A study on distance metric learning by using different metric matrices in each category

Distance metric learning is the method of learning the relevant distance metric from a training dataset by considering statistical characteristics. In order to gain a desirable distance metric, the optimization problem under an arbitrary constraint is solved. However, the representative algorithms of distance metric learning need to perform eigendecomposition at each iteration. Therefore, if the dimensions of the input data become large, the computational cost will increase drastically and it is difficult to calculate the optimal solution in a realistic amount of time. In addition, those distance metric learning methods are formulated by assuming a global (unique) metric matrix for the total vector space. Therefore, the global metric matrix cannot take into account the difference in statistical characteristics between each category. To improve those problems, the authors introduce different metric matrices for each category and propose a way to estimate the plural matrices using category information that applies the method of Mochihashi et al. The estimated metric matrices reflect the statistical characteristics of each category. The formulation of classifications by template matching and the k-NN method making effective use of the metric matrices is proposed. To verify the effectiveness of the proposed method, a simulation experiment is conducted using the benchmark data of high-dimensional and low-dimensional input data.