Dimensionality reduction based unsupervised metric learning consists in finding meaningful compact data representations previously to clustering and classification problems. One of the major aspects of these algorithms is the approximation of the underlying manifold by a weighted graph. A limitation with most manifold learning algorithms is that edge weights in the proximity graph rely heavily on the Euclidean distance, which is known to be quite sensitive to the presence of outliers. In this paper, we propose to improve the Locality Preserving Projections (LPP) algorithm by incorporating a recently proposed graph inference method called Probabilistic Nearest Neighbors (PNN), an extension of the Clustering with Adaptive Neighbors (CAN) approach, used with success in graph-based semi-supervised learning. The proposed PNN-LPP algorithm is able to achieve better classification results than regular LPP, showing competitive performance against state-of-the-art approaches for dimensionality reduction, such as the UMAP algorithm, especially in datasets with a limited number of samples.

Manifold learning, Dimensionality reduction, Locality Preserving Projections, Probabilistic Nearest Neighbors, Unsupervised Metric Learning