Commonality and Individuality-Based Subspace Learning

Subspace learning (SL) plays a key role in various learning tasks, especially those with a huge feature space. When processing multiple high-dimensional learning tasks simultaneously, it is of great importance to make use of the subspace extracted from some tasks to help learn others, so that the learning performance of all tasks can be enhanced together. To achieve this goal, it is crucial to answer the following question: How can the commonality among different learning tasks and, of equal importance, the individuality of each single learning task, be characterized and extracted from the given datasets, so as to benefit the subsequent learning, for example, classification? Existing multitask SL methods usually focused on the commonality among the given tasks, while neglecting the individuality of the learning tasks. In order to offer a more general and comprehensive framework for multitask SL, in this article, we propose a novel method dubbed commonality and individuality-based SL (CISL). First, we formally define the notions and objective functions of both commonality and individuality with respect to multiple SL tasks. Then, we design an iterative algorithm to solve the formulated objective functions, with the convergence of the algorithm being guaranteed. To show the generality of the proposed method, we theoretically analyze its connections to existing single-task and multitask SL methods. Finally, we demonstrate the necessity and effectiveness of incorporating both commonality and individuality by interpreting the learned subspaces and comparing the performance of CISL (in terms of the subsequent classification accuracy) with that of classical and state-of-the-art SL approaches on both synthetic and real-world multitask datasets. The empirical evaluation validates the effectiveness of the proposed method in characterizing the commonality and individuality for multitask SL.