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

Area of Science:

• Neuroscience
• Data Science
• Computational Biology

Background:

• Quantifying feature distribution in point clouds is crucial for analyzing complex data.
• Neuroscience applications include neural manifold investigation, neurophysiological signal analysis, and anatomical segmentation.

Purpose of the Study:

• Introduce the Structure Index (SI), a directed graph-based metric.
• Quantify the distribution of feature values in arbitrary D-dimensional spaces.
• Assess local versus global organization and directionality of feature distribution.

Main Methods:

• Define SI based on overlapping distributions of data points with similar feature values within neighborhoods.
• Apply SI to scalar and vectorial features.
• Utilize graph-based analysis of point cloud data.

Main Results:

• SI quantifies the degree and directionality of local and global feature organization.
• Demonstrates consistent structure retrieval in high- and low-dimensional representations of head-direction cells.
• Shows potential for sound and image categorization tasks.

Conclusions:

• The Structure Index (SI) offers a versatile method for analyzing feature distribution in diverse D-dimensional datasets.
• SI has broad applications in neuroscience and data science for uncovering complex data structures.
• Enables quantification of feature organization in both scalar and vectorial data types.