# A Dataset-Level Geometric Framework for Ensemble Classifiers

arXiv: https://arxiv.org/abs/2106.08658 · HTML: https://mlsanity.com/paper/2106.08658/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [To tune or not to tune the number of trees in random forest?](https://mlsanity.com/paper/1705.05654/) (2017)
- [Maximizing Overall Diversity for Improved Uncertainty Estimates in Deep Ensembles](https://mlsanity.com/paper/1906.07380/) (2019)
- [Less Is More: A Comprehensive Framework for the Number of Components of Ensemble Classifiers](https://mlsanity.com/paper/1709.02925/) (2017)
- [GOOWE: Geometrically Optimum and Online-Weighted Ensemble Classifier for Evolving Data Streams](https://mlsanity.com/paper/1709.02800/) (2017)

## Built on by (most cited first, 2 of 2)

- [Leveraging Linear Independence of Component Classifiers: Optimizing Size and Prediction Accuracy for Online Ensembles](https://mlsanity.com/paper/2308.14175/) (2023)
- [Ensemble Performance Through the Lens of Linear Independence of Classifier Votes in Data Streams](https://mlsanity.com/paper/2511.21465/) (2025)

## Abstract (arXiv)

Ensemble classifiers have been investigated by many in the artificial intelligence and machine learning community. Majority voting and weighted majority voting are two commonly used combination schemes in ensemble learning. However, understanding of them is incomplete at best, with some properties even misunderstood. In this paper, we present a group of properties of these two schemes formally under a dataset-level geometric framework. Two key factors, every component base classifier's performance and dissimilarity between each pair of component classifiers are evaluated by the same metric - the Euclidean distance. Consequently, ensembling becomes a deterministic problem and the performance of an ensemble can be calculated directly by a formula. We prove several theorems of interest and explain their implications for ensembles. In particular, we compare and contrast the effect of the number of component classifiers on these two types of ensemble schemes. Empirical investigation is also conducted to verify the theoretical results when other metrics such as accuracy are used. We believe that the results from this paper are very useful for us to understand the fundamental properties of these two combination schemes and the principles of ensemble classifiers in general. The results are also helpful for us to investigate some issues in ensemble classifiers, such as ensemble performance prediction, selecting a small number of base classifiers to obtain efficient and effective ensembles.