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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta http-equiv="X-UA-Compatible" content="ie=edge">
<title>Iterative Decomposition Model V3</title>
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<body>
<h1>Iterative Decomposition Model V3</h1>
<details>
<summary>
<caption>Table of Contents</caption>
</summary>
<ul>
<li><a href="#Streaming Iterative Decomposition">Streaming Iterative Decomposition</h1></a></li>
<li><a href="#Future Work">Future Work</h1></a><ul>
<li><a href="#Better Perceptual Audio Losses">Better Perceptual Audio Losses</h2></a></li>
<li><a href="#Model Size, Training Time and Dataset">Model Size, Training Time and Dataset</h2></a></li>
<li><a href="#Different Event Generator Variants">Different Event Generator Variants</h2></a></li>
</ul>
</li>
<li><a href="#Cite this Article">Cite this Article</h1></a></li>
<li><a href="#Event Scatterplot">Event Scatterplot</h1></a></li>
<li><a href="#Streaming Algorithm for Arbitrary-Length Audio Segments">Streaming Algorithm for Arbitrary-Length Audio Segments</h1></a><ul>
<li><a href="#Original (Streaming)">Original (Streaming)</h2></a></li>
<li><a href="#Reconstruction (Streaming)">Reconstruction (Streaming)</h2></a></li>
</ul>
</li>
<li><a href="#Examples">Examples</h1></a><ul>
<li><a href="#Example 1">Example 1</h2></a></li>
<li><a href="#Example 2">Example 2</h2></a></li>
<li><a href="#Example 3">Example 3</h2></a></li>
<li><a href="#Example 4">Example 4</h2></a></li>
<li><a href="#Example 5">Example 5</h2></a></li>
</ul>
</li>
<li><a href="#Notes">Notes</h1></a></li>
</ul>
</details>
<a id="Streaming Iterative Decomposition"></a>
<h1>Streaming Iterative Decomposition</h1>
<p>This article covers the continuation of work I've been pursuing in the area of sparse, interpretable audio models. Our
goal is to decompose recordings of acoustic instruments (orchestral music from the
<a href="https://zenodo.org/records/5120004#.Yhxr0-jMJBA">MusicNet dataset</a> dataset) into constituent "events", which are encoded
as low-dimensional vectors carrying information about attack envelopes and physical resonances of both the instrument being
played and the room in which the performance occurs.</p>
<p>Some previous iterations of this work:</p>
<ul>
<li><a href="https://blog.cochlea.xyz/v4blogpost.html">Iterative Decomposition Model V4</a></li>
<li><a href="https://blog.cochlea.xyz/gamma-audio-splat.html">Gaussian/Gamma Splatting for Audio</a></li>
</ul>
<p><strong>In this newest version, we introduce a streaming algorithm so that audio segments of arbitrary lengths can be decomposed into
constituent events.</strong></p>
<p>All training and model code can be
<a href="https://github.com/JohnVinyard/matching-pursuit/blob/main/iterativedecomposition.py">found here</a>.</p>
<a id="Future Work"></a>
<h1>Future Work</h1>
<a id="Better Perceptual Audio Losses"></a>
<h2>Better Perceptual Audio Losses</h2>
<p>Recent experiments use a greedy, per-event loss which maximizes the energy removed from the signal at each step, as well
as a learned, adversarial loss. Reconstruction quality will likely benefit from a more perceptually-aligned loss and a
larger, more diverse dataset.</p>
<a id="Model Size, Training Time and Dataset"></a>
<h2>Model Size, Training Time and Dataset</h2>
<p>Firstly, this model is relatively small, weighing in at ~26M parameters (~117 MB on disk) and has only been trained for
around 24 hours, so it seems there is a lot of space to increase the model size, dataset size and training time to
further improve. The reconstruction quality of the examples on this page is not amazing, certainly not good enough
even for a lossy audio codec, but the structure the model extracts seems like it could be used for many interesting
applications. The training data should be expanded beyond the MusicNet dataset.</p>
<a id="Different Event Generator Variants"></a>
<h2>Different Event Generator Variants</h2>
<p>The decoder side of the model is very interesting, and all sorts of physical modelling-like approaches could yield
better, more realistic, and sparser renderings of the audio.</p>
<a id="Cite this Article"></a>
<h1>Cite this Article</h1>
<p>If you'd like to cite this article, you can use the following <a href="https://bibtex.org/">BibTeX block</a>.</p>
<citation-block
tag="johnvinyarditerativedecompositionv3"
author="Vinyard, John"
url="https://blog.cochlea.xyz/iterative-decomposition-v3.html"
header="Iterative Decomposition V3"
year="2024">
</citation-block>
<a id="Event Scatterplot"></a>
<h1>Event Scatterplot</h1>
<p>Here is a scatterplot mapping events from four different audio segments onto a 2D plane using t-SNE.<br />
Each 32-dimensional event vector encodes information about attack, resonance, and room impulse response.</p>
<p>You can play around with a larger scatterplot of events sampled from MusicNet reconstructions <a href="https://blog.cochlea.xyz/scatterv7.html">here</a>.</p>
<scatter-plot
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</scatter-plot>
<a id="Streaming Algorithm for Arbitrary-Length Audio Segments"></a>
<h1>Streaming Algorithm for Arbitrary-Length Audio Segments</h1>
<p>In this latest iteration of the work, we introduce a "streaming" algorithm so that we can decompose audio segments of
arbitrary lengths.</p>
<a id="Original (Streaming)"></a>
<h2>Original (Streaming)</h2>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/streamingorig_f67903a0d96b470e449ac7d4b86c79fc5f6e4bdb"
height="100"
samples="256"
scale="4"
controls
></audio-view>
<a id="Reconstruction (Streaming)"></a>
<h2>Reconstruction (Streaming)</h2>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/streamingrecon_c3b7a48a3c24ef7793960a4e8ff7f36f665aa270"
height="100"
samples="256"
scale="4"
controls
></audio-view>
<a id="Examples"></a>
<h1>Examples</h1>
<a id="Example 1"></a>
<h2>Example 1</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_b1b9d9e64c2f5d5ab2c5336d43bc32165c69f7ed"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_a0df5f0249f5966c29fdb7d624f517696d8d81c3"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_337f39fd94a0664af0930ae0661a5b1ec11fa995"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_eb55531f35ea6bd19c9b63f56a93a50588a0e8b0"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<img src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_5c21fc03497386669eaf333cb387b284c6d0f6f1" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Events clustered using <a href="https://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html">t-SNE</a></p>
<scatter-plot
width="300"
height="300"
radius="0.04"
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</scatter-plot>
<a id="Individual Audio Events"></a>
<h3>Individual Audio Events</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event0_106086e4754ff1a95db48a253de5bf70ac8635af"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
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height="25"
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<audio-view
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height="25"
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scale="1"
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<audio-view
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height="25"
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<audio-view
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<audio-view
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<audio-view
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height="25"
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<audio-view
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height="25"
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<audio-view
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height="25"
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<audio-view
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<audio-view
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height="25"
samples="256"
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<audio-view
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height="25"
samples="256"
scale="1"
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height="25"
samples="256"
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<audio-view
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height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event21_40d55751f33fa111d6213f59dfa0be746cdb22c7"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event22_07a94b1d5e6f3aae382650497568d2d91370c7e9"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event23_8ab1e2123af37d59fb9a6b9a43ebd782977fd7ff"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event24_7a01ab9ed86784587758e38b90e520bfd8d1f933"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event25_12f57394ed7200e12ed6da814986d77bf66da111"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event26_dfe98c5ac0dfead3401f825b370fee6e13d9805c"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event27_c1b44c1e59e61db3a9ee760cf68b30cfd9dc226a"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event28_68afc379bd00a800edc3b4f13cb204ac1e4a649a"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event29_21f3dc6d2ba6aa28426ecea969833c5d12b8a7d3"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event30_89498421baa7f564ddd6b311319c2a2f0cc10966"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event31_9e38c892f6ebaf590993436ecf8643333630c388"
height="25"
samples="256"
scale="1"
></audio-view>
<a id="Example 2"></a>
<h2>Example 2</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_729a1cafe6fc3ec8111c598a347047253dd13823"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_d96843325f046ac76a88b50594cec1919ee9fcbe"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_d81a775d367d1666e34647d1062011c58d545424"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_f5dc623c5d5852a715dba10c61f0062f6f9383a1"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<img src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_5ebcb33e3ad70c0b18fcd55727eaffd290dd6a63" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Events clustered using <a href="https://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html">t-SNE</a></p>
<scatter-plot
width="300"
height="300"
radius="0.04"
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</scatter-plot>
<a id="Individual Audio Events"></a>
<h3>Individual Audio Events</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event0_0b6c3f7fcdbcfaf40a0aeb61008d9faa3aa18d2e"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event1_998783f4c69b3d2871fff6d022e1deb769d9ac75"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event2_abf1ee51a030c5d8dce9e60ec7132b90b7fd2986"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event3_365b82b0a0e28f93c4ab971d12018f1745eec343"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event4_2bbd6706b1d3d0ca21815bdd4f352023513370fe"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event5_eef5e85f091bfab0044a53d6264326269e873b58"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event6_7e646aa387d2d617b5af09266b04ec6bae4283f3"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event7_6ed2811da842146d98cd6e9d5364879bb7d5f495"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event8_eda729ab7d429d5057af889e62dfbac49d2fbcf3"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event9_d029e2d5b62c4b184f033bb18d8b50961fce3a12"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event10_57acf25f9bf337cd387f916140945c8a5b64a72a"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event11_57907a84ff1ba26570a6fca5966e48381b4c044d"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event12_79b37f1974977250ae3094152907ad1d93b10b02"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event13_ef8ac886c179fb1796a3c2396fa9eb7868b6455c"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event14_63d5571e0aeb5901bd2a2c94f9a108b8d16474f3"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event15_0a73e6c243518b4a36c125b415dbba2141ba5e57"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event16_fbe029e66f519274694cfb746a3de8ad3a53b026"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event17_b89667732935c5a67b9d6d22a2ddd44fac38f2b3"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event18_b4993dfd5566af0d00749fbfb1aaa3623b7abd01"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event19_8e82233f5059c1849ef1dcef7ac6a16ea1cfe31c"
height="25"
samples="256"
scale="1"
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<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event20_e1ab93545b83f18fc03ba2714cceb8fcc2aa1a76"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event21_0caa821daf0acad8426e8f9407924829f5aa8a12"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event22_5c204555ddc271e880bd138050919a4c3061d7ec"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event23_9bc67cde5c54d755301a9c2bdae8a018a9c9ac04"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event24_10dc28be9f11a34d7b2474318ba5946c32cb7865"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event25_a09d9c7c6656df21b2a09388d0997abe398eac3a"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event26_3472256d1cfd830a03634645e33941d348ee798d"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event27_32229a13dc6aabcaffb0209507c0147a5bf480b9"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event28_2af34e09e29156171c42064f02a6d837720f2840"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event29_b96ca56e947077e9cd2e4040a6cb3b48713700f5"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event30_d5895d5ebc137d0fc7f6fcef7939c8796e11ffad"
height="25"
samples="256"
scale="1"
></audio-view>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/event31_66297949460c0daecddd7c4c61681584ab99ca7b"
height="25"
samples="256"
scale="1"
></audio-view>
<a id="Example 3"></a>
<h2>Example 3</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_dfde6ded58d70c01e721ce9a7c79e510f2d2a4ac"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_56150a7a76e6c74d86acaae3774c6cc551a43d36"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_dfcdb25356dc0ae86b3564a68cb00eeea0430aeb"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_744d8080f6b2e0c96156421be1804f4ddb370ff8"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<img src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_b1c9e28cbe8f22dd335c832fb796dde75d249b14" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Events clustered using <a href="https://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html">t-SNE</a></p>
<scatter-plot
width="300"
height="300"
radius="0.04"
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<a id="Individual Audio Events"></a>
<h3>Individual Audio Events</h3>
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