关键词: 流形学习, 孪生网络, 两级邻域, 样本对训练

Abstract:

Manifold learning is a special kind of nonlinear problem that is to recover the low-dimensional manifold structure from high-dimensional sampled data to achieve the purpose of dimensionality reduction. It is an important method in pattern recognition and data visualization. There are many numerical methods for manifold learning based on local linear assumptions, that is, explicitly defining the local linear mapping model and then performing global optimization. These methods are sensitive to the shape of the manifold and the way of sampling. Another nonlinear tool, neural network, is theoretically robust because it does not rely on the specific mathematical models. However, due to the special nonlinearity of manifold learning, the traditional neural network is difficult to achieve satisfactory results. In order to solve these problems, this paper improves a homogeneous dual channel neural network, siamese network, and applies it to manifold learning. For the two channels of siamese network, a triple structure is designed, namely dimension increasing layer, filtering layer and dimension reducing layer. At the same time, based on the concept of two-level neighborhood, a loss function including positive and negative sample pairs is proposed. After the training of “sample pair”, the spatial relationship of adjacent data is maintained after dimension reduction. By using the siamese network to reduce the dimension of the simulation data（Swiss roll）, and compared with the traditional methods, it is found that the siamese network can more truly restore the internal structure of high-dimensional manifold. At the same time, the siamese network is used for the two-dimensional visualization of real data（handwritten digits）, and compared with the traditional methods, it is found that the clustering effect of siamese network is also obvious, and the classification distribution is more uniform, and the boundary is easier to identify.

Key words: manifold learning, siamese network, two-level neighborhood, sample pairs training