HITSnDIFFS: A fast algorithm for consecutive ones with applications in item labeling

Abstract

We analyze a general problem in a crowd-sourced setting: users pick a label from a set of candidates for a set of items; the problem is to determine the most likely label for each item, as well as a ranking of the users based on their ability to pick correct labels for the items.
We start by defining an idealized setting for this problem where the relative performance of users is consistent across items, and observe that the response matrices in this ideal case obey the Consecutive Ones Property (C1P). While the consecutive ones problem is well understood algorithmically with various discrete algorithms, we devise a simple variant of the HITS algorithm called “HITSnDIFFS” and prove that it can recover the ideal C1P-permutation in case it exists.

Unlike fast combinatorial algorithms for finding the consecutive ones permutation (if it exists), HITSnDIFFS also returns an ordering when such a permutation does not exist, thus providing a principled heuristic for the problem that returns the correct answer in the ideal case.
We compare HITSnDIFFS’s performance with previously proposed iterative and spectral algorithms to solve similar real-world problems. Our experiments on both real and simulated datasets show that HITSnDIFFS produces user rankings and item labelings with superior accuracy compared to the various scalable methods, and is competitive with other slower state-of-the-art methods while providing an asymptotic improvement in running time.