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In this paper, a kernel-based learning algorithm, kernel rank, is presented for improving the performance of semantic concept detection. By designing a classifier optimizing the receiver operating characteristic (ROC) curve using kernel rank, we provide a generic framework to optimize any differentiable ranking function using effective smoothing functions. kernel rank directly maximizes a 1-D quality measure of ROC, i.e., AUC (area under the ROC). It exploits the kernel density estimation to model the ranking score distributions and approximate the correct ranking count. The ranking metric is then derived and the learnable parameters are naturally embedded. To address the issues of computation and memory in learning, an efficient implementation is developed based on the gradient descent algorithm. We apply kernel rank with two types of kernel density functions to train the linear discriminant function and the Gaussian mixture model classifiers. From our experiments carried out on the development set for TREC Video Retrieval 2005, we conclude that (1) kernel rank is capable of training any differentiable classifier with various kernels; and (2) the learned ranking function performs better than traditional maximization likelihood or classification error minimization based algorithms in terms of AUC and average precision (AP).