Fig. 1

Schematics of network filters. Network filters are tools that denoise real-valued biological data using a biologically meaningful network to exploit the correlation (“smoothing”) or anti-correlation (“sharpening”) among neighboring measurements. a A measurement \(x_{i}\) and its neighboring values in network, where the color intensity is proportional to the measured value. In applying the smooth filter, \(x_i\) is adjusted to be more similar to its neighbors; in applying the sharp filter, \(x_i\) is adjusted to be more distant from its neighbors. b Measurements can also first be partitioned into groups (dashed line) by detecting structural modules within the network, and then different filters applied to different modules, ignoring between-module edges, e.g., if the signals are assortative in some communities and disassortative in others