# Optimal Projections for Classification with Naive Bayes

arXiv: https://arxiv.org/abs/2409.05635 · HTML: https://mlsanity.com/paper/2409.05635/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 24 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 2 of 2)

- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Optimal Projections for Gaussian Discriminants](https://mlsanity.com/paper/2004.03294/) (2020)

## Built on by (most cited first, 1 of 1)

- [Bags of Projected Nearest Neighbours: Competitors to Random Forests?](https://mlsanity.com/paper/2503.09651/) (2025)

## Abstract (arXiv)

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