Developing a Ranking Problem Library (RPLIB) from a data-oriented perspective

We present an improved library for the ranking problem called RPLIB. RPLIB includes the following data and features. (1) Real and artificial datasets of both pairwise data (i.e., information about the ranking of pairs of items) and feature data (i.e., a vector of features about each item to be ranked). These datasets range in size (e.g., from small $n=10$ item datasets to large datasets with hundred of items), application (e.g., from sports to economic data), and source (e.g. real versus artificially generated to have particular structures). (2) RPLIB contains code for the most common ranking algorithms such as the linear ordering optimization method and the Massey method. (3) RPLIB also has the ability for users to contribute their own data, code, and algorithms. Each RPLIB dataset has an associated .JSON model card of additional information such as the number and set of optimal rankings, the optimal objective value, and corresponding figures.

Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization

It is well known that good initializations can improve the speed and accuracy of the solutions of many nonnegative matrix factorization (NMF) algorithms. Many NMF algorithms are sensitive with respect to the initialization of W or H or both. This is especially true of algorithms of the alternating least squares (ALS) type, including the two new ALS algorithms that we present in this paper. We compare the results of six initialization procedures (two standard and four new) on our ALS algorithms. Lastly, we discuss the practical issue of choosing an appropriate convergence criterion.