## 3 Overview of Our Proposed Multi-Layer Fusing Facial Recognition Approach  
Previous work has demonstrated that fusion based facial expression recognition approaches including multiple features and classifiers outperform the single techniques. These approaches have the advantage of integrating the complementarity of each source. Additionally, applying FACS, developed by American psychologists [PERSON] and [PERSON] [32], helps to improve the performance of facial expression recognition by integrating the action prediction of affective related action units. Motivated by the good performance of the fusion strategy, we propose a multi-view fusion approach that deploys stacking architecture to integrate AU blocks with multiple typical features and classifiers. Furthermore, to facilitate counting the contribution of AUs for the different expressions, an AU-weighted matrix is utilized at the top level of facial expression recognition. The associated rule algorithm is employed in mining each AU's contribution to each basic expression. From the global point of view, the flow chart diagram of the overall method is illustrated in Figure 1.  
As shown in Figure 1, there are two layers to our facial expression recognition methods. The first layer, called base-level classifier, works on the AU prediction. In this part, each AU block is represented with multiple features. Then, each feature is input to several classifiers separately and obtains the relative AU prediction probability. The second layer, viz. meta-level classifier, works on facial recognition. At this layer, the obtained AU prediction probability pool from first layer is weighted. Then, the weighted probability pool is input to the meta-level classifier which outputs the expression determination results.  
The architecture of our proposed approach is shown in Figure 2. There are two learning functional modules. One is the two-layer fusion for recognition with the stacking framework. The other is AU contribution learning, which utilizes association rules to explore AUs' weight matrix for expression estimation. The details of the processing procedure are illustrated as follows.  
Firstly, facial images are separated into several AU blocks. Then, four kinds of feature extraction methods are used separately in describing every AU set. After that, the occurrence probability of each AU action is predicted with the base-level classifier. Finally, the facial expression classification is done, with the obtained AU probability as an input at the meta-level. Note that the probability of AU occurring is weighted before classification in the paper. The weights refer to the contribution  
Figure 1: Flow chart diagram of the fusion-based expression recognition approach.  
of each AU in determining each basic expression. We describe it as a weight matrix, as shown at the bottom right of Figure 2. This is obtained by sample learning at the second process, where we utilize association rules to explore AUs' weight matrix. As manual labelling of AU in each expression is difficult, we still use the automatic AU labelling on expression instances. In this paper, we use only a simple feature and classifier to train and obtain the corresponding AU label of each expression instance in the dataset. By excavating a strong relationship between AUs and expressions from the dataset, AUs' weight matrix is set.  
In our proposed method, we take full consideration of a variety of each AU block in facial expression interpretation and make full use of the complementarity of different features and classifiers on facial expression recognition. The stacking ensemble architecture ensures the contribution of each source view derived from the data learning. In this way, the effectiveness and robustness of facial expression recognition is supposed to be improved.