BIMSA >
BIMSA-HSE Joint Seminar on Data Analytics and Topology
Analysis of brain networks with blurred magnitude homology
Analysis of brain networks with blurred magnitude homology
Organizers
Speaker
Alexander Kachura
Time
Monday, January 19, 2026 8:00 PM - 9:00 PM
Venue
Online
Online
Zoom 468 248 1222
(BIMSA)
Abstract
The seminar is scheduled online for Monday from 20:00 to 21:00(Beijing Time)/15:00 to 16:00(Moscow Time).
Alexander Kachura, joint work with Vsevolod Chernyshev
One of the approaches to analyze multivariate time series with interdependent components is to construct a complete weighted graph with nodes corresponding to the components of the time series and edge weights representing the strength of dependence between the pair of components corresponding to their ends. Neuroscience is among the many fields where this methodology is popular. A prominent example is the analysis of functional connectomes [1], brain networks whose nodes represent brain regions. These networks exhibit nontrivial structure, so their topological characteristics are useful for analysis. The level of interconnection between brain regions is usually measured using non-directional correlations, while the functional connections between brain regions are inherently directional. Topological characteristics of graphs can be analyzed with persistent homology [2], an increasingly popular dataanalysis tool that can also be applied to graphs. The essence of this approach is to track the moments of the appearance and disappearance of topological structures as the scale varies, using algebraic invariants called homology. When applied to weighted graphs – including functional connectomes – persistent homology allows us to study how the topological structure of a graph changes as the edgefiltering threshold varies. This enables identification of noise-robust topological features, which is crucial when the graph structure is not given a priori but estimated from data. Several homology theories exist. Simplicial homology – historically the first one used to compute persistent homology – cannot account for the directions of graph edges. The most direct generalization of this homology theory to digraphs is the homology of directed flag complexes [3]. However, it still discards some directional information. One of the homology theories that makes it possible to preserve a large proportion of information about the directions of edges is blurred magnitude homology [4].
In this work we introduce a method for classifying directed functional connectomes using blurred magnitude homology, specifically its Betti curves, a popular numerical descriptor of persistent homology. As an example, we apply the developed technique to study graphs constructed from fMRI scans of individuals with ASD and typically developing controls.
We experimentally tested the approach on the ABIDE dataset.
This work was supported by the Russian Science Foundation, Grant No. 24-68-00030.
References
1. Uddin, L. Q., Yeo, B. T., & Spreng, R. N. (2019). Towards a universal taxonomy of macro-scale functional human brain networks. Brain topography, 32(6), 926-942.
2. Edelsbrunner, H., Harer, J. (2010). Computational topology: an introduction. American Mathematical Society.
3. Lütgehetmann, D., Govc, D., Smith, J. P., Levi, R. (2020). Computing persistent homology of directed flag complexes. Algorithms, 13(1), 19.
4. Otter, N. (2018). Magnitude meets persistence. Homology theories for filtered simplicial sets. arXiv preprint arXiv:1807.01540.
Alexander Kachura, joint work with Vsevolod Chernyshev
One of the approaches to analyze multivariate time series with interdependent components is to construct a complete weighted graph with nodes corresponding to the components of the time series and edge weights representing the strength of dependence between the pair of components corresponding to their ends. Neuroscience is among the many fields where this methodology is popular. A prominent example is the analysis of functional connectomes [1], brain networks whose nodes represent brain regions. These networks exhibit nontrivial structure, so their topological characteristics are useful for analysis. The level of interconnection between brain regions is usually measured using non-directional correlations, while the functional connections between brain regions are inherently directional. Topological characteristics of graphs can be analyzed with persistent homology [2], an increasingly popular dataanalysis tool that can also be applied to graphs. The essence of this approach is to track the moments of the appearance and disappearance of topological structures as the scale varies, using algebraic invariants called homology. When applied to weighted graphs – including functional connectomes – persistent homology allows us to study how the topological structure of a graph changes as the edgefiltering threshold varies. This enables identification of noise-robust topological features, which is crucial when the graph structure is not given a priori but estimated from data. Several homology theories exist. Simplicial homology – historically the first one used to compute persistent homology – cannot account for the directions of graph edges. The most direct generalization of this homology theory to digraphs is the homology of directed flag complexes [3]. However, it still discards some directional information. One of the homology theories that makes it possible to preserve a large proportion of information about the directions of edges is blurred magnitude homology [4].
In this work we introduce a method for classifying directed functional connectomes using blurred magnitude homology, specifically its Betti curves, a popular numerical descriptor of persistent homology. As an example, we apply the developed technique to study graphs constructed from fMRI scans of individuals with ASD and typically developing controls.
We experimentally tested the approach on the ABIDE dataset.
This work was supported by the Russian Science Foundation, Grant No. 24-68-00030.
References
1. Uddin, L. Q., Yeo, B. T., & Spreng, R. N. (2019). Towards a universal taxonomy of macro-scale functional human brain networks. Brain topography, 32(6), 926-942.
2. Edelsbrunner, H., Harer, J. (2010). Computational topology: an introduction. American Mathematical Society.
3. Lütgehetmann, D., Govc, D., Smith, J. P., Levi, R. (2020). Computing persistent homology of directed flag complexes. Algorithms, 13(1), 19.
4. Otter, N. (2018). Magnitude meets persistence. Homology theories for filtered simplicial sets. arXiv preprint arXiv:1807.01540.