Incomplete multi-view learning via half-quadratic minimization

In real applications, to deal with incomplete multi-view data, incomplete multi-view learning has experienced rapid development in recent years. Among various incomplete multi-view learning methods, a considerable number of methods were developed with the matrix factorization technique. Most of the existing matrix factorization based methods adopt the sum of squared ℓ2-norm as loss functions directly, which is known to be susceptible to value missing. To overcome this issue, we propose a new matrix factorization method, named Incomplete Multi-view Learning via Half-quadratic Minimization (IMLHM). Different from previous methods, a robust estimator based on half-quadratic minimization theory is imported to our loss function to overcome the sensitivity of ℓ2-norm to noise. The influence of bad recovered instances is decreased via the automatic weighting scheme derived from the half-quadratic minimization process, thereby improving the robustness of the proposed method. Additionally, a nuclear norm is introduced to exploit the low-rank structure of the learned representation matrix, further improving the robustness of the proposed method against to noise. An alternating iterative algorithm is developed to optimize the objective function. Comprehensive experimental results on seven data sets verify the effectiveness of the proposed method.