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Ensembles, which employ a set of classifiers to enhance classificationaccuracy collectively, are crucial in the era of big data. However, althoughthere is general agreement that the relation between ensemble size and itsprediction accuracy, the exact nature of this relationship is still unknown. Weintroduce a novel perspective, rooted in the linear independence ofclassifier's votes, to analyze the interplay between ensemble size andprediction accuracy. This framework reveals a theoretical link, consequentlyproposing an ensemble size based on this relationship. Our study builds upon ageometric framework and develops a series of theorems. These theorems clarifythe role of linear dependency in crafting ensembles. We present a method todetermine the minimum ensemble size required to ensure a target probability oflinearly independent votes among component classifiers. Incorporating real andsynthetic datasets, our empirical results demonstrate a trend: increasing thenumber of classifiers enhances accuracy, as predicted by our theoreticalinsights. However, we also identify a point of diminishing returns, beyondwhich additional classifiers provide diminishing improvements in accuracy.Surprisingly, the calculated ideal ensemble size deviates from empiricalresults for certain datasets, emphasizing the influence of other factors. Thisstudy opens avenues for deeper investigations into the complex dynamicsgoverning ensemble design and offers guidance for constructing efficient andeffective ensembles in practical scenarios.

Leveraging Linear Independence of Component Classifiers: Optimizing Size and Prediction Accuracy for Online Ensembles