<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Jiang, T.</style></author><author><style face="normal" font="default" size="100%">Vavasis, S.</style></author><author><style face="normal" font="default" size="100%">Zhai., C. W.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Recovery of a mixture of Gaussians by sum-of-norms clustering</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Machine Learning Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://jmlr.org/papers/volume21/19-218/19-218.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">21</style></volume><pages><style face="normal" font="default" size="100%">1-16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;span style=&quot;left:183.208px;top:652.985px;16.6043px;sans-serif;transform:scaleX(0.984627);&quot;&gt;Sum-of-norms clustering is a method for assigning&lt;/span&gt;&lt;span style=&quot;left:553.975px;top:652.985px;16.6043px;sans-serif;&quot;&gt; n &lt;/span&gt;&lt;span style=&quot;left:569.58px;top:652.985px;16.6043px;sans-serif;transform:scaleX(1.02966);&quot;&gt;points in &lt;/span&gt;&lt;span style=&quot;left:639.063px;top:652.985px;16.6043px;sans-serif;&quot;&gt;R&lt;/span&gt;&lt;span style=&quot;left:653.383px;top:649.155px;11.623px;monospace;&quot;&gt;d &lt;/span&gt;&lt;span style=&quot;left:666.763px;top:652.985px;16.6043px;sans-serif;transform:scaleX(1.06375);&quot;&gt;to&lt;/span&gt;&lt;span style=&quot;left:687.16px;top:652.985px;16.6043px;sans-serif;&quot;&gt; K &lt;/span&gt;&lt;span style=&quot;left:708.088px;top:652.985px;16.6043px;sans-serif;transform:scaleX(0.965163);&quot;&gt;clusters, 1&lt;/span&gt;&lt;span style=&quot;left:786.105px;top:652.055px;16.6043px;sans-serif;&quot;&gt;≤&lt;/span&gt;&lt;span style=&quot;left:803.803px;top:652.985px;16.6043px;sans-serif;&quot;&gt;K&lt;/span&gt;&lt;span style=&quot;left:823.877px;top:652.055px;16.6043px;sans-serif;&quot;&gt;≤&lt;/span&gt;&lt;span style=&quot;left:183.208px;top:672.91px;16.6043px;sans-serif;&quot;&gt;n&lt;/span&gt;&lt;span style=&quot;left:193.175px;top:672.91px;16.6043px;sans-serif;transform:scaleX(0.949803);&quot;&gt;, using convex optimization. Recently, Panahi et al. (2017) proved that sum-of-norms &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:692.837px;16.6043px;sans-serif;transform:scaleX(1.0181);&quot;&gt;clustering is guaranteed to recover a mixture of Gaussians under the restriction that the &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:712.762px;16.6043px;sans-serif;transform:scaleX(0.945846);&quot;&gt;number of samples is not too large. The purpose of this note is to lift this restriction, &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:732.687px;16.6043px;sans-serif;transform:scaleX(0.982827);&quot;&gt;that is, show that sum-of-norms clustering can recover a mixture of Gaussians even as the&lt;/span&gt;&lt;span style=&quot;left:183.208px;top:752.612px;16.6043px;sans-serif;transform:scaleX(0.947623);&quot;&gt; number of samples tends to infinity. Our proof relies on an interesting characterization &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:772.537px;16.6043px;sans-serif;transform:scaleX(0.993851);&quot;&gt;of clusters computed by sum-of-norms clustering that was developed inside a proof of the&lt;/span&gt;&lt;span style=&quot;left:183.208px;top:792.462px;16.6043px;sans-serif;transform:scaleX(0.999485);&quot;&gt; agglomeration conjecture by Chiquet et al. (2017). Because we believe this theorem has &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:812.388px;16.6043px;sans-serif;transform:scaleX(0.992218);&quot;&gt;independent interest, we restate and reprove the Chiquet et al. (2017) result herein.&lt;/span&gt;</style></abstract><issue><style face="normal" font="default" size="100%">225</style></issue><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;http://arxiv.org/abs/1902.07137&quot;&gt;http://arxiv.org/abs/1902.07137&lt;/a&gt;</style></notes></record></records></xml>