Thread:Talk:DrussGT/Understanding DrussGT/Reason behind using Manhattan distance/reply (6)

From RoboWiki
(Difference between revisions)
Jump to: navigation, search
 
m
 
Line 11: Line 11:
 
[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)
 
[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)
  
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.
+
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.

Latest revision as of 17:05, 28 August 2018

Suppose there are 3 data points:

1 reference data point:

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

And 2 data points in the database:

[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)

[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)

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.

Personal tools