The Intrinsic Dimensionality of Data
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Summary
This paper provides a rationale for fractals in natural data by proving a theorem that determines the minimum dimensions associated with the data and this result is consistent with the result that base-e is optimal for number representation.
- Type
- article
- Published
- 2020-11-04
- Cited by
- 21
- References
- 39
- OpenAlex
- https://openalex.org/W3097774776
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:228828242
Keywords
Curse of dimensionality, Intrinsic dimension, Relevance (law), Computer science, Dimension (graph theory)
References
- Ubiquitous Quantum Structure
- A cosmic crisis?: Dark doings in the universe
- Fractals and fractional calculus in continuum mechanics
- Quantum Models of Cognition and Decision
- Theory and Applications of Fractional Differential Equations
- Fractals in Science
- Fast Classification Networks For Signal Processing
- Decision theory with prospect interference and entanglement
- Axiomatic basis for spaces with noninteger dimension
- On training feedforward neural networks
- Fractal Geometry: Mathematical Foundations and Applications
- Discovering significant rules
- Anisotropic fractal media by vector calculus in non-integer dimensional space
- Optical implementation of the Kak neural network
- Alternative Interest Measures for Mining Associations in Databases
- PCA-Based Parameter Set Mappings for LPV Models With Fewer Parameters and Less Overbounding
- Quantum Structure in Cognition
- Analytic solutions of topologically disjoint systems
- State Ensembles and Quantum Entropy
- Fractal Geometry of Nature
Cited by
- Logic of Representation and Information
- Information Theory of Evolutionary Stages in Noninteger Dimensional Spaces
- Asymptotic freedom and noninteger dimensionality
- Asymptotic Freedom in Noninteger Dimensional Spaces
- Information-theoretic View of the Variation of the Gravitational Constant
- Significance Testing in Natural and Biological Systems: A Review
- Fractals with Optimal Information Dimension
- Two Classes of Regular Symmetric Fractals
- The e-Dimensionality of Genetic Information
- New Classes of Regular Symmetric Fractals
- The Iterated Newcomb-Benford Distribution for Structured Systems
- Number of autonomous agents in a neural network
- Information-theoretic view of the gravitational constant in Dirac’s large numbers hypothesis
- Black holes, disk structures, and cosmological implications in e-dimensional space
- Self-similarity and the maximum entropy principle in the genetic code
- Optimal representation in biological systems
- Noninteger Dimensionality, Nonlocal Noise and Self-Decoherence
- Information optimality and the geometry of chromatin
- Dimensionality of time and the information paradox
- Number of autonomous agents in a neural network
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