Neuronal classification from network connectivity via adjacency spectral embedding

Abstract

This work presents a novel strategy for classifying neurons, represented by nodes of a directed graph, based on their circuitry (edge connectivity). We assume a stochastic block model (SBM) in which neurons belong together if they connect to neurons of other groups according to the same probability distributions. Following adjacency spectral embedding of the SBM graph, we derive the number of classes and assign each neuron to a class with a Gaussian mixture model-based expectation-maximization (EM) clustering algorithm. To improve accuracy, we introduce a simple variation using random hierarchical agglomerative clustering to initialize the EM algorithm and picking the best solution over multiple EM restarts. We test this procedure on a large (≈212–215 neurons), sparse, biologically inspired connectome with eight neuron classes. The simulation results demonstrate that the proposed approach is broadly stable to the choice of embedding dimension, and scales extremely well as the number of neurons in the network increases. Clustering accuracy is robust to variations in model parameters and highly tolerant to simulated experimental noise, achieving perfect classifications with up to 40% of swapped edges. Thus, this approach may be useful to analyze and interpret large-scale brain connectomics data in terms of underlying cellular components.

Circuit Analysis of the Drosophila Brain using Connectivity-based Neuronal Classification Reveals Organization of Key Communication Pathways

“…We refer to these classes as connectivity-based classes . To this aim, we employ a recently developed mathematical framework [8] that models the connectome as a SBM graph, uses spectral graph clustering to predict the number of connectivity-based classes, and assign each neuron to a class.…”

“…Recent attempts of applying the SBM framework to model and identify network community structures within small connectomic datasets originating from a variety of sources have yielded considerable success (Betzel, Medaglia, & Bassett 2018; Faskowitz, Yan, Zuo, & Sporns 2018; Jonas & Kording 2015; Moyer et al 2015; Pavlovic, Vértes, Bullmore, Schafer, & Nichols 2014; Priebe et al 2017, 2019). Specifically, in Mehta et al (2021) we developed a mathematical framework that uses SBMs in conjunction with spectral graph clustering to accurately identify connectivity-based classes in large ( ≈ 2 12 − 2 15 neurons), and sparse ( ≈ 4% edge connectivity) biologically inspired connectomes. Given an artificial surrogate connectome generated using a SBM, the spectral graph clustering was shown to be effective in recovering the true blockmodel structure and accurately assigning each neuron to its respective class, even in the presence of artificially simulated noise (tolerant to as much as 40% pre- and post-synaptic edge misspecification).…”

“…. , ρ k ) in the unit simplex ρ i = 1, which partitions the n vertices into k disjoint subsets, and (ii) a k×k block Specifically, in Mehta et al (2021) we developed a mathematical framework that uses SBMs in conjunction with spectral graph clustering to accurately identify connectivity-based classes in large (≈ 2 12 −2 15 neurons), and sparse (≈ 4% edge connectivity) biologically inspired connectomes. Given an artificial surrogate connectome generated using a SBM, the spectral graph clustering was shown to be effective in recovering the true blockmodel structure and accurately assigning each neuron to its respective class, even in the presence of artificially simulated noise (tolerant to as much as 40% pre-and post-synaptic edge misspecification).…”

“…The spectral graph clustering is a two-step process comprising of adjacency spectral embedding (ASE) in conjunction with Gaussian mixture model (GMM)-based modeling (Mehta et al 2021). In the first step, the adjacency matrix is embedded into a lower dimensional space via spectral decomposition of the matrix into its latent vectors.…”

“…To address these challenges, we construct a mesoscopic level circuit of neuron types as classified exclusively based on their patterns of potential synaptic connectivity. We leverage a recently developed mathematical framework (Mehta et al 2021), which models a connectome as a directed stochastic block model (SBM) graph, to group neurons together into a common “cell class” if they connect to neurons of other classes according to the same probability distributions. Here we build and expand upon that approach applying it to a 19,902-neuron potential connectome of Drosophila melanogaster .…”