通过最优投影提升朴素贝叶斯分类性能，兼顾降维与可视化。
Optimal Projections for Classification with Naive Bayes
- 寻找最优线性投影替代原始坐标轴，优化分类因子分解
- 在162个数据集上显著优于主流概率判别模型
- 适合需要可解释性与高效降维的分类任务
朴素贝叶斯分类模型中，类条件密度被建模为沿坐标轴方向边缘密度的乘积。本文研究如何通过寻找新的基向量来改进这一因式分解，以增强分类模型的区分能力。问题被形式化为投影追踪，目标是找到使分类性能最优的线性投影方向，优化标准基于多项式似然，其中概率通过投影后数据的朴素贝叶斯因式分解估计。该方法兼具降维与可视化优势。我们讨论了其与类条件独立分量分析的直观联系，并在实际应用中展示了可视化效果。在包含162个公开基准数据集的大规模实验中，所提方法显著优于其他主流概率判别分析模型，且与支持向量机性能相当。相关R代码已开源：https://github.com/DavidHofmeyr/OPNB。
原文摘要 · Abstract (English)
In the Naive Bayes classification model the class conditional densities are estimated as the products of their marginal densities along the cardinal basis directions. We study the problem of obtaining an alternative basis for this factorisation with the objective of enhancing the discriminatory power of the associated classification model. We formulate the problem as a projection pursuit to find the optimal linear projection on which to perform classification. Optimality is determined based on the multinomial likelihood within which probabilities are estimated using the Naive Bayes factorisation of the projected data. Projection pursuit offers the added benefits of dimension reduction and visualisation. We discuss an intuitive connection with class conditional independent components analysis, and show how this is realised visually in practical applications. The performance of the resulting classification models is investigated using a large collection of (162) publicly available benchmark data sets and in comparison with relevant alternatives. We find that the proposed approach substantially outperforms other popular probabilistic discriminant analysis models and is highly competitive with Support Vector Machines. Code to implement the proposed approach, in the form of an R package, is available from https://github.com/DavidHofmeyr/OPNB
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。