Network clustering via kernel-ARMA modeling and the Grassmannian: The brain-network case

Ye, Cong; Slavakis, Konstantinos; Patil, Pratik V.; Nakuci, Johan; Muldoon, Sarah F.; Medaglia, John D.

doi:10.1016/j.sigpro.2020.107834

Cited by 7 publications

(13 citation statements)

References 52 publications

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“…] ∈ H Tw|L| gather information from all layers. Then, following the kernel-autoregressivemoving-average (kARMA) model of [31], it is assumed that there exist (unknown) matrices C ∈ R Tw|L|×ρ , A ∈ R ρ×ρ for some userdefined parameter ρ ∈ Z>0, and latent ψt ∈ H ρ , υt ∈ H Tw|L| , and ωt ∈ H ρ , which model noise and approximation errors, such that ∀t, ϕt = Cψt + υt and ψt = Aψt−1 + ωt. For a userdefined parameter m ∈ Z>0, the so-called observability matrix [32] is defined as: O := [C , (CA) , .…”

Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

“…, (CA m−1 ) ] ∈ R mTw|L|×ρ . An estimateÔt of O per time instance t is computed here by the same sequential way employed in the clustering frameworks of [20,31]. Due to space limitations, the description of such a procedure is omitted.…”

Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

“…In community classification, where features per nodal time series need to be extracted, V := ν, for ν ∈ N , and for a time-window length τw ∈ Z>0, with q := τw, let y [20,31] adapts to this case as ϕ (l)…”

Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

“…per node ν and layer l. As in state classification, the way by which estimates of an observability matrix are obtained sequentially in [20,31] is also used here to compute an estimateÔ…”

Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

“…k from the landmark points L k are mapped to the tangent space [21,22] of the Riemannian manifold at point x (i) k via the manifold logarithmic map [22] in Lines 5 and 6; see also Figure 1b. Ways to compute the manifold logarithmic map for a couple of well-known Riemannian manifolds, such as the Grassmannian one, are detailed in [20,31]. The computation of the manifold logarithmic map seems to be the most computationally intensive task in Algorithm 1, and examples of such complexities can be found in [20,31].…”

Section: Online Classification In Riemannian Manifoldsmentioning

confidence: 99%

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Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

Ye¹,

Slavakis²,

Nakuci³

et al. 2021

Preprint

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<div>This work exploits Riemannian manifolds to introduce a geometric framework for online state and community classification in dynamic multilayer networks where nodes are annotated with time series. A bottom-up approach is followed, starting from the extraction of Riemannian features from nodal time series, and reaching up to online/sequential classification of features via geodesic distances and angular information in the tangent spaces of a Riemannian manifold. As a case study, features in the Grassmann manifold are generated by fitting a kernel autoregressive-moving-average model to the nodal time series of the multilayer network. The paper highlights also numerical tests on synthetic and real brain-network data, where it is shown that the proposed geometric framework outperforms state-of-the-art deep-learning models in classification accuracy, especially in cases where the number of training data is small with respect to the number of the testing ones.</div><div><br></div><div>-------</div><div><br></div><div>© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<br></div><div><br></div>

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Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

“…per node ν and layer l. As in state classification, the way by which estimates of an observability matrix are obtained sequentially in [20,31] is also used here to compute an estimateÔ…”

Section: Extracting Grassmannian Featuresmentioning

confidence: 99%

Section: Online Classification In Riemannian Manifoldsmentioning

confidence: 99%

See 3 more Smart Citations

Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

Ye¹,

Slavakis²,

Nakuci³

et al. 2021

Preprint

Self Cite

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show abstract

Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

Slavakis

Nakuci

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

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This work exploits Riemannian manifolds to introduce a geometric framework for online state and community classification in dynamic multilayer networks where nodes are annotated with time series. A bottom-up approach is followed, starting from the extraction of Riemannian features from nodal time series, and reaching up to online/sequential classification of features via geodesic distances and angular information in the tangent spaces of a Riemannian manifold. As a case study, features in the Grassmann manifold are generated by fitting a kernel autoregressive-moving-average model to the nodal time series of the multilayer network. The paper highlights also numerical tests on synthetic and real brain-network data, where it is shown that the proposed geometric framework outperforms state-ofthe-art deep-learning models in classification accuracy, especially in cases where the number of training data is small with respect to the number of the testing ones.

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Clustering Complex Subspaces in Large Dimensions

Pereira

Mestre

Gregoratti

2022

ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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A methodology to cluster multiple sets of Gaussian multivariate complex observations based on the alignment of their column spaces is presented. These subspaces are identified with points in the Grassmann manifold and compared according to a similarity measure drawn from a chosen manifold distance, which is proportional to the squared projection-Frobenius norm. In order to guarantee that distances between subspaces of different dimensions are comparable, we proposed to normalise the corresponding decision statistics with respect to their asymptotic mean and variance, assuming that (i) the dimensions of both the observation and the involved subspaces are large but comparable in magnitude and (ii) both subspaces are generated by the same statistical law. A procedure is derived to estimate these normalisation parameters, leading to a new statistic that can be built exclusively from the observations. The method is applied to a MIMO wireless channel clustering problem, where is shown to outperform conventional similarity measures in terms of classification performance.

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Network clustering via kernel-ARMA modeling and the Grassmannian: The brain-network case

Cited by 7 publications

References 52 publications

Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

Clustering Complex Subspaces in Large Dimensions

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