random projections

Abstract: The Grassmannian manifold \(G(k, n)\) serves as a fundamental tool in signal processing, computer vision, and machine learning, where problems often involve classifying, clustering, or comparing subspaces. In this work, we propose a sketching-based approach to approximate Grassmannian kernels using random projections.

Abstract: Random embedding techniques, such as random Fourier features, are widely used to sketch initial data to a new, kernelised feature space. In this work, we leverage a specific property of random rank-one projection operators, the sign product embedding, to approximate a quadratic polynomial kernel using the scalar product of a pair asymmetric vector embeddings, with one taking only binary values.

Abstract: Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals.

Abstract: Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome.

(joint work with V. Cambareri and C. Xu). See also arXiv:1702.04664 for the corresponding preprint.

Abstract: Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel geometry-preserving embeddings or to estimate the information/bits stored in this reduced data representation.

2016 Invited speaker, talk on “”.

Abstract: This paper focuses on the estimation of low-complexity signals when they are observed through \(M\) uniformly quantized compressive observations. Among such signals, we consider 1-D sparse vectors, low-rank matrices, or compressible signals that are well approximated by one of these two models.

Last January, I was honored to be invited in RWTH Aachen University by Holger Rauhut and Sjoerd Dirksen to give a talk on the general topic of quantized compressed sensing. In particular, I decided to focus my presentation on the quasi-isometric embeddings arising in 1-bit compressed sensing, as developed by a few researchers in this field (e.