Interpretable Structural Analysis of Traffic Matrix

Structural analysis is concerned with the decomposition of traffic matrix into basis vectors, which corresponds to temporal patterns. In general, the effectiveness of basis vectors is determined by the extent to which it approximates the current week as well as subsequent consecutive week traffic matrix, i.e., the basis vectors should be temporally stable. Principal component analysis (PCA) is the most commonly employed matrix decomposition method in literature. Unfortunately being the linear combination of up to all OD flows, the basis vectors of PCA are i) notoriously difficult to interpret in terms of PoP pairs generating it, and ii) are obtained with the assumption that the variables in question are continuous random variables. To overcome these issues, we propose CUR decomposition for decomposition of traffic matrices. Experimental results shows that basis vectors obtained using CUR decomposition i) are temporally more stable, ii)are 100% interpretable in terms of PoP pairs generating it, and iii) provides an improved classification of temporal patterns into periodic, spikes and noise pattern.