Robust outlier detection using commute time and eigenspace embedding

We present a method to find outliers using 'commute distance' computed from a random walk on graph. Unlike Euclidean distance, commute distance between two nodes captures both the distance between them and their local neighborhood densities. Indeed commute distance is the Euclidean distance in the space spanned by eigenvectors of the graph Laplacian matrix. We show by analysis and experiments that using this measure, we can capture both global and local outliers effectively with just a distance based method. Moreover, the method can detect outlying clusters which other traditional methods often fail to capture and also shows a high resistance to noise than local outlier detection method. Moreover, to avoid the O(n³) direct computation of commute distance, a graph component sampling and an eigenspace approximation combined with pruning technique reduce the time to O(nlogn) while preserving the outlier ranking.