Connectome smoothing via low-rank approximations

Tange, Runze; Ketcha, Michael D.; Badea, Alexandra; Calabrese, Evan; Margulies, Daniel S.; Vogelstein, Joshua T.; Priebe, Carey E.; Sussman, Daniel L.

doi:10.1109/tmi.2018.2885968

Cited by 32 publications

(35 citation statements)

References 43 publications

(84 reference statements)

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“…It has been suggested that the information encoded in patterns of brain connectivity can uniquely identify different subjects [49], [50], and there is some evidence of low-rank structure in those differences [51], [52]. We study how lowdimensional representations can capture inter-individual variability by using the HNU1 data to classify subject scans.…”

Section: Real Data Experiments 1: Subject Classification On Hnu1 Datamentioning

confidence: 99%

“…First, we consider clustering of each graph separately by doing ASE on the English graph A en (ASE+EN), or equivalently, JE on A en , and ASE on the French Graph A f r (ASE+FR), and compare with the individual latent positions obtained by JEĤD 1 2 en (JE+EN) andĤD 1 2 f r (JE+FR). We also consider methods to estimate joint latent positions, by doing ASE on the mean of both graphsĀ = (A en + A f r )/2 (ASE+(EN+FR)) [51], and the matrixĤ obtained by JE on both graphs (JE+ (EN,FR)). The dimension d is set to 3 for all approaches, and the latent positions are scaled to have norm 1 for degree correction.…”

Section: Real Data Experiments 3: Joint Embedding To Cluster Verticesmentioning

confidence: 99%

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Joint Embedding of Graphs

Wang

Arroyo

Vogelstein

et al. 2021

IEEE Trans. Pattern Anal. Mach. Intell.

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Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks.

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Section: Real Data Experiments 1: Subject Classification On Hnu1 Datamentioning

confidence: 99%

Section: Real Data Experiments 3: Joint Embedding To Cluster Verticesmentioning

confidence: 99%

Joint Embedding of Graphs

Wang

Arroyo

Vogelstein

et al. 2021

IEEE Trans. Pattern Anal. Mach. Intell.

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“…Random Dot Product Graphs (RDPGs) are a class of Latent Position Models [14] developed to analyse social networks [31,47], and then extended to many other applications and types of networks [3,9,25,37,43]. To describe interactions in a network, such models assume that the probability of observing an interaction between two nodes is a function of the nodes' features [31,47].…”

Section: The Random Dot Product Graph Modelmentioning

confidence: 99%

“…Block Models-based approaches, such as the probabilistic generative family of Stochastic Block Models (and variants), aggregate nodes into groups based on their similarity of interactions [15,45]. Graph embedding methods on the other hand rely on projecting nodes onto an abstract latent feature space, so that the interaction probabilities depend on these latent features [2,5,43].…”

Section: Introductionmentioning

confidence: 99%

Exploiting node metadata to predict interactions in large networks using graph embedding and neural networks

Runghen

Stouffer

Riva

2021

Preprint

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Collecting network interaction data is difficult. Non-exhaustive sampling and complex hidden processes often result in an incomplete data set. Thus, identifying potentially present but unobserved interactions is crucial both in understanding the structure of large scale data, and in predicting how previously unseen elements will interact. Recent studies in network analysis have shown that accounting for metadata (such as node attributes) can improve both our understanding of how nodes interact with one another, and the accuracy of link prediction. However, the dimension of the object we need to learn to predict interactions in a network grows quickly with the number of nodes. Therefore, it becomes computationally and conceptually challenging for large networks. Here, we present a new predictive procedure combining a graph embedding method with machine learning techniques to predict interactions on the base of nodes' metadata. Graph embedding methods project the nodes of a network onto a---low dimensional---latent feature space. The position of the nodes in the latent feature space can then be used to predict interactions between nodes. Learning a mapping of the nodes' metadata to their position in a latent feature space corresponds to a classic---and low dimensional---machine learning problem. In our current study we used the Random Dot Product Graph model to estimate the embedding of an observed network, and we tested different neural networks architectures to predict the position of nodes in the latent feature space. Flexible machine learning techniques to map the nodes onto their latent positions allow to account for multivariate and possibly complex nodes' metadata. To illustrate the utility of the proposed procedure, we apply it to a large dataset of tourist visits to destinations across New Zealand. We found that our procedure accurately predicts interactions for both existing nodes and nodes newly added to the network, while being computationally feasible even for very large networks. Overall, our study highlights that by exploiting the properties of a well understood statistical model for complex networks and combining it with standard machine learning techniques, we can simplify the link prediction problem when incorporating multivariate node metadata. Our procedure can be immediately applied to different types of networks, and to a wide variety of data from different systems. As such, both from a network science and data science perspective, our work offers a flexible and generalisable procedure for link prediction.

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“…Diagonal augmentation (diag-aug) is a method for imputing the diagonals of adjacency matrices from graphs with no self-loops [66,87,101]. The diagonals are imputed with with the average of the non-diagonal entries of each row, which corresponds to the degree of each vertex divided by n − 1.…”

Section: Diagonal Augmentationmentioning

confidence: 99%

Statistical Connectomics

Chung¹,

Bridgeford²,

Arroyo³

et al. 2020

Preprint

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The data science of networks is a rapidly developing field with myriad applications. In neuroscience, the brain is commonly modeled as a connectome, a network of nodes connected by edges. While there have been thousands of papers on connectomics, the statistics of networks remains limited and poorly understood. Here, we provide an overview from the perspective of statistical network science of the kinds of models, assumptions, problems, and applications that are theoretically and empirically justified for analysis of connectome data. We hope this review spurs further development and application of statistically grounded methods in connectomics.

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Connectome smoothing via low-rank approximations

Cited by 32 publications

References 43 publications

Joint Embedding of Graphs

Joint Embedding of Graphs

Exploiting node metadata to predict interactions in large networks using graph embedding and neural networks

Statistical Connectomics

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