# Multiple Network Fusion with Low-Rank Representation for Image-Based Age Estimation
## 4 Experimental Evaluation
### Comparison of Different Methods for Age Estimation  
For age estimation, we compared the following methods, including the proposed Multiple Network Fusion with Low-Rank Representation (MNF-LRR):  
* Multiple Network Fusion with Low-Rank Representation (MNF-LRR): The proposed method using multiple neural network fusion and low-rank representation.
* Linear Regression (LR) [17]: This method estimates ages directly by linear regression against feature vectors of facial images. In this paper, HOG [35] was used as image features. Ridge regression (RR-LR) and relevance vector machine (RVM-LR) regression were both implemented by the authors. Their results were similar. We used RVM-LR and set \(\
u=1000\) in the experimental comparison.
* Twin Gaussian Processes (TGPs) [18]: This method applies Gaussian process priors on both covariates and responses. Two Gaussian processes are then modeled as normal distributions over finite index sets of training and testing examples. Finally, outputs can be estimated by minimizing the Kullback-Leibler (K-L) divergence between them. The authors have provided several different implementations of TGP, such as Twin Gaussian Processes with K Nearest Neighbors (TGPKNN), Weighted K-Nearest Neighbor Regression (WKNNRegressor), Gaussian Process Regression (GPR), Hilbert-Schmidt Independent Criterion with K Nearest Neighbors (HSICKNN) and Kernel Target Alignment with K Nearest Neighbors (KTAKNN). We found that TGPKNN outperformed all other methods. Therefore, we used HOG for image features and TGPKNN as the regressor.
* Convolutional Neural Networks (CNNs) [36]. This method uses a simple convolutional net architecture. The network is composed of three convolutional layers and two fully connected layers. The authors have provided the Caffe model for age classification and deployed prototext.
* Deep Expectation (DEX) [30]. The authors here treated age estimation as a classification problem based on deep learning, which was followed by an expected value refinement with softmax. The key to DEX for age regression contains deep learning models with a large amount of data, a robust face alignment process, and softmax-based expected value formulation.  
The results of the experimental comparison are shown in Figure 6. Based on the results, we can make the following summarizations:  
1. The performance of general mapping learning methods such as LR and TGP is not satisfactory. They are fast and use traditional features such as HOG, but the definition of mapping relationship is oversimplified.  
Figure 5: Different feature fusion methods. (**a**) Results of IMDB; (**b**) Results of WIKI.  
2. The methods based on neural networks such as CNNs and DEX can achieve a stable performance. Neural networks provide descriptive features but require a large amount of training data. Besides, previous neural-network-based methods have not considered multiple features.
3. The performance of the proposed MNF-LRR outperformed the state of the art. We made use of multiple features from different network types and found a reasonable way to fuse them.