Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Clustering of tau-immunoreactive pathology in chronic traumatic encephalopathy

Chronic traumatic encephalopathy (CTE) is a neurodegenerative disorder which may result from repetitive brain injury. A variety of tau-immunoreactive pathologies are present, including neurofibrillary tangles (NFT), neuropil threads (NT), dot-like grains (DLG), astrocytic tangles (AT), and occasional neuritic plaques (NP). In tauopathies, cellular inclusions in the cortex are clustered within specific laminae, the clusters being regularly distributed parallel to the pia mater. To determine whether a similar spatial pattern is present in CTE, clustering of the tau-immunoreactive pathology was studied in the cortex, hippocampus, and dentate gyrus in 11 cases of CTE and 7 cases of Alzheimer’s disease neuropathologic change (ADNC) without CTE. In CTE: (1) all aspects of tau-immunoreactive pathology were clustered and the clusters were frequently regularly distributed parallel to the tissue boundary, (2) clustering was similar in two CTE cases with minimal co-pathology compared with cases with associated ADNC or TDP-43 proteinopathy, (3) in a proportion of cortical gyri, estimated cluster size was similar to that of cell columns of the cortico-cortical pathways, and (4) clusters of the tau-immunoreactive pathology were infrequently spatially correlated with blood vessels. The NFT and NP in ADNC without CTE were less frequently randomly or uniformly distributed and more frequently in defined clusters than in CTE. Hence, the spatial pattern of the tau-immunoreactive pathology observed in CTE is typical of the tauopathies but with some distinct differences compared to ADNC alone. The spread of pathogenic tau along anatomical pathways could be a factor in the pathogenesis of the disease.