## 4 Experimental Results  
### Multi-Attribute Recognition on the CMU Multi-PIE Dataset  
As a benchmark database, we took CMU (Carnegie Mellon University) Multi-PIE (Pose, Illumination, and Expressions) which is a well-known dataset with facial attributes [17]. From the original data with more than 750,000 images of 337 subjects with some variations in pose, flash, and time, we selected images about 30 subjects for experiment. Other than pre-labeled identity and expression class, we manually labeled three facial attributes: Gender, race, and age for attribute recognition tasks. The total number of labeled da ta was 23,863, of which 5086 (20%) were used for training, and the remaining 18,777 (80%) were used for the test. The data was divided in a way that kept the composition ratio of the attributes. The table of experimental data configuration is shown in our previous work [18]. We composed five data settings for cross validation, and conducted all the experiments on the same 30,000 epochs training for three random initializations, and obtained average results. Since we used images for 30 individuals, we treated 30 identities as 30 different attributes for identity recognition. Obviously, these identities were in a mutually exclusive relationship. Similarly, we treated the six variations in facial expression as six distinct attributes. Moreover, we manually labeled two attributes concerning gender, four different attributes concerning race (Caucasian, Mongolian, Negroid, and Middle-eastern) according to the race category used in [19], as well as five attributes concerning age groups (20s, 30s, 40s, 50s, 60s). Since the size of the image in the dataset varied, we resized all data to \(32\times 32\). Figure 6 shows the example of the Mulit-PIE data used in the experiment. Figure 5: Output representation for three attribute recognition tasks (gender, race, and age): (a) Representation for independent tasks and (b) for correlated tasks. We first grouped the mutually exclusive attributes into five tasks (identity, gender, race, age, and expression recognition), and conducted the single task learning for each task, so as to compare the results with the proposed multi-task learning method. We applied the proposed output representation methods for independent and correlated relationships to various combinations of two or more tasks. For the basis of the experiment, we conducted dual task learning for all possible combinations of two recognition tasks. For each experiment, we implemented two different settings: (a) The output representation for independent tasks, and (b) for correlated tasks, of which the results are shown in the Table 1. The diagonal elements of the tables show the performance of single task learning, and the value in the \(i\)th row and \(j\)th column represents the classification error for \(i\)th task in the dual-combination learning of the \(i\)th task and \(j\)th task. For example, the first row indicated the error of the identity classification when the identity task was combined with other tasks. The underlined value in each row corresponds to the minimum misclassification rate for each task, and the shaded cells show the cases in which improved performance was obtained by applying multi-task learning. The values in bold imply improved performance in the comparison of two different settings (a) and (b). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**(a)** & **Identity** & **Expression** & **Gender** & **Race** & **Age** \\ \hline Identity & 0.48 & **0.40** & **0.43** & 0.52 & **0.46** \\ \hline Expression & 9.68 & 11.48 & **10.86** & 10.97 & **10.42** \\ \hline Gender & 0.16 & 0.61 & 0.77 & 0.33 & 0.24 \\ \hline Race & 0.27 & **0.67** & 0.48 & 0.78 & **0.34** \\ \hline Age & 0.46 & **1.30** & 0.67 & 0.73 & 1.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Recognition error (%) of dual task learning with independent tasks (**a**), and correlated tasks (**b**). Figure 6: Examples of CMU Multi-PIE data.