SemanticGaps

Research

Published research

Investigations into semantic patterns and topological structures across complex domains.

Study

Discrete Morse Theory for Content Categorization

Discrete Morse Theory offers a mathematically grounded framework for content categorization, where peaks define categories, saddle points define boundaries, and hierarchy can emerge from the data's topology.

  • •Discrete Morse Theory decomposes information landscapes into peaks (categories), saddle points (boundaries), and valleys (gaps) using gradient flow
  • •Compared with HAC or HDBSCAN, DMT offers a richer structural model and can inherit principled stability arguments through persistence-based formulations
  • •The hierarchy emerges naturally from the data's topology rather than being imposed by algorithmic parameters
  • •Persistence diagrams provide a mathematically grounded method to determine the right number of categories at each level
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Study

Market Topology

Markets generate dense networks of information. Topology provides a way to study how this information organizes, clusters, and flows.

  • •Market information self-organizes into semantic clusters
  • •Topology reveals the shape; semantics reveals the meaning
  • •Gaps between clusters represent opportunity spaces
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Study

Semantic Clustering Methods

Not all clustering algorithms handle semantic embeddings equally. In many semantic settings, density-based methods outperform centroid methods.

  • •Density-based clustering (DBSCAN, HDBSCAN) often outperforms k-means for semantic embeddings
  • •Semantic clusters have irregular shapes that centroid methods cannot capture
  • •Dimensionality reduction improves results; 10-50 dimensions is often optimal
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Study

Topology in Finance

Financial markets generate complex, high-dimensional data. Topological data analysis can reveal structural patterns that traditional statistics may miss.

  • •Topological methods can reveal market structure that is easy to miss in traditional statistics
  • •Persistent homology identifies features that persist across time and scale
  • •Topology may capture regime changes earlier than some mean/variance measures
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