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A3S: A General Active Clustering Method with Pairwise Constraints

Xun Deng, Junlong Liu, Han Zhong, Fuli Feng, Chen Shen, Xiangnan He, Jieping Ye, Zheng Wang

TL;DR

The paper addresses the high query costs of active clustering in large, multi-class scenarios by introducing A3S, a general cluster-adjustment framework. It combines an adaptive initialization to determine a suitable initial clustering with an active aggregation and splitting stage guided by an $NMI$-gain analysis and a Purity Test, using must-link/cannot-link constraints and transitive inference. The authors provide a theoretical guarantee that aggregation can be non-deteriorating under mild purity conditions and demonstrate substantial reductions in required human queries while achieving superior clustering quality across diverse real-world datasets, including large-scale MS1M subsets. Collectively, A3S advances scalable, information-theoretically guided active clustering that adapts to unknown or evolving data distributions without relying on precise priors about $K$ or class membership.

Abstract

Active clustering aims to boost the clustering performance by integrating human-annotated pairwise constraints through strategic querying. Conventional approaches with semi-supervised clustering schemes encounter high query costs when applied to large datasets with numerous classes. To address these limitations, we propose a novel Adaptive Active Aggregation and Splitting (A3S) framework, falling within the cluster-adjustment scheme in active clustering. A3S features strategic active clustering adjustment on the initial cluster result, which is obtained by an adaptive clustering algorithm. In particular, our cluster adjustment is inspired by the quantitative analysis of Normalized mutual information gain under the information theory framework and can provably improve the clustering quality. The proposed A3S framework significantly elevates the performance and scalability of active clustering. In extensive experiments across diverse real-world datasets, A3S achieves desired results with significantly fewer human queries compared with existing methods.

A3S: A General Active Clustering Method with Pairwise Constraints

TL;DR

The paper addresses the high query costs of active clustering in large, multi-class scenarios by introducing A3S, a general cluster-adjustment framework. It combines an adaptive initialization to determine a suitable initial clustering with an active aggregation and splitting stage guided by an -gain analysis and a Purity Test, using must-link/cannot-link constraints and transitive inference. The authors provide a theoretical guarantee that aggregation can be non-deteriorating under mild purity conditions and demonstrate substantial reductions in required human queries while achieving superior clustering quality across diverse real-world datasets, including large-scale MS1M subsets. Collectively, A3S advances scalable, information-theoretically guided active clustering that adapts to unknown or evolving data distributions without relying on precise priors about or class membership.

Abstract

Active clustering aims to boost the clustering performance by integrating human-annotated pairwise constraints through strategic querying. Conventional approaches with semi-supervised clustering schemes encounter high query costs when applied to large datasets with numerous classes. To address these limitations, we propose a novel Adaptive Active Aggregation and Splitting (A3S) framework, falling within the cluster-adjustment scheme in active clustering. A3S features strategic active clustering adjustment on the initial cluster result, which is obtained by an adaptive clustering algorithm. In particular, our cluster adjustment is inspired by the quantitative analysis of Normalized mutual information gain under the information theory framework and can provably improve the clustering quality. The proposed A3S framework significantly elevates the performance and scalability of active clustering. In extensive experiments across diverse real-world datasets, A3S achieves desired results with significantly fewer human queries compared with existing methods.
Paper Structure (31 sections, 2 theorems, 40 equations, 8 figures, 4 tables, 3 algorithms)

This paper contains 31 sections, 2 theorems, 40 equations, 8 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Notation and Definition
  4. Theoretical Analysis
  5. Adaptive Active Aggregation and Splitting
  6. Initialization via Adaptive Clustering
  7. Active Aggregation and Splitting
  8. Discussion.
  9. Experiments
  10. Experimental Setup
  11. Comparison with SOTA Active Clustering Methods
  12. A3S for Different Clustering Algorithms
  13. Influence of Estimated Pairwise Probability Quality
  14. Performance of A3S on Large datasets.
  15. Case Study for A3S
  16. ...and 16 more sections

Key Result

Theorem 2.5

Denote the clustering of $N$ samples as $\Omega$, the ground truth clustering as $C$, and the NMI value of $\Omega$ with respect to $C$ as $n_1$. For any two clusters in $\Omega$, say $w_1$ and $w_2$, suppose they have a common dominant class $c_1$ with purities $t_1$ and $t_2$ respectively, where $

Figures (8)

  • Figure 1: The workflow of A3S which consists of the adaptive clustering stage and active aggregation and splitting stage.
  • Figure 2: Case study for A3S. In iteration 1, the cluster $w_6$ does not pass the purity test and the oracle invests 12 queries to split it into two pure subclusters. In iteration 2, the query result for the two central samples is must-link and they are merged into one cluster.
  • Figure 3: Comparing the performance of A3S and baselines on four datasets in terms of query count. More queries are invested for baselines to illustrate their characteristics.
  • Figure 4: Performance of A3S on MK100 and Humbi-Face when utilizing different clustering algorithms to generate the initial clustering result.
  • Figure 5: Performance of A3S on Handwritten when 1, 2, or 4 views of the feature are used.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 2.1: Active Clustering
  • Definition 2.2: Cluster Adjustment Scheme
  • Definition 2.3: NMI
  • Definition 2.4: Purity
  • Theorem 2.5: Guarantee for Cluster Aggregation
  • Definition 2.6: Expected NMI Gain
  • proof : Proof of Theorem \ref{['lemma:purity']}
  • proof : Derivation of Eq. \ref{['prob:ori']}
  • Theorem 1.1: Completeness of FTI
  • proof : Proof of Theorem \ref{['lemma:tic']}