![[2601.01679] Simplex Deep Linear Discriminant Analysis](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2601.01679] Simplex Deep Linear Discriminant Analysis
Summary
The paper presents a novel approach to Deep Linear Discriminant Analysis (Deep LDA) by introducing a constrained formulation that stabilizes maximum likelihood estimation, improving classification performance on various datasets.
Why It Matters
This research addresses the limitations of traditional Deep LDA methods, which can lead to poor classification performance due to overlapping class clusters. By proposing a geometric constraint that fixes class means, the study enhances the interpretability and effectiveness of deep learning classifiers, which is crucial for applications in machine learning and data science.
Key Takeaways
- Conventional Deep LDA suffers from degenerate solutions affecting classification.
- The proposed constrained Deep LDA stabilizes maximum likelihood estimation.
- The method achieves competitive accuracy with interpretable latent geometry.
- Improvements were validated on diverse datasets including images and texts.
- Geometric constraints enhance the separation of class clusters in latent space.
Statistics > Machine Learning arXiv:2601.01679 (stat) [Submitted on 4 Jan 2026 (v1), last revised 19 Feb 2026 (this version, v2)] Title:Simplex Deep Linear Discriminant Analysis Authors:Maxat Tezekbayev, Arman Bolatov, Zhenisbek Assylbekov View a PDF of the paper titled Simplex Deep Linear Discriminant Analysis, by Maxat Tezekbayev and 2 other authors View PDF HTML (experimental) Abstract:We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of how to train the resulting deep classifier by maximum likelihood estimation (MLE). We first show that end-to-end MLE training of an unconstrained Deep LDA model ignores discrimination: when both the LDA parameters and the encoder parameters are learned jointly, the likelihood admits a degenerate solution in which some of the class clusters may heavily overlap or even collapse, and classification performance deteriorates. Batchwise moment re-estimation of the LDA parameters does not remove this failure mode. We then propose a constrained Deep LDA formulation that fixes the class means to the vertices of a regular simplex in the latent space and restricts the shared covariance to be spherical, leaving only the priors and a single variance parameter to be learned along with the encoder. Under these geometric constraints, MLE becomes stable and yields well-se...
