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.

A penny for your thoughts! Patterns of fMRI activity reveal the content and the spatial topography of visual mental images

Visual mental imagery is a complex process that may be influenced by the content of mental images. Neuropsychological evidence from patients with hemineglect suggests that in the imagery domain environments and objects may be represented separately and may be selectively affected by brain lesions. In the present study, we used functional magnetic resonance imaging (fMRI) to assess the possibility of neural segregation among mental images depicting parts of an object, of an environment (imagined from a first-person perspective), and of a geographical map, using both a mass univariate and a multivariate approach. Data show that different brain areas are involved in different types of mental images. Imagining an environment relies mainly on regions known to be involved in navigational skills, such as the retrosplenial complex and parahippocampal gyrus, whereas imagining a geographical map mainly requires activation of the left angular gyrus, known to be involved in the representation of categorical relations. Imagining a familiar object mainly requires activation of parietal areas involved in visual space analysis in both the imagery and the perceptual domain. We also found that the pattern of activity in most of these areas specifically codes for the spatial arrangement of the parts of the mental image. Our results clearly demonstrate a functional neural segregation for different contents of mental images and suggest that visuospatial information is coded by different patterns of activity in brain areas involved in visual mental imagery. Hum Brain Mapp 36:945-958, 2015.