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2024-03-28T22:20:08Z
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MN at 17:05, 28 August 2018
2018-08-28T17:05:46Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 17:05, 28 August 2018</td>
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<tr><td class='diff-marker'> </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>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] (Euclidean distance = 4, Squared Euclidean distance = 16, Manhattan distance = 4)</div></td><td class='diff-marker'> </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>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] (Euclidean distance = 4, Squared Euclidean distance = 16, Manhattan distance = 4)</div></td></tr>
<tr><td class='diff-marker'> </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'> </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>If noise changes a single 0 into a 4, it will affect Euclidean distance 4x times higher than Manhattan distance. Euclidean distance will pick the first, Manhattan distance will pick the second<del class="diffchange diffchange-inline">. If you divide all numbers by 10 and keep them all between 0 and 0.4, so they all have less energy than the main dimensions, the result will still be the same</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>If noise changes a single 0 into a 4, it will affect Euclidean distance 4x times higher than Manhattan distance. Euclidean distance will pick the first, Manhattan distance will pick the second.</div></td></tr>
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MN
http://robowiki.net/w/index.php?title=Thread:Talk:DrussGT/Understanding_DrussGT/Reason_behind_using_Manhattan_distance/reply_(6)&diff=54777&oldid=prev
MN: Reply to Reason behind using Manhattan distance
2018-08-28T16:51:37Z
<p>Reply to <a href="/wiki/Thread:Talk:DrussGT/Understanding_DrussGT/Reason_behind_using_Manhattan_distance/reply_(5)" title="Thread:Talk:DrussGT/Understanding DrussGT/Reason behind using Manhattan distance/reply (5)">Reason behind using Manhattan distance</a></p>
<p><b>New page</b></p><div>Suppose there are 3 data points:<br />
<br />
1 reference data point:<br />
<br />
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]<br />
<br />
And 2 data points in the database:<br />
<br />
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (Euclidean distance = 3.87, Squared Euclidean distance = 15, Manhattan distance = 15)<br />
<br />
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] (Euclidean distance = 4, Squared Euclidean distance = 16, Manhattan distance = 4)<br />
<br />
If noise changes a single 0 into a 4, it will affect Euclidean distance 4x times higher than Manhattan distance. Euclidean distance will pick the first, Manhattan distance will pick the second. If you divide all numbers by 10 and keep them all between 0 and 0.4, so they all have less energy than the main dimensions, the result will still be the same.</div>
MN