# Yet Another Algorithm for Supervised Principal Component Analysis: Supervised Linear Centroid-Encoder

arXiv: https://arxiv.org/abs/2306.04622 · HTML: https://mlsanity.com/paper/2306.04622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [Supervised Dimensionality Reduction and Visualization using Centroid-encoder](https://mlsanity.com/paper/2002.11934/) (2020)
- [The classification for High-dimension low-sample size data](https://mlsanity.com/paper/2006.13018/) (2020)
- [Iterative Supervised Principal Components](https://mlsanity.com/paper/1710.06229/) (2017)
- [Supervised PCA: A Multiobjective Approach](https://mlsanity.com/paper/2011.05309/) (2020)

## Abstract (arXiv)

We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) citepghosh2022supervised. SLCE works by mapping the samples of a class to its class centroid using a linear transformation. The transformation is a projection that reconstructs a point such that its distance from the corresponding class centroid, i.e., centroid-reconstruction loss, is minimized in the ambient space. We derive a closed-form solution using an eigendecomposition of a symmetric matrix. We did a detailed analysis and presented some crucial mathematical properties of the proposed approach. %We also provide an iterative solution approach based solving the optimization problem using a descent method. We establish a connection between the eigenvalues and the centroid-reconstruction loss. In contrast to Principal Component Analysis (PCA) which reconstructs a sample in the ambient space, the transformation of SLCE uses the instances of a class to rebuild the corresponding class centroid. Therefore the proposed method can be considered a form of supervised PCA. Experimental results show the performance advantage of SLCE over other supervised methods.