Hypergraph canonical correlation analysis for multi-label classification

•We employ hypergraph canonical correlation analysis for multi-label classification.•We construct a hypergraph to exploit the high-order label relations.•A least-squares approximation is given to address the scalable issue.•Its efficacy is validated by empirical studies on several multi-label datasets.

In recent years, multi-label classification has attracted lots of attention due to its widespread applications, such as multi-topic image annotation and webpage categorization. To this end, a number of methods have been developed to explore the inherent correlations existing among multiple labels, which are essentially important for multi-label models. However, most of them cannot employ the high-order relationships among labels to learn better models. To overcome this shortcoming, we propose to construct a hypergraph for exploiting the high-order label relations and present a novel framework for multi-label classification named Hypergraph Canonical Correlation Analysis (HCCA). This approach is based on canonical correlation analysis, and it further takes into account the high-order label structure information via hypergraph regularization. Thus, the label relations can be better respected both globally by the normalized similarity matrix of CCA and locally by the normalized hypergraph Laplacian in a unified framework. In concrete, the objective function can be optimized by solving a generalized eigenvalue problem, but this requests heavy computational overheads for large-scale data. Therefore, we show a more efficient method that approximates the original problem by the least squares formulation under a mild condition. Furthermore, we have studied the influences of the ridge regularization on our method. Experimental results on several real-world multi-label data sets have justified the effectiveness of the proposed method.