Isometric Manifold Learning Using Hierarchical Flow

We propose the Hierarchical Flow (HF) model constrained by isometric regularizations for manifold learning that combines goals such as dimensionality reduction, inference, sampling, projection and density estimation into one unified framework. Our proposed HF is regularized to not only produce embeddings preserving geometric structure of manifold, but also project samples onto in a manner conforming rigorous definition projection. Theoretical guarantees are provided our satisfy two desired properties. In order detect real we two-stage reduction algorithm, which time-efficient algorithm thanks hierarchical architecture design model. Experimental results justify theoretical analysis, demonstrate superiority cost training time, verify effect aforementioned properties improving performances on downstream tasks anomaly detection.