https://primo.ai/index.php?action=history&feed=atom&title=Convolution_vs._Cross-Correlation_%28Autocorrelation%29 2026-07-12T15:29:43Z Revision history for this page on the wiki MediaWiki 1.31.0 https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=36932&oldid=prev 2024-04-28T20:25:08Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 20:25, 28 April 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14" >Line 14:</td> <td colspan="2" class="diff-lineno">Line 14:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Perspective]] ... [[Context]] ... [[In-Context Learning (ICL)]] ... [[Transfer Learning]] ... [[Out-of-Distribution (OOD) Generalization]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Perspective]] ... [[Context]] ... [[In-Context Learning (ICL)]] ... [[Transfer Learning]] ... [[Out-of-Distribution (OOD) Generalization]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Signal Processing]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Signal Processing]]</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There is a lot of subtlety between the meanings of convolution and correlation. Both belong to the broader idea of inner products and projections in linear algebra, i.e. projecting one vector onto another to determine how &quot;strong&quot; it is in the direction of the latter.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There is a lot of subtlety between the meanings of convolution and correlation. Both belong to the broader idea of inner products and projections in linear algebra, i.e. projecting one vector onto another to determine how &quot;strong&quot; it is in the direction of the latter.</div></td></tr> </table>

BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=36931&oldid=prev 2024-04-28T20:24:54Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 20:24, 28 April 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11" >Line 11:</td> <td colspan="2" class="diff-lineno">Line 11:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://www.bing.com/news/search?q=ai+Convolution+Autocorrelation+Cross-Correlation&amp;qft=interval%3d%228%22 ...Bing News]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://www.bing.com/news/search?q=ai+Convolution+Autocorrelation+Cross-Correlation&amp;qft=interval%3d%228%22 ...Bing News]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [[Causation vs. Correlation]] ... [[Autocorrelation]] ... [[Convolution vs. Cross-Correlation (Autocorrelation)]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* [[Causation vs. Correlation]] ... [[Autocorrelation]] ...[[Convolution vs. Cross-Correlation (Autocorrelation)<ins class="diffchange diffchange-inline">]] </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* [[Perspective]] ... [[Context]] ... [[In-Context Learning (ICL)]] ... [[Transfer Learning]] ... [[Out-of-Distribution (OOD) Generalization</ins>]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Signal Processing]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Signal Processing]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> </table>

BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=31191&oldid=prev 2023-07-07T03:09:30Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 03:09, 7 July 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10" >Line 10:</td> <td colspan="2" class="diff-lineno">Line 10:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://news.google.com/search?q=ai+Convolution+Autocorrelation+Cross-Correlation ...Google News]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://news.google.com/search?q=ai+Convolution+Autocorrelation+Cross-Correlation ...Google News]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://www.bing.com/news/search?q=ai+Convolution+Autocorrelation+Cross-Correlation&amp;qft=interval%3d%228%22 ...Bing News]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[https://www.bing.com/news/search?q=ai+Convolution+Autocorrelation+Cross-Correlation&amp;qft=interval%3d%228%22 ...Bing News]</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Causation vs. Correlation]] ... 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BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=24502&oldid=prev 2023-03-28T11:34:36Z

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BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=23686&oldid=prev 2023-03-19T17:52:43Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 17:52, 19 March 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5" >Line 5:</td> <td colspan="2" class="diff-lineno">Line 5:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|description=Helpful resources for your journey with artificial intelligence; videos, articles, techniques, courses, profiles, and tools &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; 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BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=23685&oldid=prev 2023-03-19T17:48:59Z

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BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=9166&oldid=prev 2019-07-27T18:42:31Z

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BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=9164&oldid=prev 2019-07-27T18:37:23Z

<p>BPeat moved page <a href="/index.php?title=Convolution_vs._Cross-Correlation_vs._Autocorrelation&amp;action=edit&amp;redlink=1" class="new" title="Convolution vs. Cross-Correlation vs. Autocorrelation (page does not exist)">Convolution vs. Cross-Correlation vs. Autocorrelation</a> to <a href="/index.php/Convolution_vs._Cross-Correlation_(Autocorrelation)" title="Convolution vs. Cross-Correlation (Autocorrelation)">Convolution vs. Cross-Correlation (Autocorrelation)</a> without leaving a redirect</p> <table class="diff diff-contentalign-left" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:37, 27 July 2019</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=9163&oldid=prev 2019-07-27T18:36:48Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:36, 27 July 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l38" >Line 38:</td> <td colspan="2" class="diff-lineno">Line 38:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>http://i.stack.imgur.com/nGZQ1.png</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>http://i.stack.imgur.com/nGZQ1.png</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;youtube&gt;<del class="diffchange diffchange-inline">ek9jwRA2Jio</del>&lt;/youtube&gt;</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;youtube&gt;<ins class="diffchange diffchange-inline">MQm6ZP1F6ms</ins>&lt;/youtube&gt;</div></td></tr> </table>

BPeat https://primo.ai/index.php?title=Convolution_vs._Cross-Correlation_(Autocorrelation)&diff=9162&oldid=prev 2019-07-27T18:34:43Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:34, 27 July 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9" >Line 9:</td> <td colspan="2" class="diff-lineno">Line 9:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Autocorrelation]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Autocorrelation]]</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [[<del class="diffchange diffchange-inline">Convolution </del>vs. <del class="diffchange diffchange-inline">Cross-</del>Correlation <del class="diffchange diffchange-inline">vs. Autocorrelation</del>]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* [[<ins class="diffchange diffchange-inline">Causation </ins>vs. Correlation]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">One </del>of the <del class="diffchange diffchange-inline">most basic tenants </del>of <del class="diffchange diffchange-inline">statistics </del>is that <del class="diffchange diffchange-inline">correlation does not imply causation</del>. In <del class="diffchange diffchange-inline">turn</del>, a <del class="diffchange diffchange-inline">signal’s predictive power does not necessarily imply </del>in <del class="diffchange diffchange-inline">any way </del>that that signal is <del class="diffchange diffchange-inline">actually related </del>to <del class="diffchange diffchange-inline">or explains </del>the <del class="diffchange diffchange-inline">phenomena being predicted</del>. <del class="diffchange diffchange-inline">This distinction matters when </del>it <del class="diffchange diffchange-inline">comes </del>to <del class="diffchange diffchange-inline">machine learning because many </del>of the <del class="diffchange diffchange-inline">strongest signals these algorithms pick </del>up in <del class="diffchange diffchange-inline">their training </del>data are <del class="diffchange diffchange-inline">not actually related </del>to the thing <del class="diffchange diffchange-inline">being measured</del>. <del class="diffchange diffchange-inline">[http://www</del>.<del class="diffchange diffchange-inline">forbes</del>.<del class="diffchange diffchange-inline">com</del>/<del class="diffchange diffchange-inline">sites/kalevleetaru/2019/01/15</del>/a-<del class="diffchange diffchange-inline">reminder</del>-that-<del class="diffchange diffchange-inline">machine-learning-is-about-correlations-</del>not<del class="diffchange diffchange-inline">-causation</del>/<del class="diffchange diffchange-inline">#2ca509766161 A Reminder That Machine Learning Is About Correlations Not Causation | Kalev Leetaru - Forbes]</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">There is a lot of subtlety between the meanings </ins>of <ins class="diffchange diffchange-inline">convolution and correlation. Both belong to </ins>the <ins class="diffchange diffchange-inline">broader idea </ins>of <ins class="diffchange diffchange-inline">inner products and projections in linear algebra, i.e. projecting one vector onto another to determine how &quot;strong&quot; it </ins>is <ins class="diffchange diffchange-inline">in the direction of the latter.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">This idea extends into the field of neural networks, where we project a data sample onto each row of a matrix, to determine how well it &quot;fits&quot; </ins>that <ins class="diffchange diffchange-inline">row. Each row represents a certain class of objects. For example, each row could classify a letter in the alphabet for handwriting recognition. It&#039;s common to refer to each row as a neuron, but it could also be called a matched filter</ins>.</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In <ins class="diffchange diffchange-inline">essence, we&#039;re measuring how similar two things are, or trying to find a specific feature in something</ins>, <ins class="diffchange diffchange-inline">e.g. </ins>a <ins class="diffchange diffchange-inline">signal or image. For example, when you convolve a signal with a bandpass filter, you&#039;re trying to find out what content it has in that band. When you correlate a signal with a sinusoid, e.g. the DFT, you&#039;re looking for the strength of the sinusoid&#039;s frequency in the signal. Note that </ins>in <ins class="diffchange diffchange-inline">the latter case, the correlation doesn&#039;t slide, but you&#039;re still &quot;correlating&quot; two things. You&#039;re using an inner product to project the signal onto the sinusoid.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">So then, what&#039;s the difference? Well, consider </ins>that <ins class="diffchange diffchange-inline">with convolution the signal is backwards with respect to the filter. With a time-varying signal, this has the effect that the data is correlated in the order it enters the filter. For a moment, let&#039;s define correlation simply as a dot product, i.e. projecting one thing onto another. So, at the start, we&#039;re correlating the first part of the signal with the first part of the filter. As the signal continues through the filter, the correlation becomes more complete. Note </ins>that <ins class="diffchange diffchange-inline">each element in the </ins>signal is <ins class="diffchange diffchange-inline">only multiplied with the element of the filter it&#039;s &quot;touching&quot; at that point in time.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">So then, with convolution, we&#039;re correlating in a sense, but we&#039;re also trying </ins>to <ins class="diffchange diffchange-inline">preserve the order in time that changes occur as the signal interacts with </ins>the <ins class="diffchange diffchange-inline">system</ins>. <ins class="diffchange diffchange-inline">If the filter is symmetrical, however, as it often is, </ins>it <ins class="diffchange diffchange-inline">doesn&#039;t actually matter. Convolution and correlation will yield the same results.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">With correlation, we&#039;re just comparing two signals, and not trying </ins>to <ins class="diffchange diffchange-inline">preserve an order </ins>of <ins class="diffchange diffchange-inline">events. To compare them, we want them facing in </ins>the <ins class="diffchange diffchange-inline">same direction, i.e. to line </ins>up<ins class="diffchange diffchange-inline">. We slide one signal over the other so we can test their similarity </ins>in <ins class="diffchange diffchange-inline">each time window, in case they&#039;re out of phase with each other or we&#039;re looking for a smaller signal in a larger one.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">In image processing, things are a little different. We don&#039;t care about time. Convolution still has some useful mathematical properties, though. However, if you&#039;re trying to match parts of a larger image to a smaller one (i.e. matched filtering), you won&#039;t want to flip it because then the features won&#039;t line up. Unless, of course, the filter is symmetrical. In image processing, correlation and convolution are sometimes used interchangeably, particularly with neural nets. Obviously, time is still relevant if the image is an abstract representation of 2-dimensional </ins>data<ins class="diffchange diffchange-inline">, where one dimension is time - e.g. spectrogram.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">So in summary, both correlation and convolution </ins>are <ins class="diffchange diffchange-inline">sliding inner products, used to project one thing onto another as they vary over space or time. Convolution is used when order is important, and is typically used </ins>to <ins class="diffchange diffchange-inline">transform </ins>the <ins class="diffchange diffchange-inline">data. Correlation is typically used to find a smaller thing inside of a larger </ins>thing<ins class="diffchange diffchange-inline">, i</ins>.<ins class="diffchange diffchange-inline">e</ins>. <ins class="diffchange diffchange-inline">to match</ins>. <ins class="diffchange diffchange-inline">If at least of one of the two &quot;things&quot; is symmetrical, then it doesn&#039;t matter which you use. orodbhen on Stack Exchange</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* For statisticians, a correlation is a value that measures how close two variables are </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* Use the convolution to get output</ins>/<ins class="diffchange diffchange-inline">result of a system which have two blocks</ins>/<ins class="diffchange diffchange-inline">signals and they are directly next to each other (in series) in the time domain.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* If you are performing </ins>a <ins class="diffchange diffchange-inline">linear, time</ins>-<ins class="diffchange diffchange-inline">invariant filtering operation, you convolve the signal with the system&#039;s impulse response.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* If you are &quot;measuring the similarity&quot; between two signals, then you cross</ins>-<ins class="diffchange diffchange-inline">correlate them.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* Note </ins>that <ins class="diffchange diffchange-inline">when the signals involved are symmetric, convolution and cross</ins>-<ins class="diffchange diffchange-inline">correlation become the same operation </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* be careful </ins>not <ins class="diffchange diffchange-inline">to confuse correlation, covariance, and correlation coefficient. </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">http://i.stack.imgur.com</ins>/<ins class="diffchange diffchange-inline">nGZQ1.png</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;youtube&gt;ek9jwRA2Jio&lt;/youtube&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;youtube&gt;ek9jwRA2Jio&lt;/youtube&gt;</div></td></tr> </table>

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