Quantifying the distribution of feature values over data represented in arbitrary dimensional spaces

Identifying the structured distribution (or lack thereof) of a given feature over a point cloud is a general research question. In the neuroscience field, this problem arises while investigating representations over neural manifolds (e.g., spatial coding), in the analysis of neurophysiological signals (e.g., sensory coding) or in anatomical image segmentation. We introduce the Structure Index (SI) as a directed graph-based metric to quantify the distribution of feature values projected over data in arbitrary D-dimensional spaces (defined from neurons, time stamps, pixels, genes, etc). The SI is defined from the overlapping distribution of data points sharing similar feature values in a given neighborhood of the cloud. Using arbitrary data clouds, we show how the SI provides quantification of the degree and directionality of the local versus global organization of feature distribution. SI can be applied to both scalar and vectorial features permitting quantification of the relative contribution of related variables. When applied to experimental studies of head-direction cells, it is able to retrieve consistent feature structure from both the high- and low-dimensional representations, and to disclose the local and global structure of the angle and speed represented in different brain regions. Finally, we provide two general-purpose examples (sound and image categorization), to illustrate the potential application to arbitrary dimensional spaces. Our method provides versatile applications in the neuroscience and data science fields.Author summary: Many fields of science require analyzing data represented in high- and low-dimensional spaces in the form of point clouds. A common problem that emerges is how to quantify how features of interest are represented over these point clouds. In neuroscience, this problem arises while investigating neural representations, in the analysis of electrophysiological signals or in the segmentation of anatomical images. While many methods focus on characterizing the structure of the point cloud, there is a lack of approaches to quantify the distribution of feature values projected over the data points. Here, we introduce the Structure Index as a directed graph-based metric to quantify the distribution of feature values in a point cloud. Our method permits examination of the local and global distribution of features, whether categorical/continuous or scalar/vectorial. Using case examples, we illustrate how the method can be applied to a wide range of data, from neural representations of the head-direction system, to sound and image categorization.