Distance metric learning based on different ℓ₁ regularized metric matrices in each category

The distance metric learning is the method to learn the distance metric from training data considering its statistical characteristics under the arbitrary constraints. To obtain the desirable distance metric, the optimization problem is solved. Most of the distance metric learning methods aim to gain the global optimal metric matrix. However there is a possibility that the global metric matrix cannot express the statistical characteristics of each category in detail. In addition, if the dimension of input data increase, the computational cost of calculating distance between data increases either. To avoid this problem, we adopt the way to use the l₁ regularization to gain sparse metric matrix. By combining those, we focus on the way to deriving the plural metric matrices with a sparse structure in this study. To verify the effective ness of our proposed method, we conduct simulation experiments by using UCI machine learning repository.