Neighborhood Geometric Structure-Preserving Variational Autoencoder for Smooth and Bounded Data Sources.

Area of Science:

• Machine Learning
• Computer Vision
• Data Representation

Background:

• Low-dimensional data manifolds, like human poses, require effective representation learning.
• Existing encoder-decoder networks often fail to preserve data relationships in latent space, leading to issues like 'holes' and unpredictable outputs for tasks such as denoising.
• The lack of effective latent space regularization is a key limitation in current representation learning methods.

Purpose of the Study:

• To develop a novel variational autoencoder that preserves neighborhood geometric structures in the latent space.
• To address the issue of 'holes' in the latent space by learning approximate manifold boundaries.
• To improve the quality of learned low-dimensional representations for various data types, including human poses and facial images.

Main Methods:

• Proposed a neighborhood geometric structure-preserving variational autoencoder (SP-VAE).
• SP-VAE maximizes the evidence lower bound while ensuring latent variables maintain their ambient space structures.
• Introduced learning a set of small surfaces to bound the learned manifold, mitigating latent space holes.

Main Results:

• SP-VAE learns significantly smoother data manifolds compared to baseline methods.
• Experimental validation on synthetic data, human poses, and facial images demonstrated superior performance.
• The approach achieved better results in human pose refinement and facial expression image interpolation.

Conclusions:

• The proposed SP-VAE effectively preserves geometric structures in latent space, leading to more robust data representations.
• The method successfully addresses limitations of traditional autoencoders in handling complex data manifolds.
• SP-VAE offers improved performance for downstream tasks like denoising, refinement, and interpolation.