Intrinsic dimensionality detection criterion based on Locally Linear Embedding

• Autorzy: Meng L. , Breitkopf P.

Identyfikatory

DOI

10.7494/csci.2018.19.3.2866

• Języki publikacji: EN

Abstrakty

EN

In this work, we revisit the Locally Linear Embedding (LLE) algorithm that is widely employed in dimensionality reduction. With a particular interest to the correspondences of the nearest neighbors in the original and embedded spaces, we observe that, when prescribing low-dimensional embedding spaces, LLE remains merely a weight-preserving rather than a neighborhood-preserving algorithm. Thus, we propose a \neighborhood-preserving ratio" criterion to estimate the minimal intrinsic dimensionality required for neighborhood preservation. We validate its efficiency on sets of synthetic data, including S-curve, Swiss roll, and a dataset of grayscale images.

Słowa kluczowe

EN

LLE; dimensionality reduction; intrinsic dimensionality; neighborhood; preserving

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2018
• Tom: Vol. 19 (3)
• Strony: 345--356
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Meng L.

• State IJR Center of Aerospace Design and Additive Manufacturing, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi'an Shaanxi, 710072

autor

Breitkopf P.

• Sorbonne Universites, Universite de Technologie de Compiegne, UMR UTC-CNRS 7337, Compiegne 60200, France

Bibliografia

• [1] Balasubramanian M., Schwartz E.L., Tenenbaum J.B., de Silva V., Langford J.C.: The isomap algorithm and topological stability, Science, vol. 295(5552), pp. 7-7, 2002.
• [2] Cox T., Cox M.: Multidimensional Scaling, Chapman & Hall, London, UK, 1994.
• [3] Jolliffe I.: Principal component analysis. Wiley Online Library, 2002.
• [4] Polito M., Perona P.: Grouping and Dimensionality Reduction by Locally Linear Embedding, 2002.
• [5] Saul L.K., Roweis S.T.: An Introduction to Locally Linear Embedding. https: //cs.nyu.edu/~roweis/lle/papers/lleintroa4.pdf, 2000.
• [6] Saul L.K., Roweis S.T.: Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds, The Journal of Machine Learning Research, vol. 4, pp. 119-155, 2003.
• [7] Saul L.K., Weinberger K.Q., Sha F., Ham J., Lee D.D.: Spectral Methods for Dimensionality Reduction, Semisupervised learning, pp. 293-308, 2006.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).