Ensembles, which employ a set of classifiers to enhance classification
accuracy collectively, are crucial in the era of big data. However, although
there is general agreement that the relation between ensemble size and its
prediction accuracy, the exact nature of this relationship is still unknown. We
introduce a novel perspective, rooted in the linear independence of
classifier's votes, to analyze the interplay between ensemble size and
prediction accuracy. This framework reveals a theoretical link, consequently
proposing an ensemble size based on this relationship. Our study builds upon a
geometric framework and develops a series of theorems. These theorems clarify
the role of linear dependency in crafting ensembles. We present a method to
determine the minimum ensemble size required to ensure a target probability of
linearly independent votes among component classifiers. Incorporating real and
synthetic datasets, our empirical results demonstrate a trend: increasing the
number of classifiers enhances accuracy, as predicted by our theoretical
insights. However, we also identify a point of diminishing returns, beyond
which additional classifiers provide diminishing improvements in accuracy.
Surprisingly, the calculated ideal ensemble size deviates from empirical
results for certain datasets, emphasizing the influence of other factors. This
study opens avenues for deeper investigations into the complex dynamics
governing ensemble design and offers guidance for constructing efficient and
effective ensembles in practical scenarios.

通过线性独立性分析研究集成大小和分类准确度之间的关系，提出了基于该关系的集成大小的方法。实证结果表明增加分类器数量提高准确度，但存在收益递减点。该研究为进一步研究集成设计的复杂动态提供了开拓途径，并为实际场景中构建高效有效的集成提供了指导。