this problem, we propose a novel method named adaptive flexible optimal graph (AFOG) for unsupervised dimensionality reduction. AFOG can obtain an adaptive flexible optimal graph by relaxing the linear constraint in the process of low-dimensional manifold mapping. At the same time, by using the principle of maximum separability, it can also obtain an effective projection matrix, which can solve out-of-sample problems. Experiments on six public benchmark data sets indicate that AFOG outperforms several other state-of-The-Art methods.