Local Linear Embedding with Adaptive Neighbors

Dimensionality reduction is one of the most important techniques in the field of data mining. It em-beds high-dimensional data into a low-dimensional vector space while keeping the main information as much as possible. Locally Linear Embedding (LLE) as a typical manifold learning algorithm computes neighborhood preserving embeddings of high-dimensional inputs. Based on the thought of LLE, we pro-pose a novel unsupervised dimensionality reduction model called Local Linear Embedding with Adaptive Neighbors (LLEAN). To achieve a desirable dimensionality reduction result, we impose adaptive neighbor strategy and adopt a projection matrix to project data into an optimal subspace. The relationship between every pair-wise data is investigated to help reveal the data structure. Augmented Lagrangian Multiplier (ALM) is devised in optimization procedure to effectively solve the proposed objective function. Com-prehensive experiments on toy data and benchmark datasets have been done and the results show that LLEAN outperforms other state-of-the-art dimensionality reduction methods. (c) 2022 Elsevier Ltd. All rights reserved.