An Algorithm for Finding Intrinsic Dimensionality of Data

By Keinosuke Fukunaga, David R. Olsen. 1971

Subfields: Representation & Self-Supervised Learning, Algorithms & Complexity

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Citations in the corpus

Measuring the Intrinsic Dimension of Objective Landscapes (2018, methodology): “Finally, note that although our approach is related to a rich body of work on estimating the “intrinsic dimension of a dataset” (Camastra & Vinciarelli, 2002; K ´ egl, 2003; Fukunaga & Olsen, 1971; Lev-ina & Bickel, 2005; Tenenbaum et al., 2000), it differs in a few respects.”
Segmenting Motion Capture Data into Distinct Behaviors (2004, methodology): “A number of more sophisticated approaches for computing intrinsic dimensionality of the data are available [20, 12, 4], but this simple method worked well in our experiments.”
Equations of Motion from a Data Series (1987, unknown): “[14, 30]”
Maximum Likelihood Estimation of Intrinsic Dimension (2004, methodology): “Eigenvalue methods, from the early proposal of [9] to a recent variant [10] are based on a global or local PCA, with intrinsic dimension determined by the number of eigenvalues greater than a given threshold.”
Intrinsic dimension estimation: Advances and open problems (2016, methodology): “Bruske-Sommer’s algorithm shares with Fukunaga-Olsen’s one the same limitations.”
Riemannian Manifold Learning (2008, unknown): “methods [39], [40] and geometric methods based on NN”
Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold (2003, background): “Note that mixture models for local dimensionality reduction (Fukunaga and Olsen, 1971; Ghahramani and Hinton, 1996; Kambhatla and Leen, 1997), which cluster the data and perform PCA within each cluster, do not address the problem considered here—namely, how to map high dimensional data into a…”
Estimating the Intrinsic Dimension of Data with a Fractal-Based Method (2002, methodology): “The above mentioned [3], [10] methods present some limits: Since none of the eigenvalues of the covariance matrix will be null due to noise, it is necessary to use heuristic thresholds in order to decide whether an eigenvalue is significant or not.”
An Introduction to Locally Linear Embedding (2001, background): “Note that mixture models for local dimensionality reduction[5] [6], which cluster the data and perform PCA within each cluster, do not address the problem considered here— namely, how to map high dimensional data into a single global coordinate system of lower dimensionality.”
Data dimensionality estimation methods: a survey (2003, methodology): “Besides, Fukunaga and Olsen assume that the intrinsic dimensionality of a data set can be computed by dividing the data set in small regions (Voronoi tesselation of data space).”
Automatic Choice of Dimensionality for PCA (2000, methodology): “Modeling the data manifold with localized PCA dates back to [4].”
Performance animation from low-dimensional control signals (2005, methodology): “tt ii oo nn ee rr rr oo rr (( dd ee gg rr ee ee pp ee rr jj oo ii nn tt aa nn gg ll ee )) 00 55 100 155 200 255 300 355 400 455 500 00 11 22 33 44 55 66 77 88 Global PCAA GPLVMM LLMM Our methodd 00 55 100 155 200 255 300 355 400 455 500 00 55 100 155 200 255 300”
The vulnerability of learning to adversarial perturbation increases with intrinsic dimensionality (2017, methodology): “Projection-based learning methods such as PCA [16] can produce as a byproduct an estimate of ID.”
Redundancy, Isotropy, and Intrinsic Dimensionality of Prompt-based Text Embeddings (2025, unknown): “…of dimensions required to represent the underlying structure of data representations without significant information loss, and various meth-ods have been proposed for estimating intrinsic dimensions (Bruske and Sommer, 1998; Fukunaga and Olsen, 1971; Levina and Bickel, 2004; Facco et al., 2017).”