Image-to-Class (I2C) distance has demonstrated its effectiveness for object recognition in several single-label datasets. However, for the multi-label problem, where an image may contain several regions belonging to different classes, this distance may not work well since it cannot discriminate local features from different regions in the test image and all local features have to be counted in the I2C distance calculation. In this paper, we propose to use Class-to-image (C2I) distance and show that this distance performs better than I2C distance for multi-label image classification. However, since the number of local features in a class is huge compared to that in an image, the calculation of C2I distance is much more expensive than I2C distance. Moreover, the label information of training images can be used to help select relevant local features for each class and further improve the recognition performance. Therefore, to make C2I distance faster and perform better, we propose an optimization algorithm using Ll-norm regularization and large margin constraint to learn the C2I distance, which will not only reduce the number of local features in the class feature set, but also improve the performance of C2I distance due to the use of label information. Experiments on MSRC, Pascal VOC and MirFlickr datasets show that our method can significantly speed up the C2I distance calculation, while achieves better recognition performance than the original C2I distance and other related methods for multi-labeled datasets.
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