Decomposing the Jaccard Distance and the Jaccard Index in ABCDE

ABCDE is a sophisticated technique for evaluating differences between very large clusterings. Its main metric that characterizes the magnitude of the difference between two clusterings is the JaccardDistance, which is a true distance metric in the space of all clusterings of a fixed set of (weighted) items. The JaccardIndex is the complementary metric that characterizes the similarity of two clusterings. Its relationship with the JaccardDistance is simple: JaccardDistance + JaccardIndex = 1. This paper decomposes the JaccardDistance and the JaccardIndex further. In each case, the decomposition yields Impact and Quality metrics. The Impact metrics measure aspects of the magnitude of the clustering diff, while Quality metrics use human judgements to measure how much the clustering diff improves the quality of the clustering. The decompositions of this paper offer more and deeper insight into a clustering change. They also unlock new techniques for debugging and exploring the nature of the clustering diff. The new metrics are mathematically well-behaved and they are interrelated via simple equations. While the work can be seen as an alternative formal framework for ABCDE, we prefer to view it as complementary. It certainly offers a different perspective on the magnitude and the quality of a clustering change, and users can use whatever they want from each approach to gain more insight into a change.

Evaluation of Cluster Id Assignment Schemes with ABCDE

A cluster id assignment scheme labels each cluster of a clustering with a distinct id. The goal of id assignment is semantic id stability, which means that, whenever possible, a cluster for the same underlying concept as that of a historical cluster should ideally receive the same id as the historical cluster. Semantic id stability allows the users of a clustering to refer to a concept's cluster with an id that is stable across clusterings/time. This paper treats the problem of evaluating the relative merits of id assignment schemes. In particular, it considers a historical clustering with id assignments, and a new clustering with ids assigned by a baseline and an experiment. It produces metrics that characterize both the magnitude and the quality of the id assignment diffs between the baseline and the experiment. That happens by transforming the problem of cluster id assignment into a problem of cluster membership, and evaluating it with ABCDE. ABCDE is a sophisticated and scalable technique for evaluating differences in cluster membership in real-world applications, where billions of items are grouped into millions of clusters, and some items are more important than others. The paper also describes several generalizations to the basic evaluation setup for id assignment schemes. For example, it is fairly straightforward to evaluate changes that simultaneously mutate cluster memberships and cluster ids. The ideas are generously illustrated with examples.

ABCDE: Application-Based Cluster Diff Evals

This paper considers the problem of evaluating clusterings of very large populations of items. Given two clusterings, namely a Baseline clustering and an Experiment clustering, the tasks are twofold: 1) characterize their differences, and 2) determine which clustering is better. ABCDE is a novel evaluation technique for accomplishing that. It aims to be practical: it allows items to have associated importance values that are application-specific, it is frugal in its use of human judgements when determining which clustering is better, and it can report metrics for arbitrary slices of items, thereby facilitating understanding and debugging. The approach to measuring the delta in the clustering quality is novel: instead of trying to construct an expensive ground truth up front and evaluating the each clustering with respect to that, where the ground truth must effectively pre-anticipate clustering changes, ABCDE samples questions for judgement on the basis of the actual diffs between the clusterings. ABCDE builds upon the pointwise metrics for clustering evaluation, which make the ABCDE metrics intuitive and simple to understand. The mathematical elegance of the pointwise metrics equip ABCDE with rigorous yet practical ways to explore the clustering diffs and to estimate the quality delta.

Pointwise Metrics for Clustering Evaluation

This paper defines pointwise clustering metrics, a collection of metrics for characterizing the similarity of two clusterings. These metrics have several interesting properties which make them attractive for practical applications. They can take into account the relative importance of the various items that are clustered. The metric definitions are based on standard set-theoretic notions and are simple to understand. They characterize aspects that are important for typical applications, such as cluster homogeneity and completeness. It is possible to assign metrics to individual items, clusters, arbitrary slices of items, and the overall clustering. The metrics can provide deep insights, for example they can facilitate drilling deeper into clustering mistakes to understand where they happened, or help to explore slices of items to understand how they were affected. Since the pointwise metrics are mathematically well-behaved, they can provide a strong foundation for a variety of clustering evaluation techniques. In this paper we discuss in depth how the pointwise metrics can be used to evaluate an actual clustering with respect to a ground truth clustering.