Abstract
Background 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., auditory coding) or in anatomical image segmentation.
New method We 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.
Results Using 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 methods Most 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.
Conclusions The method provides versatile applications in the neuroscience and data science fields
Highlights
The Structure Index is a graph-based topological metric
It quantifies the distribution of feature values in arbitrary dimensional spaces
It can be applied to both scalar and vectorial features
When applied to the head-direction neural system, it extracts concordant information from high- and low-dimensional representations
It can be extended to sound and image categorization, expanding the range of applications
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
↵# Co-first authors
