Dimensionality Reduction via Multiple Locality-Constrained Graph Optimization

In recent years, graph-based dimensionality reduction methods became increasingly more significant since they have been successfully applied in various computer vision and machine learning problems. The key point in graph-based dimensionality reduction methods is how to construct an appropriate graph to reflect the underlying distribution of data. However, most existing methods usually consider graph construction and dimensionality reduction as two separate processes. To overcome this limitation, a multiple locality-constrained graph optimization for dimensionality reduction (MLGODR) algorithm is proposed in this paper. The proposed MLGODR possesses two characteristics. First, MLGODR integrates graph optimization and dimensionality reduction into a unified framework. Thus, a graph that characterizes the distribution of input data and a matrix that projects the input data into a low-dimensional subspace can be learned simultaneously. Second, to better exploit the local structure of input data, a locality constraint that adaptively combines multiple distance measurements is introduced into our objective function. Moreover, an effective updating algorithm is also designed to solve the proposed MLGODR. Extensive experiments are performed on four image databases and four UCI data sets. The experimental results demonstrate that our method outperforms the compared approaches in both classification and cluster tasks.