## Results  
### Robust Feature Selection Method  
In this work the Adience database is used to test and evaluate the proposed work. For each image sample, the facial and the superpixels feature sets are extracted. Then, the proposed robust features are extracted for each feature set. For each image sample, the facial, superpixels, and their derived robust features are concatenated and two DNNs and one NN are trained for age classification task. The first DNN is used for finding the projection matrix and the second DNN is used for training the original features concatenated with their robust features. Both DNNs consist of two hidden layers and one input layer of 4096 and 512 nodes. The size of the input features for the first DNN is 4096 and the size of the input features for the second DNN is 4104. Dropout rate of 0.7, learning rate of 0.01, and weight decay of \(10^{-4}\) are used in both networks. Since the resulted robust feature sets are relatively small in size, a neural network with one hidden layer (NN) is used to report the accuracy results as the robust feature set is used as input features (Lines 3 and 6 in Table 1). The input for this network consists of eight features, which is the robust feature set size for each image sample in the database. The hidden layer consists of 50 nodes. The dropout rate is chosen to be 0.5 and the learning rate is set to 0.01. Table 1 shows the overall accuracies using all feature sets, the facial, superpixels, derived robust for facial, derived robust for superpixels, facial concatenated with its robust, and superpixels concatenated with its robust features. As it can be seen in Table 1, the robust features achieved classification accuracies that are comparable to the performance of the original features (facial and superpixels feature sets). As an advantage the dimension of the robust features is much smaller than the dimension of the original features. These obtained results by using the robust features verify the effectiveness of the proposed model in finding efficient and distinctive features (robust features) for the age classification from wild facial images. Moreover, using NN with the robust feature sets instead of using DNN at the classification stage reduces the computational time. DNN is used to find the accuracy results for the other feature sets (lines 2, 4, 5, 7 in Table 1). DNN consists of several hidden layers, while NN consists of one hidden layer. As well as, the number of nodes in each DNN layer much bigger than the number of nodes in the NN single hidden layer. This means that the number of connection between the nodes in the DNN is much higher than those in the NN, and this increases computation complexity in the DNN. The concatenation of the original features and their robust features improve the classification accuracies by a wide margin. Based on the results in Table 1, it can be observed that features based on the facial feature set performed better than the superpixels feature sets. There are two main reasons. Firstly, the facial feature set was extracted from a pre-trained model on VGG-Face for face identification and classification problem; whereas the superpixels feature set was extracted from a model that was pre-trained for depth estimation problem. Facial and robust facial feature sets contain more age-related information and more relevant to age estimation task. Secondly, the database (about two million unconstrained face images) used in pre-training the VGG-Face model is much larger than the database (about tens of thousands of images that not all are face images) used in pre-training the depth estimation model. The concatenation of both feature sets with their robust features improves the classification accuracy significantly. A classification process depends on two main factors: feature extraction and classification process. The facial and superpixels features have shown significant improvements in age classification.