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

Abstract

BackgroundIdentifying 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., auditory coding) or in anatomical image segmentation. New methodWe introduce the Structure Index (SI) as a graph-based topological metric to quantify the distribution of feature values projected over data in arbitrary D-dimensional spaces (neurons, time stamps, pixels). The SI is defined from the overlapping distribution of data points sharing similar feature values in a given neighborhood. ResultsUsing model data clouds we show how the SI provides quantification of the degree of 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. Finally, we provide two general-purpose examples (sound and image categorization), to illustrate the potential application to arbitrary dimensional spaces. Comparison with existing methodsMost methods for quantifying structure depend on cluster analysis, which are suboptimal for continuous features and non-discrete data clouds. SI unbiasedly quantifies structure from continuous data in any dimensional space. ConclusionsThe method provides versatile applications in the neuroscience and data science fields HighlightsO_LIThe Structure Index is a graph-based topological metric C_LIO_LIIt quantifies the distribution of feature values in arbitrary dimensional spaces C_LIO_LIIt can be applied to both scalar and vectorial features C_LIO_LIWhen applied to the head-direction neural system, it extracts concordant information from high- and low-dimensional representations C_LIO_LIIt can be extended to sound and image categorization, expanding the range of applications C_LI