Moran’s I quantifies spatio-temporal pattern formation in neural imaging data

Abstract

MotivationNeural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran’s I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus.ResultsWe found that Moran’s I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran’s I accounts for the spatial organization of any interacting units. Moran’s I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran’s I and the traditional Kuramoto order parameter R in a complementary fashion.Availability and implementationPython 2.7 code of illustrative examples can be found in the Supplementary Material.Supplementary information Supplementary data are available at Bioinformatics online.

Significant spatial patterns from the GCM seasonal forecasts of global precipitation

“…In terms of computation, global climate forecasting is as complex as the simulation of the human brain and of the evolution of the early universe (Bauer et al, 2015). Advances in super-computing facilitate the forecasting and make GCM forecasts readily available for hydrological, environmental, and agricultural modelling (Sheffield et al, 2014;Vecchi et al, 2014;Bellprat et al, 2019;Pappenberger et al, 2019;Zhao et al, 2019a).…”

Significant spatial patterns from the GCM seasonal forecasts of global precipitation

“…We have identified significant spatial patterns [Anselin, 1995;Miller, 2004;Schmal et al, 2017] from spatial plots of anomaly correlation, which have been widely used to illustrate the predictive performance of GCM forecasts. The test of significance is conducted by global and local Moran's I for ten sets of forecasts in NMME.…”

“…The spatial clustering is a popular approach to geographical, ecological, and environmental modelling [e.g., Anselin, 1995Anselin, , 2006Miller, 2004;Hao et al, 2016;Schmal et al, 2017]. Meanwhile, its use appears to be uncommon in the forecasting area.…”

“…The spatial clustering associates anomaly correlation at neighbouring grid cells to one another and tests the significance of the patterns by random permutation. Following the standard formulations of spatial statistics [Anselin, 1995[Anselin, , 2006, the global Moran's I is calculated to examine the association among anomaly correlation at the global scale In which N is the number of grid cells indexed by i and j across the globe; r is the mean value of anomaly correlation; and , ij w is the spatial weighting coefficient that usually decays with the distance between i and j [Miller, 2004;Hao et al, 2016;Schmal et al, 2017]. At the right-hand side of Eq.…”

“…As for the clusters, Figure 2 presents a thorough test of the relationships using the global Moran's I. Specifically, for all the grid cells across the globe, the anomaly correlation at each grid cell is plotted against the spatially-weighted and -averaged anomaly correlation, i.e., spatial lag [Miller, 2004;Hao et al, 2016;Schmal et al, 2017], at the surrounding grid cells. Figure 2 uses a viridis heatmap to indicate the density of scatter points.…”