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Local Intrinsic Dimensionality, Entropy and Statistical Divergences.
James Bailey1, Michael E Houle1, Xingjun Ma2
1School of Computing and Information Systems, The University of Melbourne, Melbourne, VIC 3010, Australia.
Entropy (Basel, Switzerland)
|September 23, 2022
Summary
Local intrinsic dimensionality (LID) is a key measure for understanding data distributions. This study connects LID to entropy and statistical distances, revealing LID
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.
Keywords:
cumulative entropyentropyentropy powerintrinsic dimensionalitylocal intrinsic dimensionstatistical distancesstatistical divergencestail entropyMore Related Videos
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