Otto Sumray: Multiscale extensions of the Laplacian score for feature selection in single cell transcriptomics

Abstract.

The Laplacian score is used for feature selection on networks by measuring variation in graph signals with respect to the graph. However, in practice different interesting signals in data may have variation on different scales and location but will not be distinguished by the Laplacian score. We present three multiscale extensions of the Laplacian score for ranking and visualisation of graph signals. Eigenscores use the eigendecomposition of the graph Laplacian; the multiscale Laplacian score uses continuous random walks; the persistent Rayleigh quotient uses the Kron reduced or persistent Laplacian and a given filtration. We are primarily motivated by extracting biologically relevant genes from single cell transcriptomics data, where understanding gene expression patterns elucidates cell type and gene regulation.