Random embeddings and efficient representations for signal processing and subspace methods
(2026)
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- Authors
- Supervisors
- Laurent Jacques
- Abstract
- This manuscript studies random quadratic embeddings as compact representations for signal processing and subspace learning tasks. We first investigate how information can be extracted directly from quadratic embeddings without reconstructing original signals. We then construct random features for subspace-valued data on the Grassmannian manifold. Binary, aggregated and periodic rank-one features are shown to approximate well-defined Grassmannian kernels, with uniform guarantees. Finally, we investigate efficient implementations through structured Hadamard-diagonal transformations and optical processing units. For the latter, we develop an encoder and decoder adapted to the binary-input constraints of the device and analyse the effect of physical noise on the reconstructed embeddings. Numerical experiments illustrate the approximation quality, computational gains and practical limitations of the proposed methods.
- Affiliations
Citations
Delogne, R. (2026). Random embeddings and efficient representations for signal processing and subspace methods. https://hdl.handle.net/2078.5/280577