# Semi-supervised Clustering with Two Types of Background Knowledge: Fusing Pairwise Constraints and Monotonicity Constraints

arXiv: https://arxiv.org/abs/2302.14060 · HTML: https://mlsanity.com/paper/2302.14060/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 25 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis](https://mlsanity.com/paper/1606.04316/) (2016)
- [Understanding artificial intelligence ethics and safety](https://mlsanity.com/paper/1906.05684/) (2019)
- [Monotonic classification: an overview on algorithms, performance measures and data sets](https://mlsanity.com/paper/1811.07155/) (2018)
- [Recent Trends in the Use of Statistical Tests for Comparing Swarm and Evolutionary Computing Algorithms: Practical Guidelines and a Critical Review](https://mlsanity.com/paper/2002.09227/) (2020)
- [Seeking Commonness and Inconsistencies: A Jointly Smoothed Approach to Multi-view Subspace Clustering](https://mlsanity.com/paper/2203.08060/) (2022)
- [A semi-supervised sparse K-Means algorithm](https://mlsanity.com/paper/2003.06973/) (2020)
- [Monotonic models for real-time dynamic malware detection](https://mlsanity.com/paper/1804.03643/) (2018)
- [Fuzzy k-Nearest Neighbors with monotonicity constraints: Moving towards the robustness of monotonic noise](https://mlsanity.com/paper/2003.02601/) (2020)

## Abstract (arXiv)

This study addresses the problem of performing clustering in the presence of two types of background knowledge: pairwise constraints and monotonicity constraints. To achieve this, the formal framework to perform clustering under monotonicity constraints is, firstly, defined, resulting in a specific distance measure. Pairwise constraints are integrated afterwards by designing an objective function which combines the proposed distance measure and a pairwise constraint-based penalty term, in order to fuse both types of information. This objective function can be optimized with an EM optimization scheme. The proposed method serves as the first approach to the problem it addresses, as it is the first method designed to work with the two types of background knowledge mentioned above. Our proposal is tested in a variety of benchmark datasets and in a real-world case of study.