Deep Scattering Spectrum

By Joakim Andén, Stéphane Mallat. 2013

625 citations recorded by the source corpus.

A scattering transform defines a locally translation invariant representation which is stable to time-warping deformation. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades of wavelet convolutions and modulus operators. Second-order scattering coefficients characterize transient phenomena such as attacks and amplitude modulation. A frequency transposition invariant representation is obtained by applying a scattering transform along log-frequency. State-the-of-art classification results are obtained for musical genre and phone classification on GTZAN and TIMIT databases, respectively.

Subfields: Computer Vision and Pattern Recognition, Signal Processing

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Citations in the corpus

Learning Filterbanks from Raw Speech for Phone Recognition (2017, methodology): “This is the foundation of the deep scattering spectrum [12], which cascades scattering transforms to retrieve information that is lost in the MFSC.”
Differentially Private Learning Needs Better Features (or Much More Data) (2020, background): “Another interesting direction is to extend our results to domains beyond vision, e.g., with handcrafted features for text (Manning & Schutze, 1999) or speech (Andén & Mallat, 2014).”
Understanding deep convolutional networks (2016, background): “Good music and speech classification results are then obtained with a scattering transform [20].”
Wavelet Scattering Regression of Quantum Chemical Energies (2016, background): “They have found applications for image [43, 11] and audio [10, 2] signal classifications.”
Tensor Switching Networks (2016, methodology): “SVMs using SS-ReLU and TS-ReLU kernels are implemented in Matlab based on libsvm-compact [22].”
Deep Scattering Spectrum with deep neural networks (2014, methodology): “However, [13] performed a “scatter transfer” operation, shown in Equation 1, which was found to be effective for S2.”
A deep scattering spectrum — Deep Siamese network pipeline for unsupervised acoustic modeling (2016, methodology): “We focus on one particular model, the ABnet [2, 5], a Siamese network that learns a phone representation from pairs of words, and we study the effect of switching its input representation from mel-filterbanks to the scattering spectrum [6].”
DNN-based stochastic postfilter for HMM-based speech synthesis (2014, methodology): “The FFT convolution is equivalent to the weighted sum in a network unit of the convolutional DNN [20], and the next deep layer of a DNN trained in the spectrum domain may therefore contain an MS-related representation.”
Audio Texture Synthesis with Scattering Moments (2013, methodology): “Second order scattering moments recover information on audio-modulations and transients by computing the wavelet coefﬁcients of each | X ⋆ ψ λ 1 | , and their ﬁrst order moment: These multiscale variations of each envelop | X ⋆ψ j 1 | , specify the amplitude modulations of X ( t ) [6].”
Discriminative template learning in group-convolutional networks for invariant speech representations (2015, background): “Previous work on group-invariant speech representations focused on feed-forward, unsupervised networks using either random templates under speech-specific transformations [11, 12] or predefined wavelets under scaling and translations [16].”
Intermittent process analysis with scattering moments (2013, background): “First- and second-order scattering moments applied to image and audio textures as well as intrapartum electro-cardiograms for fetal monitoring provide state of the art classification errors [2, 9, 13, 35], but these results are strictly numerical.”
Audio augmentation for speech recognition (2015, background): “In [8] it was shown that this corresponds approximately to a shift of the spectrum in the mel spectrogram, since the mel scale is approximately logarithmic.”
Kymatio: Scattering Transforms in Python (2018, methodology): “In 1D and 2D, we use Morlet wavelets which are close to analytic ( i.e. , complex-valued with low energy in the negative frequencies) and the non-linearity is the complex modulus ρ ( t ) = | t | for t ∈ C (And´en and Mallat, 2014; Bruna and Mallat, 2013).”
A Deep Generative Architecture for Postfiltering in Statistical Parametric Speech Synthesis (2015, methodology): “The FFT convolution is equivalent to the weighted sum in a network unit of the convolutional DNN [43], and the next deep layer of a DNN trained in the spectrum domain may therefore contain a representation related to MS.”
Acoustic Modelling from the Signal Domain Using CNNs (2016, background): “The Fourier modulus is translation invariant and stable to additive noise but unstable to small deformations at high frequencies [20].”
A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction (2015, background): “Moreover, Mallat’s scattering networks lead to state-of-the-art results in various classiﬁcation tasks [23]–[25].”
ABX-Discriminability Measures and Applications. (Mesures de discriminabilité ABX et applications) (2016, background): “A study published after the initial session of the challenge [103] also showed that replacing the original input features (Mel-filterbanks) with richer scattering spectrum coefficients [104] improved the performance of Siamese Network acoustic models (17.”
A time delay neural network architecture for efficient modeling of long temporal contexts (2015, background): “Feature representations such as TRAPs [8], wavelet based multi-scale spectro-temporal representations [9], deep scattering spectra [10] and other modulation feature representations [11] have been proposed to represent long term spectrotemporal dynamics of the signal.”