Learning Clusterwise Similarity with First-Order Features
Many clustering problems can be reduced to the task of partitioning a weighted graph into highly-connected components. The weighted edges indicate pairwise similarity between two nodes and can often be estimated from training data. However, in many domains, there exist higherorder dependencies not captured by pairwise metrics. For example, there may exist soft constraints on aggregate features of an entire cluster, such as its size, mean or mode. We propose clusterwise similarity metrics to directly measure the cohesion of an entire cluster of points. We describe ways to learn a clusterwise metric from labeled data, using weighted, first-order features over clusters. Extending recent work equating graph partitioning with inference in graphical models, we frame this approach within a discriminatively-trained Markov network. The advantages of our approach are demonstrated on the task of coreference resolution. 1 Clusterwise Similarity The input to a clustering algorithm is often a weighted undirected graph, where the weight between two nodes indicates their similarity. The goal of clustering is to partition the graph into components with heavy intra-cluster edges and light inter-cluster edges. Recently, these weights have been estimated from training data using maximum likelihood [1, 2]. While effective, by factoring the similarity metric into a set of pairwise functions, this approach sacrifices expressivity for tractability. For many domains, there exist clusterwise soft constraints that cannot be represented by pairwise functions. Consider the task of coreference resolution (also called identity uncertainty or deduplication), in which mentions referring to the same underlying object are clustered together. For example, given a database of research paper citations, we would like to cluster together citations referring to the same paper. Examples of clusterwise constraint include (1) a paper is rarely referenced more than 100 times or (2) an author’s name is unlikely to be misspelled 5 different ways. To represent these clusterwise constraints, we propose using similarity metrics to measure the compatibility of a cluster of nodes, rather than simply pairs of nodes. The challenge lies in constructing efficient methods to estimate these metrics from training samples and to partition the resulting graph. Given a deduplicated training database, we estimate the clusterwise metric by sampling positive and negative example clusters. We then specify a set of first-order predicates as features to describe the compatibility of the nodes in each cluster. Each of these predicates has an associated weight, which is estimated by maximizing the conditional log-likelihood of the training data. We approximate the optimal partitioning of a graph with an agglomerative algorithm that greedily merges clusters based on their predicted compatibility scores. We apply our technique to deduplicate authors and citations in a publications database and find that the clusterwise metric achieves higher F1 scores than the pairwise metric on 5 of 7 datasets. For more details, we refer the reader to our technical report [3].