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 interpretable 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 resolution 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 continuously 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.
Original language | English (US) |
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Pages (from-to) | 118-152 |
Number of pages | 35 |
Journal | Proceedings of Machine Learning Research |
Volume | 145 |
State | Published - 2021 |
Event | 2nd Mathematical and Scientific Machine Learning Conference, MSML 2021 - Virtual, Online Duration: Aug 16 2021 → Aug 19 2021 |
Keywords
- Audio Classification
- Chirplet
- Cohen Class
- Environmental Sounds
- Explain-ability
- Gabor Transform
- Interpretability
- Learnable Time-Frequency Representation
- Spectrogram
- Speech Recognition
- Super-Resolution
- Time-Series
- Wavelet
- Wigner-Ville
- bioacoustics
- biosonar
ASJC Scopus subject areas
- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability