Soft adaptive loss based Laplacian eigenmaps

Baihua Chen, Yunlong Gao, Shunxiang Wu, Jinyan Pan, Jinghua Liu, Yuling Fan

Abstract: The Laplacian eigenmaps (LE) is one of the most commonly used nonlinear dimensionality reduction methods and aims to find a low-dimensional representation to preserve the topological relationship between sample points in the original data. However, the ℓ2-norm based loss function makes LE unable to preserve the relationship in many cases. Additionally, the topological relationship does not represent the real intrinsic structure of data. For example, the overemphasis of the topological relationship by LE easily breaks the manifold structure into multiple local areas in the embedding space, which makes the spectral clustering analysis of multi-manifold data more difficult to carry out. To solve this problem, we propose the soft adaptive loss based LE (SALE). With the soft adaptive loss, SALE can adaptively emphasize the topological relationship between sample points and the clustering structure of data. The model is tested and validated on UCI, face and gene expression data sets, and compared with some state-of-the-art models. The experimental results show that the method is robust to noise.