Understanding KNN with a Simple Example

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The K-Nearest Neighbors (KNN) algorithm is one of the simplest yet most effective classification methods in machine learning. It classifies a new data point based on the majority label of its K nearest neighbors. Let’s analyze the given code snippet.

The Code

from sklearn.neighbors import KNeighborsClassifier  

X_train = [[1, 50], [2, 60], [3, 70], [4, 80]]  
y_train = [0, 0, 1, 1]  

knn = KNeighborsClassifier(n_neighbors=3)  
knn.fit(X_train, y_train)  

X_test = [[2.5, 64]]  
print(knn.predict(X_test))

Step 1: Training Data

We have 4 training samples:

Feature (x1, x2) Label
(1, 50) 0
(2, 60) 0
(3, 70) 1
(4, 80) 1

So the dataset is well-balanced:

  • Class 0 → First two points

  • Class 1 → Last two points

Step 2: Test Point

We want to classify:

Xtest=(2.5,64)X_{test} = (2.5, 64)

Step 3: Compute Distances

We calculate Euclidean distance:

d=(x1−x1t)2+(x2−x2t)2d = \sqrt{(x_1 - x_{1t})^2 + (x_2 - x_{2t})^2}

  • Distance to (1, 50):
    (1−2.5)2+(50−64)2=2.25+196=198.25≈14.09\sqrt{(1-2.5)^2 + (50-64)^2} = \sqrt{2.25 + 196} = \sqrt{198.25} \approx 14.09

  • Distance to (2, 60):
    (2−2.5)2+(60−64)2=0.25+16=16.25≈4.03\sqrt{(2-2.5)^2 + (60-64)^2} = \sqrt{0.25 + 16} = \sqrt{16.25} \approx 4.03

  • Distance to (3, 70):
    (3−2.5)2+(70−64)2=0.25+36=36.25≈6.02\sqrt{(3-2.5)^2 + (70-64)^2} = \sqrt{0.25 + 36} = \sqrt{36.25} \approx 6.02

  • Distance to (4, 80):
    (4−2.5)2+(80−64)2=2.25+256=258.25≈16.08\sqrt{(4-2.5)^2 + (80-64)^2} = \sqrt{2.25 + 256} = \sqrt{258.25} \approx 16.08

Step 4: Nearest 3 Neighbors

The 3 nearest neighbors are:

  1. (2, 60) → Label 0 → Distance ≈ 4.03

  2. (3, 70) → Label 1 → Distance ≈ 6.02

  3. (1, 50) → Label 0 → Distance ≈ 14.09

Step 5: Majority Vote

Among the 3 neighbors:

  • Class 0 → 2 votes

  • Class 1 → 1 vote

✅ Majority class = 0

Final Output

The code will print:

[0]

Key Takeaways

  • KNN assigns labels based on the majority class of the nearest neighbors.

  • The choice of k (number of neighbors) has a big impact on results.

  • Here, with k=3, the model predicts class 0 for the test point.

✨ This example shows how KNN works step by step with distances and voting.

Would you like me to extend this blog by showing what happens if we change n_neighbors to 1 or 4 to compare the decision?

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