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29 votes
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Wavelet Scattering explanation?

Wavelet Scattering is an equivalent deep convolutional network, formed by cascade of wavelets, modulus nonlinearities, and lowpass filters. It yields representations that are time-shift invariant, ...
OverLordGoldDragon's user avatar
7 votes
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Wavelet Scattering properties & implementation?

Scattering overview provided in this answer. Computational structure Fig 4, Deep Scattering Spectrum In steps: (First order begins) $x$ convolves with $\psi1_i$ --> $W1_i$ Modulus, $W1_i \...
OverLordGoldDragon's user avatar
5 votes
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What is "spin" for the 2D (separable) Morlet?

cause it s p i n Explanation, ground up When there's complex numbers, there's rotation. Recall, multiplying by $e^{j\theta}$ rotates a number by $\theta$ radians: and since $|e^{jX}|=1$ for any (...
OverLordGoldDragon's user avatar
3 votes
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Joint Time-Frequency Scattering explanation?

JTFS is an extension of Wavelet Scattering that exploits time-frequency structure, adding sensitivity to frequency-dependent time shifts, invariance to frequency transposition, and stability against ...
OverLordGoldDragon's user avatar
2 votes
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Classification of Signals using Features Extracted from Wavelet Scattering Coefficients

Expanding on my related answer but for wavelet scattering: Higher T -> greater time-shift invariance. Higher Q -> greater ...
OverLordGoldDragon's user avatar
1 vote

Can finite Multi-Resolution Analysis satisfy the Littlewood-Paley Criterion (unity partition)?

The Littlewood-Paley criterion is satisfied by an appropriate "generator rule" that relates a given filter to its successor, $\psi_{i + 1} = \text{rule}(\psi_i)$. The neat thing is, this ...
OverLordGoldDragon's user avatar
1 vote
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Littlewood-Paley Conditions, Scattering, and Multi-Resolution Analysis

General remarks I'm not familiar with Littlewood-Paley theory beyond the norm-preserving equation and its significance, or the concept of "unitary" beyond "self * adjoint = identity&...
OverLordGoldDragon's user avatar
1 vote
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Wavelet Scattering (Kymatio) Zero Divison Error

Latest release is incomplete. Use dev pip install git+https://github.com/kymatio/kymatio.git@dev or latest stable branch with all functionality ...
OverLordGoldDragon's user avatar
1 vote

Choosing a good low pass filter in the wavelet scattering transform

The choice of $\phi$ affects: Time-shift invariance: slower decay in time will increase it Time-warp stability: slower decay in time will increase it mainly for deformations along time (but not only ...
OverLordGoldDragon's user avatar
1 vote
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Time support for wavelets in scattering transform

It's indeed only a statement on proportionality. Wavelets aren't compat, so any notion of "support" invokes a heuristic (engineered criterion). However, it's not applicable to all wavelets: ...
OverLordGoldDragon's user avatar
1 vote
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Building the low pass filter in the wavelet scattering transform

It keeps the scale of the largest scale wavelet $\leq T$ while still tiling the entire frequency axis. using a single low pass filter built with a single scaling function would not achieve this: $\...
OverLordGoldDragon's user avatar
1 vote
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Joint Time-Frequency Scattering structure & implementation?

JTFS overview provided in this post. Computational structure JTFS breaks the tree structure of time scattering by convolving along frequency, exploiting the joint time-frequency geometry: $$ \begin{...
OverLordGoldDragon's user avatar

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