# Methods for Brain Connectivity Analysis with Applications to Rat Local Field Potential Recordings

## TL;DR

This paper introduces various statistical and machine learning methods to analyze brain connectivity using rat LFP data, focusing on understanding neural dynamics and interactions.

## Contribution

The paper provides a comprehensive comparison of classical and advanced methods for brain connectivity analysis, emphasizing their strengths and limitations.

## Key findings

- Exploratory methods like correlation and coherence provide foundational insights into brain connectivity.
- Advanced techniques like Granger causality and spectral transfer entropy capture dynamic and nonlinear neural interactions.
- Topological data analysis and deep learning frameworks offer new perspectives for multi-scale connectivity modeling.

## Abstract

Modeling the brain dependence network is central to understanding underlying neural mechanisms such as perception, action, and memory. In this study, we present a broad range of statistical methods for analyzing dependence in a brain network. Leveraging a combination of classical and cutting-edge approaches, we analyze multivariate hippocampal local field potential (LFP) time series data concentrating on the encoding of nonspatial olfactory information in rats. We present the strengths and limitations of each method in capturing neural dynamics and connectivity. Our analysis begins with exploratory techniques, including correlation, partial correlation, spectral matrices, and coherence, to establish foundational connectivity insights. We then investigate advanced methods such as Granger causality (GC), robust canonical coherence analysis, spectral transfer entropy (STE), and wavelet coherence to capture dynamic and nonlinear interactions. Additionally, we investigate the utility of topological data analysis (TDA) to extract multi-scale topological features and explore deep learning-based canonical correlation frameworks for connectivity modeling. This comprehensive approach offers an introduction to the state-of-the-art techniques for the analysis of dependence networks, emphasizing the unique strengths of various methodologies, addressing computational challenges, and paving the way for future research.