# Canonical Tail Dependence for Soft Extremal Clustering of Multichannel Brain Signals

arXiv: https://arxiv.org/abs/2512.06435 · HTML: https://mlsanity.com/paper/2512.06435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 64 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Decompositions of Dependence for High-Dimensional Extremes](https://mlsanity.com/paper/1612.07190/) (2016)
- [k-means clustering of extremes](https://mlsanity.com/paper/1904.02970/) (2019)
- [Spectral Dependence](https://mlsanity.com/paper/2103.17240/) (2021)
- [Quantile-based fuzzy clustering of multivariate time series in the frequency domain](https://mlsanity.com/paper/2109.03728/) (2021)
- [GPDFlow: Generative Multivariate Threshold Exceedance Modeling via Normalizing Flows](https://mlsanity.com/paper/2503.11822/) (2025)
- [FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis](https://mlsanity.com/paper/2505.07276/) (2025)
- [KenCoh: A Ranked-Based Canonical Coherence](https://mlsanity.com/paper/2412.10521/) (2024)
- [Generative modelling of multivariate geometric extremes using normalising flows](https://mlsanity.com/paper/2505.02957/) (2025)
- [Conex-Connect: Learning Patterns in Extremal Brain Connectivity From Multi-Channel EEG Data](https://mlsanity.com/paper/2101.09352/) (2021)
- [Partial Tail-Correlation Coefficient Applied to Extremal-Network Learning](https://mlsanity.com/paper/2210.07351/) (2022)
- [Club Exco: clustering brain extreme communities from multi-channel EEG data](https://mlsanity.com/paper/2212.04338/) (2022)
- [Extreme Value Statistics for Analysing Simulated Environmental Extremes](https://mlsanity.com/paper/2312.13725/) (2023)
- [Statistics of Extremes for Neuroscience](https://mlsanity.com/paper/2404.09157/) (2024)
- [Spectral Extremal Connectivity of Two-State Seizure Brain Waves](https://mlsanity.com/paper/2503.04169/) (2025)
- [Separation-based causal discovery for extremes](https://mlsanity.com/paper/2505.08008/) (2025)
- [Modeling Nonstationary Extremal Dependence via Deep Spatial Deformations](https://mlsanity.com/paper/2505.12548/) (2025)
- [MOPED: A moving sum method for change point detection in pairwise extremal dependence](https://mlsanity.com/paper/2509.00585/) (2025)
- [Clustering of multivariate tail dependence using conditional methods](https://mlsanity.com/paper/2510.20424/) (2025)

## Abstract (arXiv)

We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of extreme events (e.g., seizures) that can help to identify their occurrence. Numerous studies have established that connectivity-based features are effective for discriminating brain states. Here, we demonstrate the advantage of the proposed approach: that tail connectivity provides additional discriminatory power, enabling more accurate identification of extreme-related events and improved seizure risk management. Common approaches in tail dependence modeling use pairwise summary measures or parametric models. However, these approaches do not identify channels that drive the maximal tail dependence between two groups of signals -- an information that is useful when analyzing electroencephalography of epileptic patients where specific channels are responsible for seizure occurrences. A familiar approach in traditional signal processing is canonical correlation, which we extend to the tails to develop a visualization of extremal channel-contributions. Through the tail pairwise dependence matrix (TPDM), we develop a computationally-efficient estimator for our canonical tail dependence measure. Our method is then used for accurate frequency-based soft clustering of neonates, distinguishing those with seizures from those without.