Fast unsupervised embedding learning with anchor-based graph

As graph technology is widely used in unsupervised dimensionality reduction, many methods automatically construct a full connection graph to learn the structure of data, and then preserve critical information on data in subspace. The construction of a full connection graph with heavy computational complexity, however, is separated from the optimization of transformation matrix. In order to solve significant computational burden, we design anchor-based graph and unify the construction of graph and optimization of transformation matrix into a framework called fast unsupervised embedding learning with anchor-based graph (FUAG) which not only can avoid the impact of noises and redundant features in original space, but also can capture local structure of data in subspace precisely. Our method additionally incorporates the discriminant information of data captured by using trace difference form. Meanwhile, it optimizes the anchor-based graph partitioning problem with Constrained Laplacian Rank in order to ensure that the number of connected components is exactly equal to the number of classes. We also impose ℓ₀ norm constraint on each point to avoid trivial solutions and propose an efficient iterative algorithm. Experimental results on both synthetic and real-world datasets demonstrate the promising performance of the proposed algorithm.