  Analysis of large-scale sequential data has been one of the most crucial
tasks in areas such as bioinformatics, text, and audio mining. Existing string
kernels, however, either (i) rely on local features of short substructures in
the string, which hardly capture long discriminative patterns, (ii) sum over
too many substructures, such as all possible subsequences, which leads to
diagonal dominance of the kernel matrix, or (iii) rely on non-positive-definite
similarity measures derived from the edit distance. Furthermore, while there
have been works addressing the computational challenge with respect to the
length of string, most of them still experience quadratic complexity in terms
of the number of training samples when used in a kernel-based classifier. In
this paper, we present a new class of global string kernels that aims to (i)
discover global properties hidden in the strings through global alignments,
(ii) maintain positive-definiteness of the kernel, without introducing a
diagonal dominant kernel matrix, and (iii) have a training cost linear with
respect to not only the length of the string but also the number of training
string samples. To this end, the proposed kernels are explicitly defined
through a series of different random feature maps, each corresponding to a
distribution of random strings. We show that kernels defined this way are
always positive-definite, and exhibit computational benefits as they always
produce \emph{Random String Embeddings (RSE)} that can be directly used in any
linear classification models. Our extensive experiments on nine benchmark
datasets corroborate that RSE achieves better or comparable accuracy in
comparison to state-of-the-art baselines, especially with the strings of longer
lengths. In addition, we empirically show that RSE scales linearly with the
increase of the number and the length of string.
