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AI & Data Mining/Week 4/Lecture 7 - Nearest Neighbor.md

@@ -12,6 +12,7 @@
 # $a_i = \frac{v_i - minv_i}{maxv_i - minv_i}$
 
 Where:
+
 - $a_i$ is normalised value for attribute $i$
 - $v_i$ is the current value for attribute $i$
 - $maxv_i$ is largest value of attribute $i$
@@ -19,8 +20,10 @@ Where:
 
 ## Example
 
- # $maxv_{humidity} = 96$
+# $maxv_{humidity} = 96$
+
 # $minv_{humidity} = 65$
+
 # $v_{humidity} = 80.5$
 
 # $a_i = \frac{80.5-65}{96-55} = \frac{15.5}{31} = 0.5$
@@ -28,8 +31,11 @@ Where:
 ## Example (Transport Dataset)
 
 # $maxv_{doors} = 5$
+
 # $minv_{doors} = 2$
+
 # $v_{doors} = 3$
+
 # $a_i = \frac{3-2}{5-2} = \frac{1}{3}$
 
 # Nearest Neighbor Applied (Transport Dataset)
@@ -39,14 +45,18 @@ Where:
 - Right most column shows euclidean distances between each vehicle and new vehicle
 - New vehicle is closest to the 1st example, a taxi, NN predicts taxi
 ![](Pasted%20image%2020241010133818.png)
+
 # $vmin_{doors} = 2$
+
 # $vmax_{doors} = 5$
+
 # $vmin_{seats} = 7$
+
 # $vmax_{seats} = 65$
 
 # Missing Values
 
-## Missing Nominal Values 
+## Missing Nominal Values
 
 - Assume missing feature is maximally different from any other value
 - Distance is:
@@ -72,7 +82,7 @@ Where:
 - Number of seats of one example = 16
 - Normalised = 9/58
 - One missing
-- 1 - 9/58  = 49/58
+- 1 - 9/58 = 49/58
 
 ## Normalised Transport Data with Missing Values
 
@@ -85,13 +95,13 @@ Where:
 
 ## Euclidean Distance
 
-# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + ... + (a_n-a_n')^2}$
+# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + … + (a_n-a_n')^2}$
 
 Where $a$ and $a'$ are two examples with $n$ attributes and $a'$ is the value of attribute $i$ for $a$
 
 ## Manhattan Distance
 
-# $|a_1-a_1'|+|a_2-a_2'|+...+|a_n-a_n'|$
+# $|a_1-a_1'|+|a_2-a_2'|+…+|a_n-a_n'|$
 
 Vertical bar means absolute value
 Negative becomes positive
@@ -109,4 +119,3 @@ Euclidean distance is generally a good compromise
 - Does not detect noise
 	- Use k-NN, get k closest examples and take majority vote on solutions
 ![](Pasted%20image%2020241011131542.png)
-

AI & Data Mining/Week 4/Tutorial 4 - Nearest Neighbor.md

@@ -1,18 +1,21 @@
-
 ![](Pasted%20image%2020241011131844.png)
 
 ## Normalisation Equation
-# $a_i = \frac{v_i - minv_i}{maxv_i - minv_i}$
-## Euclidean Distance Equation
-# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + ... + (a_n-a_n')^2}$
 
+# $a_i = \frac{v_i - minv_i}{maxv_i - minv_i}$
+
+## Euclidean Distance Equation
+
+# $\sqrt{(a_1-a_1')^2) + (a_2-a_2')^2 + … + (a_n-a_n')^2}$
 
 # $vmax_{temp} = 85$
+
 # $vmin_{temp} = 64$
 
 # $a_{temp} = \frac{v_{temp} - 64}{21}$
 
 # $vmax_{humidity} = 96$
+
 # $vmin_{humidity} = 65$
 
 # $a_{humidity} = \frac{v_{humidity} - 65}{31}$

AI & Data Mining/Week 4/Workshop 4 - Nearest Neighbor.md

@@ -39,4 +39,4 @@ Root mean squared error                  0.3409
 Relative absolute error                 90.9091 %
 Root relative squared error             90.9091 %
 Total Number of Instances                2
-```
+```