Curvature Augmented Manifold Embedding and Learning
This is an incremental improvement for researchers in machine learning and data science, offering a new physics-based approach to dimensionality reduction.
The authors tackled the problem of dimensionality reduction and data visualization by proposing CAMEL, a method that formulates the process as a physics-inspired force field model, including non-pairwise forces based on curvature. The result is a method that is applied to benchmark datasets, showing comparisons with existing models like tSNE and UMAP using 14 metrics, though no concrete performance numbers are provided in the abstract.
A new dimensional reduction (DR) and data visualization method, Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed. The key novel contribution is to formulate the DR problem as a mechanistic/physics model, where the force field among nodes (data points) is used to find an n-dimensional manifold representation of the data sets. Compared with many existing attractive-repulsive force-based methods, one unique contribution of the proposed method is to include a non-pairwise force. A new force field model is introduced and discussed, inspired by the multi-body potential in lattice-particle physics and Riemann curvature in topology. A curvature-augmented force is included in CAMEL. Following this, CAMEL formulation for unsupervised learning, supervised learning, semi-supervised learning/metric learning, and inverse learning are provided. Next, CAMEL is applied to many benchmark datasets by comparing existing models, such as tSNE, UMAP, TRIMAP, and PacMap. Both visual comparison and metrics-based evaluation are performed. 14 open literature and self-proposed metrics are employed for a comprehensive comparison. Conclusions and future work are suggested based on the current investigation. Related code and demonstration are available on https://github.com/ymlasu/CAMEL for interested readers to reproduce the results and other applications.