We introduce novel profile-based string kernels for use with support vector machines (SVMs) for the problems of protein classification and remote homology detection. These kernels use probabilistic profiles, such as those produced by the PSI-BLAST algorithm, to define position-dependent mutation neighborhoods along protein sequences for inexact matching of k-length subsequences ("k-mers") in the data. By use of an efficient data structure, the kernels are fast to compute once the profiles have been obtained. For example, the time needed to run PSI-BLAST in order to build the profiles is significantly longer than both the kernel computation time and the SVM training time. We present remote homology detection experiments based on the SCOP database where we show that profile-based string kernels used with SVM classifiers strongly outperform all recently presented supervised SVM methods. We further examine how to incorporate predicted secondary structure information into the profile kernel to obtain a small but significant performance improvement. We also show how we can use the learned SVM classifier to extract "discriminative sequence motifs"--short regions of the original profile that contribute almost all the weight of the SVM classification score--and show that these discriminative motifs correspond to meaningful structural features in the protein data. The use of PSI-BLAST profiles can be seen as a semi-supervised learning technique, since PSI-BLAST leverages unlabeled data from a large sequence database to build more informative profiles. Recently presented "cluster kernels" give general semi-supervised methods for improving SVM protein classification performance. We show that our profile kernel results also outperform cluster kernels while providing much better scalability to large datasets.