Extend co-factor analysis to tensor/multi-layer citation networks

Extend the co-factor analysis approach that models citation networks as partially observed directed adjacency matrices and estimates latent co-factors via AdaptiveImpute-based matrix completion followed by varimax rotation to the tensor or multi-layer citation network setting with multiple explicitly labeled types of citations, such as those present in U.S. Court Opinions.

Background

The paper proposes a co-factor analysis method for directed citation networks that treats forward-in-time citations as structurally missing and estimates latent outgoing and incoming factors using a specialized implementation of AdaptiveImpute, followed by varimax rotation. This framework operates on a single-layer adjacency matrix with an upper-triangular observation pattern imposed by chronology.

In the Discussion, the authors point to an extension where documents may use multiple distinct citation types, motivating a tensor or multi-layer representation. Such datasets (e.g., U.S. Court Opinions) naturally lead to multi-layer structures requiring methods that generalize the current single-layer co-factor model and its computational machinery to tensor or multi-layer settings.