Cross-domain Fisher Discrimination Criterion: A Domain Adaptive Method Based on the Nature of Classifier

Most domain adaptive methods enhance the classification performance of target domain via overcoming the distribution difference between source and target domains while ignoring the nature of classifier, i.e., the data being correctly classified by classifier is due to the high separability of data. Therefore, inspired by this, we propose a simple yet effective domain adaptive method in accordance with the property of classifier, namely cross-domain Fisher discrimination criterion (CFDC). CDFC is intended to upgrade the inter-class discrimination and intra-class compactness of samples for the scenario where the target domain has few labeled samples. Specifically, we reconstruct the intra- and inter- class scatter matrices of Fisher's criterion from a geometrically intuitive perspective, enabling it to extract highly discriminative features from cross-domain samples. The reconstructed between-class scatter matrix aims to maximize the class separation of target samples, while the redefined within-class scatter matrix seeks to have samples from different domains densely clustered around the class center of target samples. Six widely used image datasets are involved to verify the effectiveness and efficiency of CFDC. Experimental results demonstrate that the performance of CFDC is significantly superior to similar methods and conventional unsupervised domain adaptation methods, comparable to non-deep semi-supervised domain adaptation methods, but with a significantly lower time consumption. Even compared with state-of-the-art deep semi-supervised domain adaptation methods, CFDC exhibits performance advantages on certain datasets.