Energy-aware adaptive bi-Lipschitz embeddings
This work addresses dimensionality reduction for data analysis, particularly in compressive sensing, but appears incremental as it builds on existing embedding methods with specific constraints.
The paper tackles the problem of designing dimensionality-reducing matrices that preserve distances between data points, proposing a deterministic Bi-Lipschitz embedding approach with a scalable algorithm called AMUSE, and demonstrates its application in compressive sensing with energy constraints.
We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as much as possible relative to their distances in original data space. This approach can be considered as a deterministic Bi-Lipschitz embedding of the data points. We introduce a scalable learning algorithm, dubbed AMUSE, and provide a rigorous estimation guarantee by leveraging game theoretic tools. We also provide a generalization characterization of our matrix based on our sample data. We use compressive sensing problems as an example application of our problem, where the Frobenius norm design constraint translates into the sensing energy.