Interpretable and Learnable Super-Resolution Time-Frequency Representation

Randall Balestriero, Herve Glotin, Richard Baranuik
Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, PMLR 145:118-152, 2022.

Abstract

We develop a novel interpretable and learnable time-frequency representation (TFR) that produces a super-resolved quadratic signal representation for time-series analysis; the proposed TFR is a Gaussian filtering of the Wigner-Ville (WV) transform of a signal parametrized with a few inter- pretable parameters. Our approach has two main hallmarks. First, by varying the filters applied onto the WV, our new TFR can interpolate between known TFRs such as spectrograms, wavelet transforms, and chirplet transforms. Beyond that, our representation can also reach perfect time and frequency localization, hence super-resolution; this generalizes standard TFRs whose resolu- tion is limited by the Heisenberg uncertainty principle. Second, our proposed TFR is interpretable thanks to an explicit low-dimensional and physical parametrization of the WV Gaussian filtering. We demonstrate that our approach enables us to learn highly adapted TFRs and is able to tackle a range of large-scale classification tasks, where we reach higher performance compared to baseline and learned TFRs. Ours is to the best of our knowledge the first learnable TFR that can contin- uously interpolate between super-resolution representation and commonly employed TFRs based on a few learnable parameters and which preserves full interpretability of the produced TFR, even after learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v145-balestriero22a, title = {Interpretable and Learnable Super-Resolution Time-Frequency Representation}, author = {Balestriero, Randall and Glotin, Herve and Baranuik, Richard}, booktitle = {Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference}, pages = {118--152}, year = {2022}, editor = {Bruna, Joan and Hesthaven, Jan and Zdeborova, Lenka}, volume = {145}, series = {Proceedings of Machine Learning Research}, month = {16--19 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v145/balestriero22a/balestriero22a.pdf}, url = {https://proceedings.mlr.press/v145/balestriero22a.html}, abstract = {We develop a novel interpretable and learnable time-frequency representation (TFR) that produces a super-resolved quadratic signal representation for time-series analysis; the proposed TFR is a Gaussian filtering of the Wigner-Ville (WV) transform of a signal parametrized with a few inter- pretable parameters. Our approach has two main hallmarks. First, by varying the filters applied onto the WV, our new TFR can interpolate between known TFRs such as spectrograms, wavelet transforms, and chirplet transforms. Beyond that, our representation can also reach perfect time and frequency localization, hence super-resolution; this generalizes standard TFRs whose resolu- tion is limited by the Heisenberg uncertainty principle. Second, our proposed TFR is interpretable thanks to an explicit low-dimensional and physical parametrization of the WV Gaussian filtering. We demonstrate that our approach enables us to learn highly adapted TFRs and is able to tackle a range of large-scale classification tasks, where we reach higher performance compared to baseline and learned TFRs. Ours is to the best of our knowledge the first learnable TFR that can contin- uously interpolate between super-resolution representation and commonly employed TFRs based on a few learnable parameters and which preserves full interpretability of the produced TFR, even after learning. } }
Endnote
%0 Conference Paper %T Interpretable and Learnable Super-Resolution Time-Frequency Representation %A Randall Balestriero %A Herve Glotin %A Richard Baranuik %B Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference %C Proceedings of Machine Learning Research %D 2022 %E Joan Bruna %E Jan Hesthaven %E Lenka Zdeborova %F pmlr-v145-balestriero22a %I PMLR %P 118--152 %U https://proceedings.mlr.press/v145/balestriero22a.html %V 145 %X We develop a novel interpretable and learnable time-frequency representation (TFR) that produces a super-resolved quadratic signal representation for time-series analysis; the proposed TFR is a Gaussian filtering of the Wigner-Ville (WV) transform of a signal parametrized with a few inter- pretable parameters. Our approach has two main hallmarks. First, by varying the filters applied onto the WV, our new TFR can interpolate between known TFRs such as spectrograms, wavelet transforms, and chirplet transforms. Beyond that, our representation can also reach perfect time and frequency localization, hence super-resolution; this generalizes standard TFRs whose resolu- tion is limited by the Heisenberg uncertainty principle. Second, our proposed TFR is interpretable thanks to an explicit low-dimensional and physical parametrization of the WV Gaussian filtering. We demonstrate that our approach enables us to learn highly adapted TFRs and is able to tackle a range of large-scale classification tasks, where we reach higher performance compared to baseline and learned TFRs. Ours is to the best of our knowledge the first learnable TFR that can contin- uously interpolate between super-resolution representation and commonly employed TFRs based on a few learnable parameters and which preserves full interpretability of the produced TFR, even after learning.
APA
Balestriero, R., Glotin, H. & Baranuik, R.. (2022). Interpretable and Learnable Super-Resolution Time-Frequency Representation. Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, in Proceedings of Machine Learning Research 145:118-152 Available from https://proceedings.mlr.press/v145/balestriero22a.html.

Related Material