A Dataset-Level Geometric Framework for Ensemble Classifiers
This work provides foundational insights for researchers and practitioners in machine learning to better understand and optimize ensemble classifiers, though it is incremental as it builds on existing combination schemes.
The paper tackles the incomplete understanding of majority and weighted majority voting in ensemble classifiers by presenting a dataset-level geometric framework that formalizes their properties using Euclidean distance to evaluate base classifier performance and dissimilarity, enabling deterministic calculation of ensemble performance and proving several theorems.
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.