# Silhouettes and quasi residual plots for neural nets and tree-based classifiers

arXiv: https://arxiv.org/abs/2106.08814 · HTML: https://mlsanity.com/paper/2106.08814/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [WASSA-2017 Shared Task on Emotion Intensity](https://mlsanity.com/paper/1708.03700/) (2017)
- [A Survey on Understanding, Visualizations, and Explanation of Deep Neural Networks](https://mlsanity.com/paper/2102.01792/) (2021)
- [Transforming variables to central normality](https://mlsanity.com/paper/2005.07946/) (2020)
- [Class maps for visualizing classification results](https://mlsanity.com/paper/2007.14495/) (2020)

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

- [Interval Fisher's Discriminant Analysis and Visualisation](https://mlsanity.com/paper/2512.11945/) (2025)

## Abstract (arXiv)

Classification by neural nets and by tree-based methods are powerful tools of machine learning. There exist interesting visualizations of the inner workings of these and other classifiers. Here we pursue a different goal, which is to visualize the cases being classified, either in training data or in test data. An important aspect is whether a case has been classified to its given class (label) or whether the classifier wants to assign it to different class. This is reflected in the (conditional and posterior) probability of the alternative class (PAC). A high PAC indicates label bias, i.e. the possibility that the case was mislabeled. The PAC is used to construct a silhouette plot which is similar in spirit to the silhouette plot for cluster analysis (Rousseeuw, 1987). The average silhouette width can be used to compare different classifications of the same dataset. We will also draw quasi residual plots of the PAC versus a data feature, which may lead to more insight in the data. One of these data features is how far each case lies from its given class. The graphical displays are illustrated and interpreted on benchmark data sets containing images, mixed features, and tweets.