[Paper Review] Factorized Binary Search: change point detection in the network structure of multivariate high-dimensional time series

Martin Ondrus, Emily Olds+1 more|arXiv (Cornell University)|Mar 10, 2021

Time Series Analysis and Forecasting4 citations

TL;DR

This paper introduces Factorized Binary Search (FaBiSearch), a novel method for detecting multiple change points in the network structure of high-dimensional multivariate time series, particularly fMRI data. By combining non-negative matrix factorization (NMF) with a binary search framework, FaBiSearch identifies dynamic shifts in functional connectivity, outperforms existing methods in simulations, and reveals stable, recurring network states across subjects in both resting-state and task-based fMRI experiments.

ABSTRACT

Functional magnetic resonance imaging (fMRI) time series data presents a unique opportunity to understand the behavior of temporal brain connectivity, and models that uncover the complex dynamic workings of this organ are of keen interest in neuroscience. We are motivated to develop accurate change point detection and network estimation techniques for high-dimensional whole-brain fMRI data. To this end, we introduce factorized binary search (FaBiSearch), a novel change point detection method in the network structure of multivariate high-dimensional time series in order to understand the large-scale characterizations and dynamics of the brain. FaBiSearch employs non-negative matrix factorization, an unsupervised dimension reduction technique, and a new binary search algorithm to identify multiple change points. In addition, we propose a new method for network estimation for data between change points. We seek to understand the dynamic mechanism of the brain, particularly for two fMRI data sets. The first is a resting-state fMRI experiment, where subjects are scanned over three visits. The second is a task-based fMRI experiment, where subjects read Chapter 9 of Harry Potter and the Sorcerer's Stone. For the resting-state data set, we examine the test-retest behavior of dynamic functional connectivity, while for the task-based data set, we explore network dynamics during the reading and whether change points across subjects coincide with key plot twists in the story. Further, we identify hub nodes in the brain network and examine their dynamic behavior. Finally, we make all the methods discussed available in the R package fabisearch on CRAN.

Motivation & Objective

• To develop a scalable method for detecting multiple change points in high-dimensional, multivariate time series, particularly in fMRI data where functional connectivity is expected to be non-stationary.
• To address the limitations of moving-window approaches and traditional change point detection by enabling accurate detection in high-dimensional, non-stationary data with minimal assumptions.
• To estimate stable, interpretable network structures between detected change points using a novel graph estimation method based on consensus matrices.
• To explore the dynamic functional connectivity of the brain in real fMRI datasets, including test-retest reliability in resting-state and network evolution during a narrative task.
• To make the method accessible via an R package (fabisearch) on CRAN for broader use in neuroscience and time series analysis.

Proposed method

• FaBiSearch uses non-negative matrix factorization (NMF) to reduce dimensionality and extract underlying dependence structures from high-dimensional time series data.
• A novel binary search algorithm is applied to efficiently locate multiple change points by recursively partitioning the time series and evaluating structural changes via NMF-based reconstruction error.
• The method assumes the number and location of change points are unknown a priori and uses a statistical criterion to determine optimal partitioning.
• Between change points, a new network estimation method constructs graphs using consensus matrices derived from binary connectivity matrices, ensuring only positive relationships (0 to 1) are modeled.
• The consensus matrix is computed as the arithmetic mean of multiple binary connectivity matrices, enhancing robustness and interpretability.
• The approach is validated through simulations and applied to two real fMRI datasets: a resting-state study with three visits and a task-based study involving reading a narrative.

Experimental results

Research questions

• RQ1 How accurately can FaBiSearch detect multiple change points in high-dimensional, non-stationary fMRI time series compared to existing methods?
• RQ2 What is the test-retest reliability of dynamic functional connectivity in resting-state fMRI data using FaBiSearch?
• RQ3 Do change points in functional connectivity during a narrative task coincide with key plot developments in the story?
• RQ4 Are there stable, recurring network states across subjects in both resting-state and task-based fMRI experiments?
• RQ5 How do hub nodes in the brain network behave dynamically across detected change points?

Key findings

• FaBiSearch outperforms the Network Change Point Detection (NCPD) method in all simulation evaluation criteria, demonstrating superior accuracy in change point detection.
• In simulations, FaBiSearch achieved significantly better detection accuracy than NCPD, though it required substantially more computation time (25.04 minutes vs. 0.75 minutes on average across 100 iterations).
• In the resting-state fMRI data, FaBiSearch detected multiple change points, revealing stable dynamic functional connectivity patterns across subjects and visits, indicating good test-retest reliability.
• In the task-based fMRI experiment, change points were found to align with key plot twists in Chapter 9 of Harry Potter, suggesting that network dynamics reflect cognitive processing of narrative structure.
• The method identified common network states across subjects, indicating consistent large-scale functional organization in both resting and task conditions.
• Hub nodes in the brain network showed dynamic behavior, with their connectivity patterns shifting across detected change points, highlighting their role in adaptive network reconfiguration.