Unsupervised Dynamic Discrete Structure Learning: A Geometric Evolution Method

Abstract

Revealing the latent low-dimensional geometric structure of high-dimensional data is a crucial task in unsupervised representation learning. Traditional manifold learning, as a typical method for discovering latent geometric structures, has provided important nonlinear insight for the theoretical development of unsupervised representation learning. However, due to the shallow learning mechanism of the existing methods, they can only exploit the simple geometric structure embedded in the initial data, such as the local linear structure. Traditional manifold learning methods are fairly limited in mining higher-order non-linear geometric information, which is also crucial for the development of unsupervised representation learning. To address the abovementioned limitations, this paper proposes a novel dynamic geometric structure learning model (DGSL) to explore the true latent nonlinear geometric structure. Specifically, by mathematically analysing the reconstruction loss function of manifold learning, we first provide universal geometric relational function between the curvature and the non-Euclidean metric of the initial data. Then, we leverage geometric flow to design a deeply iterative learning model to optimize this relational function. Our method can be viewed as a general-purpose algorithm for mining latent geometric structures, which can enhance the performance of geometric representation methods. Experimentally, we perform a set of representation learning tasks on several datasets. The experimental results show that our proposed method is superior to traditional methods.