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Journal Articles Computer Science Education Year : 2018

An intrinsic dimensionality detection criterion based on locally linear embedding

Lian Meng
  • Function : Author
Piotr Breitkopf
  • Function : Author

Abstract

We revisit in this work the Locally Linear Embedding (LLE) algorithm which is a widely employed technique in dimensionality reduction. With a particular interest on the correspondences of nearest neighbors in the original and em- bedded spaces, we observe that, when prescribing low-dimensional embedding spaces, LLE remains merely a weight preserving, rather than a neighborhood preserving algorithm. We propose thus a ”neighborhood preserving ratio” crite- rion to estimate a minimal intrinsic dimensionality required for neighbourhood preservation. We validate its efficiency on a set of synthetic data, including S-curve, swiss roll, as well as a dataset of grayscale images.

Dates and versions

hal-01993048 , version 1 (24-01-2019)

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Lian Meng, Piotr Breitkopf. An intrinsic dimensionality detection criterion based on locally linear embedding. Computer Science Education, 2018, 19 (3), pp.347. ⟨10.7494/csci.2018.19.3.2866⟩. ⟨hal-01993048⟩
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