Local Linear Embedding with Adaptive Neighbors

•Linear approximation of LLE. Our model takes the linear mapping into consideration, making it more suitable to handle both linear and non-linear data. Also, outliers can be well dealt with during the linear projection procedure.•Global and local structure. Instead of only consider the local geometry properties, we also consider the global data point relationship to preserve the intrinsic structure. And our model shows robustness to noise and uneven distribution data.•Adaptive neighbor selection. In our model, weight between data and neighbors are updated in order to adjust each data into its optimal neighborhood. Using adaptive neighbor strategy, manifold structure can be kept and then structure learning and feature extraction could be accomplished simultaneously. Dimensionality reduction is one of the most important techniques in the field of data mining. It embeds 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 propose 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. Comprehensive 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.