## 4 Experimental Results
### Multi-Attribute Recognition on the CMU Multi-PIE Dataset
As shown in Table 1, it is difficult to say that multi-task learning can always improve the performance in all attribute recognition, which corresponds with the arguments in [7]. However, we can still see that dual task learning can improve the performance in many cases (the shaded cells), which supports the empirical efficiency of multi-task learning reported in many practical applications [8,9]. Further, we can also see that the different tendency in the performances of settings (a) and (b). The setting (a) generally gave slight improvement compared to single task learning, whereas the setting (b) showed more apparent discrepancy in the performance gains and losses. This tendency can be expected from the theoretical property of the joint representation setting, in which the learning model is free from the strong independency assumption. In the experiment of expression and other tasks, expression itself was always improved in performance from both methods, but it did not help the performance of other recognition tasks when learning a joint relationship. Thus, expression is likely to improve the performance of other tasks when learning as an independent task rather than correlated task. In the experiment of identity and other tasks, identity always helped to improve the performance of other tasks, whereas identity itself did not get a positive effect by other tasks when learning a joint relationship. This seems to be due to a lack of data compared to the increasing number of nodes required. Therefore, it seems appropriate to consider identity as an independent task in order to get the performance improvement on all tasks. In particular, we found that gender, race, and age were complementarily related to each other which is marked with a red box. Thus, we further examined how expression and identity affected the learning of multiple tasks by sequentially adding them to the multi-attribute recognition problem with three (gender, race, and age) recognition tasks so as to find an optimal combination for the multi-attribute recognition of faces. Table 2 shows the recognition performances of five facial attributes under several output representation settings. G, R, A, E and I are simplified representations of the tasks: Gender, race, age, expression, and identity, respectively. The symbol '+' means that tasks are combined with the assumption that tasks are independent of each other. Another symbol '*' represents the proposed joint representation method for mutually correlated tasks. Bold numbers with underline denote the best performance for the specific tasks. The values in gray cells indicate the best recognition performance among the multi-attribute recognition experiments with the same type and number of tasks. From Table 2, multi-attribute recognition using proposed output representation methods gave better performance for most of the attributes compared to those of single task learning. When training complementarily related three attributes (gender, race, and age) at the same time, the performance of all tasks was much improved compared to the result of dual task learning, and learning with a correlated relationship showed better performance than an independent relationship. In the experiment of learning expression, gender, race, and age together, the best performance was obtained when regarding