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Local intrinsic dimensionality (LID) is a key measure for understanding data distributions. This study connects LID to entropy and statistical distances, revealing LID

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Area of Science:

  • Data Science
  • Statistical Analysis
  • Machine Learning

Background:

  • Data distribution properties are analyzed globally and locally.
  • Local Intrinsic Dimensionality (LID) measures local data geometry.
  • Existing complexity measures include entropy and statistical distances.

Purpose of the Study:

  • To explore the relationship between LID and other complexity measures.
  • To develop new analytical expressions connecting LID, entropy, and divergences.
  • To establish LID as a foundational tool for local distributional analysis.

Main Methods:

  • Asymptotic analysis.
  • Derivation of analytical expressions.
  • Comparison of LID with entropy and statistical distances.

Main Results:

  • New analytical expressions linking LID to entropy and statistical divergences were derived.
  • Demonstrated the fundamental role of LID in characterizing data distributions.
  • Showcased LID's potential as a building block for advanced distributional analysis.

Conclusions:

  • LID is a fundamental measure for local data distribution analysis.
  • The established connections provide new avenues for comparing and characterizing distributions.
  • This work opens up novel methods for localized distributional analysis.