L21

12/10/26 Mon 15:38pm

KNN / K Nearest Neighbour Algorithm

It is a widely used Machine Learning algorithm for classification and regression tasks.
It works by identifying the K closest data points to the given inputs and making prediction based on the majority class or average value of those neighbours.

Steps to implement KNN

1. Select the value of $K$ for prediction
2. Calculate Euclidian Distance from the stored dataset $\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$
3. Find the K nearest neighbour, the smallest euclidian distance
4. Apply majority voting for classification (or) taking average for regression

Q&A

Question

A transformer predicts oil temperature after 10 minutes using present loading and present oil temperature. The historic data is given below,
using K = 3 Predict the temperature after 10 minutes if the present loading is 75% and present temp is 62 $\text{celsius}$

Point	Loading %	Present Temperature	Temperature after 10 minutes
A	50	50	52
B	60	55	58
C	70	60	64
D	80	65	70
E	90	70	76
Solution:
Calculate the distance using the euclidian distance formula

$$D_A=\sqrt{(75-50{)}^2+(62-50{)}^2}=27.7$$ $$D_B=\sqrt{(75-60{)}^2+(62-55{)}^2}=16.5$$ $$D_C=\sqrt{(75-70{)}^2+(62-60{)}^2}=5.38$$ $$D_D=\sqrt{(75-80{)}^2+(62-65)}=5.83$$ $$D_E=\sqrt{(75-90{)}^2+(62-70{)}^2}=$$

Question

A pump uses two features $X_1$ as vibration and $X_2$ as flow deficit the following historical data is given below.
Classify new observation (4,3) using K=3

Data Point	$X_1$	$X_2$	Condition of Pump
A	1	1	Normal
B	2	1	Normal
C	3	3	Bearing Fault
D	4	4	Bearing Fault
E	1	5	Blockage

Manhattan Distance

$$d(x,y)=\sum _{i=1}^n|x_i-y_i|$$