Covariate-assisted spectral clustering

Abstract

SummaryBiological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications such as connectomics, social networks, and genomics, graph data are accompanied by contextualizing measures on each node. We utilize these node covariates to help uncover latent communities in a graph, using a modification of spectral clustering. Statistical guarantees are provided under a joint mixture model that we call the node-contextualized stochastic blockmodel, including a bound on the misclustering rate. The bound is used to derive conditions for achieving perfect clustering. For most simulated cases, covariate-assisted spectral clustering yields results superior both to regularized spectral clustering without node covariates and to an adaptation of canonical correlation analysis. We apply our clustering method to large brain graphs derived from diffusion MRI data, using the node locations or neurological region membership as covariates. In both cases, covariate-assisted spectral clustering yields clusters that are easier to interpret neurologically.

Detection of Community Structures in Networks With Nodal Features based on Generative Probabilistic Approach

“…The efficiency of the proposed model is demonstrated on the state-of-the-art community detection methods by considering the feature based methods and structure based ones'. On state-of-the-art feature based methods, Cesna [25], JCDC [35], NC [22], BAGC [26], SDP [36], and CASC [37] are employed in the experiments. On state-of-the-art structure based methods, BigClam [14], Fast-Greedy [13], Infomap [12], Louvain [9], and COMBO [15] are applied in the experiments.…”

“…The modified stochastic block model aligned with the features is modified in [22] to reveal the efficacy of each feature on community structures by employing the Expectation-Maximization inference stage. On the one hand, most of the model-free feature based methods suffer from the dependency to multiple tuning parameters such as JCDC [35], and CASC [37]. On the other hand, the generative feature based models on extraction of communities have some problems including the model sensitivity on the presumed graphical representation of the features and communities CESNA [25], and modeling a correlation of single feature with the community structure at a time [22].…”

Connectal Coding: Discovering the Structures Linking Cognitive Phenotypes to Individual Histories

“…A particularly popular version of these models assumes that the probability of connections between a pair of nodes is equal to the dot product between the nodes' latent positions [89][90][91]. In these models, an extensive set of theoretical investigations have established the kinds of claims we desire when using a statistical model to make inferences about our data [92,93], as well as a number of extensions, including a generalized random dot product [94], a random dot product with node-wise covariates [95], and a latent structure model [96] (for review, see [97]). However, these models typically only operate on single, unweighted networks lacking attributes.…”

A Dynamic Network Perspective on the Latent Group Structure of Cryptocurrencies

“…Recent developments suggest that using node features or covariates can greatly improve classification accuracy. For example, Binkiewicz et al (2017) add the covariance XX , with X ∈ [−J, J] R being the node covariate matrix, to the regularized graph Laplacian and perform the spectral clustering on the static similarity matrix. We extend the static similarity matrix to cover the dynamic case below:…”

“…To establish the consistency of the CASC for the dynamic SC-DCBM, we need to determine the upper bounds for the misclustering rates. Following Binkiewicz et al (2017), we denote C i,t and C i,t as the cluster centroids of the ith node at time t generated using kmedians clustering on the sample eigenvector U t and the population U t , respectively. Then, we define the set of mis-clustered nodes at each period as…”