Semi-supervised Graph Rewiring with the Dirichlet Principle

Curado, Manuel; Escolano, Francisco; Lozano, Miguel Ángel; Hancock, Edwin R.

doi:10.1109/icpr.2018.8545172

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…Then, we applied a directed version of Return Random Walk to measure the connectivity between two regions: a high value means both nodes have a good degree of connection and probably belong to the same cluster or they share an important workflow (information). We use k = 15, since this value is more adequate in similar graphs problems using Return Random Walk [ 28 , 30 ].…”

Section: Methodsmentioning

confidence: 99%

Early Detection of Alzheimer’s Disease: Detecting Asymmetries with a Return Random Walk Link Predictor

Curado

Escolano

Lozano

et al. 2020

Entropy

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Alzheimer’s disease has been extensively studied using undirected graphs to represent the correlations of BOLD signals in different anatomical regions through functional magnetic resonance imaging (fMRI). However, there has been relatively little analysis of this kind of data using directed graphs, which potentially offer the potential to capture asymmetries in the interactions between different anatomical brain regions. The detection of these asymmetries is relevant to detect the disease in an early stage. For this reason, in this paper, we analyze data extracted from fMRI images using the net4Lap algorithm to infer a directed graph from the available BOLD signals, and then seek to determine asymmetries between the left and right hemispheres of the brain using a directed version of the Return Random Walk (RRW). Experimental evaluation of this method reveals that it leads to the identification of anatomical brain regions known to be implicated in the early development of Alzheimer’s disease in clinical studies.

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Section: Methodsmentioning

confidence: 99%

Early Detection of Alzheimer’s Disease: Detecting Asymmetries with a Return Random Walk Link Predictor

Curado

Escolano

Lozano

et al. 2020

Entropy

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“…Initially, Hardt et al [27] define the densification of the graph 𝐺 = (𝑉 , 𝐸) as a new graph 𝐻 = (𝑉 , 𝐸 ′ ), 𝐸 ′ ⊇ 𝐸 such that the cardinalities of cuts in 𝐺 and 𝐻 are proportional. In [28,29] and in the Ph.D. Thesis [40] the densification was naturally applied in a clustering problem to neighborhood graphs in order to make more intra-class links and smaller overhead of inter-class links. It was shown that this makes the Laplacian of a graph better conditioned for a subsequent application of spectral methods.…”

Section: Introductionmentioning

confidence: 99%

The algebraic structure of the densification and the sparsification tasks for CSPs

Takhanov¹

2021

Preprint

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The tractability of certain CSPs for dense or sparse instances is known from the 90s. Recently, the densification and the sparsification of CSPs were formulated as computational tasks and the systematical study of their computational complexity was initiated.We approach this problem by introducing the densification operator, i.e. the closure operator that, given an instance of a CSP, outputs all constraints that are satisfied by all of its solutions. According to the Galois theory of closure operators, any such operator is related to a certain implicational system (or, a functional dependency) Σ. We are specifically interested in those classes of fixed-template CSPs, parameterized by constraint languages Γ, for which the size of an implicational system Σ is a polynomial in the number of variables 𝑛. We show that in the Boolean case, Σ is of polynomial size if and only if Γ is of bounded width. For such languages, Σ can be computed in log-space or in a logarithmic time with a polynomial number of processors. Given an implicational system Σ, the densification task is equivalent to the computation of the closure of input constraints. The sparsification task is equivalent to the computation of the minimal key. This leads to O (poly(𝑛) • 𝑁 2 )-algorithm for the sparsification task where 𝑁 is the number of non-redundant sparsifications of an original CSP.Finally, we give a complete classification of constraint languages over the Boolean domain for which the densification problem is tractable.

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The algebraic structure of the densification and the sparsification tasks for CSPs

Takhanov

2022

Constraints

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Semi-supervised Graph Rewiring with the Dirichlet Principle

Abstract: In this paper, we propose the concept of graph rewiring and we show how to exploit it in an un-supervised setting so that commute times can be better estimated by state-of-the-art methods. Our experiments show a significant improvement with respect to unsupervised graph rewiring.

Cited by 4 publications

References 14 publications

Early Detection of Alzheimer’s Disease: Detecting Asymmetries with a Return Random Walk Link Predictor

Early Detection of Alzheimer’s Disease: Detecting Asymmetries with a Return Random Walk Link Predictor

The algebraic structure of the densification and the sparsification tasks for CSPs

The algebraic structure of the densification and the sparsification tasks for CSPs

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