# Supervised Dimensionality Reduction and Visualization using Centroid-encoder

arXiv: https://arxiv.org/abs/2002.11934 · HTML: https://mlsanity.com/paper/2002.11934/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 10 of 10)

- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [Random Forest Autoencoders for Guided Representation Learning](https://mlsanity.com/paper/2502.13257/) (2025)
- [Sparse Centroid-Encoder: A Nonlinear Model for Feature Selection](https://mlsanity.com/paper/2201.12910/) (2022)
- [A Brief Survey on Representation Learning based Graph Dimensionality Reduction Techniques](https://mlsanity.com/paper/2211.05594/) (2022)
- [Yet Another Algorithm for Supervised Principal Component Analysis: Supervised Linear Centroid-Encoder](https://mlsanity.com/paper/2306.04622/) (2023)
- [Feature Selection using Sparse Adaptive Bottleneck Centroid-Encoder](https://mlsanity.com/paper/2306.04795/) (2023)
- [Sparse Linear Centroid-Encoder: A Convex Method for Feature Selection](https://mlsanity.com/paper/2306.04824/) (2023)
- [A Convex formulation for linear discriminant analysis](https://mlsanity.com/paper/2503.13623/) (2025)
- [Why Can't I See My Clusters? A Precision-Recall Approach to Dimensionality Reduction Validation](https://mlsanity.com/paper/2509.04222/) (2025)
- [Online Supervised Dimension Reduction with Random Features: Diagnostics and Computational Trade-offs](https://mlsanity.com/paper/2609.20454/) (2026)

## Abstract (arXiv)

Visualizing high-dimensional data is an essential task in Data Science and Machine Learning. The Centroid-Encoder (CE) method is similar to the autoencoder but incorporates label information to keep objects of a class close together in the reduced visualization space. CE exploits nonlinearity and labels to encode high variance in low dimensions while capturing the global structure of the data. We present a detailed analysis of the method using a wide variety of data sets and compare it with other supervised dimension reduction techniques, including NCA, nonlinear NCA, t-distributed NCA, t-distributed MCML, supervised UMAP, supervised PCA, Colored Maximum Variance Unfolding, supervised Isomap, Parametric Embedding, supervised Neighbor Retrieval Visualizer, and Multiple Relational Embedding. We empirically show that centroid-encoder outperforms most of these techniques. We also show that when the data variance is spread across multiple modalities, centroid-encoder extracts a significant amount of information from the data in low dimensional space. This key feature establishes its value to use it as a tool for data visualization.