New Robust Metric Learning Model Using Maximum Correntropy Criterion

Jie Xu (University of Pittsburgh); Lei Luo (University of Pittsburgh); Cheng Deng (Xidian University); Heng Huang (University of Pittsburgh)

Metric learning has recently become an active data mining research topic with many real-world applications. Most existing metric learning methods aim to learn an optimal Mahalanobis distance matrix M, under which data samples from the same class are forced to be close to each other and those from different classes are pushed far away. The Mahalanobis distance matrix M can be factorized as M = L’L, and the Mahalanobis distance induced by L is equivalent to the Euclidean distance after linear projection of the feature vectors on the rows of L. However, the Euclidean distance is only suitable for characterizing Gaussian noise, thus the traditional metric learning algorithms are not robust to achieve good performance when they are applied to the occlusion data, which often appear in image and video data mining applications. To overcome this limitation, we propose a new robust metric learning approach by introducing the maximum correntropy criterion to deal with real-world malicious occlusions or corruptions. In our new model, we enforce the intra-class reconstruction residual of each sample to be smaller than the inter-class reconstruction residual by a large margin. Meanwhile, we employ correntropy induced metric to fit the reconstruction residual, which has been proved to be useful in non-Gaussian data processing. Leveraging the half-quadratic optimization technique, we derive an efficient algorithm to solve the proposed new model and provide its convergence guarantee as well. Extensive experiments on various occluded data sets indicate that our proposed model can achieve more promising performance than other related methods.

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