An Algorithm for Finding Intrinsic Dimensionality of Data

1971/02/01 by K. Fukunaga, Keinosuke Fukunaga, D.R. Olsen · 346 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Algorithm #Artificial intelligence #Computer science #Curse of dimensionality #Dimensionality reduction #Face and Expression Recognition #Intrinsic dimension #Mathematics #Neural Networks and Applications

paper · doi:10.1109/t-c.1971.223208

published in IEEE Transactions on Computers C-20(2), 176-183 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1971/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

An algorithm for the analysis of multivariant data is presented along with some experimental results. The basic idea of the method is to examine the data in many small subregions, and from this determine the number of governing parameters, or intrinsic dimensionality. This intrinsic dimensionality is usually much lower than the dimensionality that is given by the standard Karhunen-Loève technique. An analysis that demonstrates the feasability of this approach is presented.

Cited by

• Abstraction Induces the Brain Alignment of Language and Speech Models
• Exploring the Intrinsic Geometry of Diffusion Models with Constrained Inverse Kinematics
• Manifold Dimension Estimation via Local Graph Structure
• Zero Generalization Error Theorem for Random Interpolators via Algebraic Geometry
• Concentration bounds for intrinsic dimension estimation using Gaussian kernels
• From Topology to Retrieval: Decoding Embedding Spaces with Unified Signatures
• Multi-View Kernel Consensus For Data Analysis
• MDIntrinsicDimension: Dimensionality-Based Analysis of Collective Motions in Macromolecules from Molecular Dynamics Trajectories
• Intrinsic Dimensionality as a Model-Free Measure of Class Imbalance
• In Situ Training of Implicit Neural Compressors for Scientific Simulations via Sketch-Based Regularization
• Curvature of high-dimensional data
• Intrinsic Dimension Estimation via Nearest Constrained Subspace Classifier
• Data analysis from empirical moments and the Christoffel function
• Quantum-inspired Benchmark for Estimating Intrinsic Dimension
• A Survey and Comparative Evaluation of Intrinsic Dimension Estimators under the Manifold Hypothesis
• On the Intrinsic Dimensionality of Image Representations
• Dataset-Adaptive Dimensionality Reduction
• A survey of dimensionality reduction techniques
• Kernel Scaling for Manifold Learning and Classification
• On Convolutions, Intrinsic Dimension, and Diffusion Models
• Adjustment for Confounding using Pre-Trained Representations
• Dimension Reduction by Local Principal Component Analysis
• Estimating a Manifold from a Tangent Bundle Learner
• Redundancy, Isotropy, and Intrinsic Dimensionality of Prompt-based Text Embeddings
• Local intrinsic dimensionality estimators based on concentration of measure
• A scale-based approach to finding effective dimensionality in manifold learning
• Handbook of Research on Machine Learning Applications and Trends
• Estimating fractal dimension
• Fractional Norms and Quasinorms Do Not Help to Overcome the Curse of Dimensionality
• Accurate Estimation of the Intrinsic Dimension Using Graph Distances: Unraveling the Geometric Complexity of Datasets. [europepmc]
• Gaussian bandwidth selection for manifold learning and classification. [europepmc]
• Fractional Norms and Quasinorms Do Not Help to Overcome the Curse of Dimensionality. [europepmc]
• Scikit-Dimension: A Python Package for Intrinsic Dimension Estimation. [europepmc]
• A scale-dependent measure of system dimensionality. [europepmc]
• IAN: Iterated Adaptive Neighborhoods for Manifold Learning and Dimensionality Estimation. [europepmc]
• Multi-sample ζ-mixup: richer, more realistic synthetic samples from a p -series interpolant. [europepmc]
• A Study on Dimensionality Reduction and Parameters for Hyperspectral Imagery Based on Manifold Learning. [europepmc]
• Rational partitioning of spectral feature space for effective clustering of massive spectral image data. [europepmc]
• Modeled grid cells aligned by a flexible attractor. [europepmc]
• Discovering patient groups in sequential electronic healthcare data using unsupervised representation learning. [europepmc]
• Robust estimation of the intrinsic dimension of data sets with quantum cognition machine learning. [europepmc]
• Lipidome visualisation, comparison, and analysis in a vector space. [europepmc]
• The topology of molecular representations and its influence on machine learning performance. [europepmc]
• Scale adaptive and robust intrinsic dimension estimation via optimal neighbourhood identification. [europepmc]

Related

• Estimating Local Intrinsic Dimensionality
• Linear Dimensionality Reduction
• A New Estimator of Intrinsic Dimension Based on the Multipoint Morisita Index
• intRinsic: an R Package for Model-Based Estimation of the Intrinsic Dimension of a Dataset
• Intrinsic dimension and its application to association rules