# Interpretable liquid crystal phase classification via two-by-two ordinal patterns

arXiv: https://arxiv.org/abs/2603.26723 · HTML: https://mlsanity.com/paper/2603.26723/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 57 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Learning physical properties of liquid crystals with deep convolutional neural networks](https://mlsanity.com/paper/2004.01691/) (2020)
- [Discriminating image textures with the multiscale two-dimensional complexity-entropy causality plane](https://mlsanity.com/paper/1609.01625/) (2016)
- [Estimating physical properties from liquid crystal textures via machine learning and complexity-entropy methods](https://mlsanity.com/paper/1901.01754/) (2019)
- [Two new parameters for the ordinal analysis of images](https://mlsanity.com/paper/2212.14643/) (2022)

## Abstract (arXiv)

Liquid crystal textures encode rich structural information, yet mapping these images to mesophase identity remains challenging because visually similar patterns can arise from distinct structures. Here we present a simple, interpretable representation that maps textures to a 75-dimensional frequency vector of two-by-two ordinal patterns, grouped into eleven symmetry-based types to characterize a large-scale dataset spanning seven mesophases. Combined with a simple machine learning classifier, this lightweight representation yields near-perfect phase recognition, including the difficult distinction between smectic A and smectic B mesophases. Our approach generalizes to unseen compounds and accurately distinguishes between phase identity and material origin. Unlike deep learning methods, each ordinal pattern is readily interpretable, and model explanations augmented with network visualizations of pattern interactions reveal the specific types and pairwise dependencies that drive each mesophase decision, providing compact, physically meaningful summaries of texture determinants. These results establish two-by-two ordinal patterns as an interpretable and scalable tool for liquid crystal image analysis, with potential applications to other complex patterned systems in materials science.