For each motif or genomic annotation, background peak sets are sampled that match the set of peaks with the motif or genomic annotation in terms of the distribution of GC content and average accessibility. These background peak sets are determined by finding possible background peaks for each peak, as described in the next section. For each background iteration, we can represent the background peak assignments as a matrix B where bj,j, is 1 if peak j has peak j′ as it’s background peak and 0 otherwise. A background motif match matrix M′ is thus computed as M′ = M * B, and a background raw deviation as: Y′=(M∗B)∗XT-(M∗B)∗ETM∗ET.
