Bidirectional visible neighborhood preserving embedding

In this paper, we propose a series of dimensionality reduction algorithms according to a novel neighborhood graph construction method. This paper begins with the presentation of a new manifold learning algorithm called bidirectional visible neighborhood preserving embedding (BVNPE). Similar with existing manifold techniques, BVNPE first links every data point with its k nearest neighbors (NNs). Then, we construct a reliable neighborhood graph by checking two criteria: bidirectional linkage and visible neighborhood preserving. Third, we assign the weights to each edge in this reliable graph based on the pairwise distance between data points. Finally, we compute the low-dimensional embedding, trying to preserve the manifold structure of input dataset by mapping nearby points on the manifold to nearby points in low-dimensional space. Moreover, this paper also proposes a linear BVNPE called BVNPE/L for straightforward embedding of new data, and a multilinear BVNPE called BVNPE/M, which represents the tensor structure of image and video data better. Experiments on various datasets validate the effectiveness of proposed algorithms.