This paper shows a way to derive positive definite kernels from edit distances. It is well-known that, if a distance d is negative definite, e-λd is positive definite for any λ > 0. This property provides us the opportunity to apply useful techniques of kernel multivariate analysis to the features of data captured by means of the distance. However, the known instances of edit distance are not always negative definite. Even worse, it is usually not easy to examine whether a given instance of edit distance is negative definite. This paper introduces alignment kernels to present an alternative means to derive kernels from edit distance. The most important advantage of the alignment kernel consists in its easy-to-check sufficient condition for the positive definiteness. In fact, when we surveyed edit distances for strings, trees and graphs, all but one are instantly verified to meet the condition and therefore proven to be positive definite.

The MPEG-1 layer-III compressed audio format, which is widely known as MP3, is the most popular for audio distribution. However, it is not equipped with security features to protect the content from unauthorized access. Although encryption ensures content security, the naive method of encrypting the entire MP3 file would destroy compliance with the MPEG standard. In this paper, we propose a low-complexity partial encryption method that is embedded during the MP3 encoding process. Our method reduces time consumption by encrypting only the perceptually important parts of an MP3 file rather than the whole file, and the resulting encrypted file is still compatible with the MPEG standard so as to be rendered by any existing MP3 players. For full-quality rendering, decryption using the appropriate cryptographic key is necessary. Moreover, the effect of encryption on audio quality can be flexibly controlled by adjusting the percentage of encryption. On the basis of this feature, we can realize the try-before-purchase model, which is one of the important business models of Digital Rights Management (DRM): users can render encrypted MP3 files for trial and enjoy the contents in original quality by purchasing decryption keys. From our experiments, it turns out that encrypting 2-10% of MP3 data suffices to generate trial music, and furthermore file size increasing after encryption is subtle.