AN INTRINSIC DIMENSIONALITY DETECTION CRITERION BASED ON LOCALLY LINEAR EMBEDDING

Lian Meng, Piotr Breitkopf

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.


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DOI: http://dx.doi.org/10.7494/csci.2018.19.3.2866

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