Topological learning for brain networks

Songdechakraiwut, Tananun; Chung, Moo K.

doi:10.1214/22-aoas1633

Cited by 8 publications

(13 citation statements)

References 117 publications

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“…Ignoring −∞, W d is the 1D persistent digram. We can show that the birth set is the MST ( Fig 3 ) [ 62 ].…”

Section: Methodsmentioning

confidence: 99%

“…The identification of W b is based on the modification to Kruskal’s or Prim’s algorithm that identifies the MST [ 6 , 62 ]. Then W d is identified as .…”

Section: Methodsmentioning

confidence: 99%

“…Optimization ( 5 ) is the standard assignment problem, which is usually solved by the Hungarian algorithm in [ 66 ]. However, for graph filtration, the distance can be computed exactly in by simply matching the order statistics on the birth or death values [ 61 , 62 , 67 ]:…”

Section: Methodsmentioning

confidence: 99%

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Topological state-space estimation of functional human brain networks

Chung,

Huang,

Carroll

et al. 2024

PLoS Comput Biol

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We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure topological differences, enabling the clustering of brain networks into distinct topological states. This technique outperforms the commonly used k-means clustering in identifying brain network state spaces by effectively incorporating the temporal dynamics of the data without the need for explicit model specification. We further investigate the genetic underpinnings of these topological features using a twin study design, examining the heritability of such state changes. Our findings suggest that the topology of brain networks, particularly in their dynamic state changes, may hold significant hidden genetic information.

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“…Ignoring −∞, W d is the 1D persistent digram. We can show that the birth set is the MST ( Fig 3 ) [ 62 ].…”

Section: Methodsmentioning

confidence: 99%

“…The identification of W b is based on the modification to Kruskal’s or Prim’s algorithm that identifies the MST [ 6 , 62 ]. Then W d is identified as .…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Topological state-space estimation of functional human brain networks

Chung,

Huang,

Carroll

et al. 2024

PLoS Comput Biol

Self Cite

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show abstract

“…During the filtration, a topological latent space is created, spanning from the minimum to maximum weights of the weighted adjacency matrix. Various metrics have been proposed to quantify the differences in structural and functional connectivity between different brain states or conditions within this latent space ( Sizemore et al, 2018 , 2019 ; Songdechakraiwut and Chung, 2023 ).…”

Section: Methodsmentioning

confidence: 99%

“…Both utilize Euclidean distance as edge weights and have monotone

-curve. However, only the graph filtration has a monotone

-curve making it more suitable for scalable Wasserstein distance computations ( Chung et al, 2019b ; Songdechakraiwut and Chung, 2023 ).…”

Section: Methodsmentioning

confidence: 99%