Robust Multi-Task Learning With Flexible Manifold Constraint
Rui Zhang, Hongyuan Zhang, Xuelong Li
Abstract
Multi-Task Learning attempts to explore and mine the sufficient information within multiple related tasks for the better solutions. However, the performance of the existing multi-task approaches would largely degenerate when dealing with the polluted data, i.e., outliers. In this paper, we propose a novel robust multi-task model by incorporating a flexible manifold constraint (FMC-MTL) and a robust loss. Specifically speaking, multi-task subspace is embedded with a relaxed and generalized Stiefel Manifold for considering point-wise correlation and preserving the data structure simultaneously. In addition, a robust loss function is developed to ensure the robustness to outliers by smoothly interpolating between <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> ℓ2,1-norm and squared Frobenius norm. Equipped with an efficient algorithm, FMC-MTL serves as a robust solution to tackling the severely polluted data. Moreover, extensive experiments are conducted to verify the superiority of our model. Compared to the state-of-the-art multi-task models, the proposed FMC-MTL model demonstrates remarkable robustness to the contaminated data.