Clique topology reveals intrinsic geometric structure in neural correlations

By Chad Giusti, E. Pastalkova, Carina Curto, Vladimir Itskov. Proceedings of the National Academy of Sciences of the United States of America, 2015

395 citations recorded by the source corpus.

Significance Detecting structure in neural activity is critical for understanding the function of neural circuits. The coding properties of neurons are typically investigated by correlating their responses to external stimuli. It is not clear, however, if the structure of neural activity can be inferred intrinsically, without a priori knowledge of the relevant stimuli. We introduce a novel method, called clique topology, that detects intrinsic structure in neural activity that is invariant under nonlinear monotone transformations. Using pairwise correlations of neurons in the hippocampus, we demonstrate that our method is capable of detecting geometric structure from neural activity alone, without appealing to external stimuli or receptive fields. Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.

Subfields: Biophysics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e98f4f63bb1dc180515857a9c9d41c667f7e5322

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biophysics

In Computational Theory and Mathematics

Citations in the corpus

Cliques and cavities in the human connectome (2016, methodology): “At the neuron level, persistent has been used to detect intrinsic structure in correlations between neural spike trains (Giusti et al. 2015), expanding our understanding of the formation of spatial”
Network neuroscience (2017, background): “Right, in many cases, however, neural systems appear to employ higher order interactions 139 , which increase the complexity of neural codes that produce the wide range of behaviors observed in these systems 140 .”
Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function (2016, background): “More recently, algebraic topology has been applied to functional networks between brain regions using fMRI (Petri et al., 2014) and between neurons using neural activity (Giusti et al., 2015), but the underlying synaptic connections (structural network) were unknown.”
Two’s company, three (or more) is a simplex (2016, methodology): “Alternately, the area under such curves was used in (Giusti et al, 2015) to detect geometric structure in the activity of hippocampal neural populations (Fig.”
Closures and Cavities in the Human Connectome (2016, background): “At the neuron level, persistent homology has been used to detect intrinsic structure in correlations between neural spike trains [28], expanding our understanding of the formation of spatial maps in the hippocampus [20].”
What are higher-order networks? (2021, background): “Computational topology and higher-order networks have proven successful for analyzing the full spectrum of brain data ranging from functional networks [257], to morphology of branching neurons [161], to structural (synaptic connectivity) [237], to place cells [121], to the C.”
Small-World Brain Networks Revisited (2016, background): “…by which small-worlds support these computations may stem from the fact that their topological structure tends to contain both large cavities and high-dimensional cliques [35], which when embedded in a physical space can strongly constrain the geometric properties of the computation [109].”
Networks beyond pairwise interactions: structure and dynamics (2020, methodology): “[625] then compared the Betti curves of the real order complex with those obtained from randomized versions, which were built by reshuffling the original correlation matrices.”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “Simplicial complex models have been successful in developing new insights into biological data [32, 92], structural and functional connectivity in the brain [57,58,104], coverage of sensor networks [42,56,90,121], signal processing [8,115], mobility analysis [54], and robotics [105].”