Unsupervised dimensionality reduction by jointing dynamic hypergraph and low-rank embedding for classification and clustering

Abstract

Hypergraph learning is largely used to handle dimensional disaster problem of high-dimensional data in view of its flexible ability to model complex data correlations. However, the following three problems limit the performance of unsupervised hypergraph-based dimensionality reduction methods: (1) most of them are unable to obtain consistently good performance for different data sets; (2) noise or outliers in the data can lead to unreliability of the fixed hypergraph; and (3) the simple K-nearest neighbor strategy generates hypergraph with a fixed number of vertices in each hyperedge. To solve the above problems, an unsupervised dimensionality reduction method named joint dynamic hypergraph and low-rank embedding (DHLRE) is proposed. Specifically, DHLRE unifies hypergraph learning and low-rank learning into a single objective function. By doing so, both global and higher-order local structural information of the data can be extracted by DHLRE, and the two structural information complement each other to make the projection matrix have stronger discriminative power. In addition, the weight of hyperedge and hypergraph in DHLRE are dynamically generated in dimension-reduced space, which suppresses the ability of noise or outlier to affect the projection matrix. To divide hyperedge in a flexible way, a new approach without neighborhood parameter is proposed. By using this approach, the number of vertices of the hyperedge can be adaptively decided for different data sets. Further, an iterative algorithm is designed to solve the objective function of DHLRE. Finally, experimental results on several real-world data sets show that DHLRE outperforms others related methods for both classification and clustering tasks.