Local conformal autoencoder for standardized data coordinates.

Area of Science:

• Data science
• Machine learning
• Computational geometry

Background:

• Scientific measurements often involve complex, nonlinear deformations of underlying data structures.
• Standardizing these coordinates is crucial for comparing observations from different instruments or experiments.
• Existing methods struggle with preserving geometric information during coordinate transformation.

Purpose of the Study:

• To develop a novel deep learning method for obtaining standardized data coordinates.
• To create an algorithm that learns an isometric embedding of scientific measurements into a latent space.
• To ensure recovered coordinates are invariant to manifold diffeomorphisms for cross-observation matching.

Main Methods:

• Proposed the Local Conformal Autoencoder (LOCA), a deep learning model.
• Modeled data observations as samples from a Riemannian manifold deformed by latent variables.
• Employed a local z-scoring procedure within LOCA to rectify deformations while preserving geometric properties.

Main Results:

• Demonstrated LOCA's ability to learn isometric embeddings in various model settings.
• Showcased superior interpolation and extrapolation capabilities compared to state-of-the-art methods.
• Validated LOCA's effectiveness in Wi-Fi localization and 3D surface reconstruction from 2D projections.

Conclusions:

• LOCA provides a robust method for standardizing scientific data coordinates.
• The algorithm effectively preserves essential geometric information, enabling invariant data matching.
• LOCA shows significant promise for applications in diverse scientific domains requiring data standardization and comparison.