# Clustered Gaussian Graphical Model via Symmetric Convex Clustering

## TL;DR

This paper introduces a new convex clustering method for Gaussian graphical models to identify functional neuron groups from activity data, with proven convergence and demonstrated effectiveness.

## Contribution

It proposes a novel symmetric convex clustering penalty within a convex optimization framework for neural data analysis.

## Key findings

- Effective clustering on synthetic data
- Successful application to real neuroscientific data
- Convergence guarantees for the ADMM algorithm

## Abstract

Knowledge of functional groupings of neurons can shed light on structures of neural circuits and is valuable in many types of neuroimaging studies. However, accurately determining which neurons carry out similar neurological tasks via controlled experiments is both labor-intensive and prohibitively expensive on a large scale. Thus, it is of great interest to cluster neurons that have similar connectivity profiles into functionally coherent groups in a data-driven manner. In this work, we propose the clustered Gaussian graphical model (GGM) and a novel symmetric convex clustering penalty in an unified convex optimization framework for inferring functional clusters among neurons from neural activity data. A parallelizable multi-block Alternating Direction Method of Multipliers (ADMM) algorithm is used to solve the corresponding convex optimization problem. In addition, we establish convergence guarantees for the proposed ADMM algorithm. Experimental results on both synthetic data and real-world neuroscientific data demonstrate the effectiveness of our approach.