Knowledge Manifold: A Riemannian Geometric Framework for Semantic Mapping and Geodesic Analysis of Scientific Literature
arXiv:2606.05907v1 Announce Type: cross Abstract: We present the knowledge manifold: a Riemannian geometric space in which a corpus of documents is arranged according to semantic positional relationships derived from character n-gram TF-IDF representations. The framework proceeds in five tightly coupled stages. First, each document is converted to a character-level n-gram TF-IDF vector (4-7 grams, up to 250,000 features, L2-normalized) and embedded in a two-dimensional knowledge map via constrained stress minimization with repulsion, variance, and centering regularizers. Second, knowledge at a
This research provides a novel approach to semantic mapping using Riemannian geometry, addressing the increasing need for advanced tools to navigate and understand vast scientific literature datasets.
A strategic reader should care because improved capabilities in semantic mapping can significantly enhance knowledge discovery, accelerate research, and inform strategic decision-making in science and technology.
The ability to map scientific literature onto a 'knowledge manifold' introduces a new methodology for understanding complex semantic relationships and identifying emerging fields or interdisciplinary connections.
- · AI/ML researchers
- · Scientific publishers
- · R&D institutions
- · Knowledge management platforms
- · Traditional literature review methods
- · Inefficient knowledge discovery processes
More efficient and accurate retrieval of scientific information will become possible.
This efficiency will enable faster recognition of research gaps and opportunities, potentially accelerating scientific breakthroughs.
The enhanced mapping could lead to the emergence of highly specialized, AI-driven scientific discovery engines that actively suggest research directions.
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Read at arXiv cs.LG