Intrinsic dimensionality detection criterion based on Locally Linear Embedding

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.

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