Spectral Jaccard Similarity: A New Approach to Estimating Pairwise Sequence Alignments

Pairwise sequence alignment is often a computational bottleneck in genomic analysis pipelines, particularly in the context of third-generation sequencing technologies. To speed up this process, the pairwise k-mer Jaccard similarity is sometimes used as a proxy for alignment size in order to filter pairs of reads, and min-hashes are employed to efficiently estimate these similarities. However, when the k-mer distribution of a dataset is significantly non-uniform (e.g., due to GC biases and repeats), Jaccard similarity is no longer a good proxy for alignment size. In this work, we introduce a min-hash-based approach for estimating alignment sizes called Spectral Jaccard Similarity, which naturally accounts for uneven k-mer distributions. The Spectral Jaccard Similarity is computed by performing a singular value decomposition on a min-hash collision matrix. We empirically show that this new metric provides significantly better estimates for alignment sizes, and we provide a computationally efficient estimator for these spectral similarity scores.