In Sunday Morning Insight: A Quick Panorama of Sensing from Direct Imaging to Machine Learning, we saw that the main difference between traditional sensing and machine learning mostly hinges on the first layer in NN parlance. In Compressive sensing, the first step is a linear one, a matrix-vector multiplication, while in Machine Learning the input space is traditionally projected nonlinearly on some other feature space.
Two years, following up on a query on LinkedIn, Matthieu Puigt, Phil Schniter and Karthikeyan Natesan Ramamurthy provided a small survey of what the next step is in compressive sensing: a nonlinear first stage. The resulting list of approaches was featured in Nonlinear Compressive Sensing
Here are some entries/papersI gathered that I had not mentioned before:
- Generalizing Compressed Sensing: GraSP implementation available
- Nonlinear Compressive Particle Filtering by Henrik Ohlsson, Michel Verhaegen, S. Shankar Sastry
- Quadratic Basis Pursuit by Henrik Ohlsson, Allen Y. Yang, Roy Dong, Michel Verhaegen, S. Shankar Sastry
- Nonlinear Basis Pursuit by Henrik Ohlsson, Allen Y. Yang, Roy Dong, S. Shankar Sastry
- Compressive Shift Retrieval by Henrik Ohlsson, Yonina C. Eldar, Allen Y. Yang, S. Shankar Sastry
- An Equivalence between the Lasso and Support Vector Machines by Martin Jaggi
- Optimized Measurements for Kernel Compressive Sensing, Karthikeyan Natesan Ramamurthy and Andreas Spanias
- A KERNEL-BASED COMPRESSED SENSING APPROACH TO DYNAMIC MRI FROM HIGHLY UNDERSAMPLED DATA Yihang Zhou, Yanhua Wang, and Leslie Ying and another one here (a kernel approach to compressed sensing parallel mri).
- Exact Rule Learning via Boolean Compressed Sensing, Dmitry M. Malioutov, Kush R. Varshney
- All the papers featured as entries on Phase Retrieval and Quantized CS
Related: Johnson-Lindenstrauss, Concentration and applications to Compressed Sensing and SVM Classiﬁcation, Devdatt Dubhashi
Do you know of any other ?
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Nonlinear regression problems with sparse parameters might be viewed as nonlinear compressive sensing problems. Then there are some results from the statistics community.
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