Adaptive incomplete multi-view learning via tensor graph completion

Abstract: With the advancement of the data acquisition techniques, multi-view learning has become a hot topic. Some multi-view learning methods assume that the multi-view data is complete, which means that all instances are present, but this too ideal. Certain tensor-based methods for handing incomplete multi-view data have emerged and have achieved better result. However, there are still some problems, such as use of traditional tensor norm which makes the computation high and is not able to handle out-of-sample. To solve these two problems, we proposed a new incomplete multi view learning method. A new tensor norm is defined to implement graph tensor data recover. The recovered graphs are then regularized to a consistent low-dimensional representation of the samples. In addition, adaptive weights are equipped to each view to adjust the importance of different views. Compared with the existing methods, our method nor only explores the consistency among views, but also obtains the low-dimensional representation of the new samples by using the learned projection matrix. An efficient algorithm based on inexact augmented Lagrange multiplier (ALM) method are designed to solve the model and convergence is proved. Experimental results on four datasets show the effectiveness of our method.