How Manhattan Distance Works in KNN Machine Learning Algorithms

Manhattan Distance in KNN (Super Simple Guide)

📚 Table of Contents

• What is KNN?
• Why Distance Matters
• What is Manhattan Distance?
• Formula
• Step-by-Step Example
• Manhattan Distance in KNN
• Code Example
• CLI Output
• When to Use It
• Key Takeaways
• Related Articles

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📖 What is KNN?

K-Nearest Neighbors (KNN) is a simple machine learning algorithm.

💡 Idea: Find the closest points → use them to predict

If most nearby points belong to Class A → new point is also Class A.

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📏 Why Distance Matters

KNN works completely based on distance.

💡 No distance → no KNN Distance decides “who is closest”

Different distance methods can give different results.

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🏙 What is Manhattan Distance?

Manhattan Distance measures distance by moving only in straight lines.

No diagonal movement allowed.

Think of moving in a city:

• Go left/right
• Go up/down
• No shortcuts

💡 Like walking on roads, not flying across buildings

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📐 Formula

Distance = sum of absolute differences

Distance = |x2 - x1| + |y2 - y1|

Distance should always be positive.

Absolute value removes negative signs.

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📊 Step-by-Step Example

Point A = (3, 5) Point B = (1, 9)

1. |3 - 1| = 2
2. |5 - 9| = 4
3. Total = 2 + 4 = 6

💡 Final Distance = 6

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🤖 Manhattan Distance in KNN

Now let’s use this inside KNN.

New Point C = (2, 7)

• X (1,5) → Class 1
• Y (3,8) → Class 2
• Z (4,6) → Class 1

C → X = 3 C → Y = 2 C → Z = 3

Closest = Y

If k = 2 → choose 2 closest → majority wins.

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💻 Code Example

from sklearn.neighbors import KNeighborsClassifier

X = [[1,5],[3,8],[4,6]]
y = [1,2,1]

model = KNeighborsClassifier(n_neighbors=2, metric='manhattan')
model.fit(X, y)

print(model.predict([[2,7]]))

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🖥 CLI Output

[1]

Prediction = Class 1

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📌 When to Use Manhattan Distance

• Grid-based movement (maps, city routes)
• When diagonal movement doesn’t make sense
• High-dimensional data (sometimes better than Euclidean)

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🎯 Key Takeaways

✔ KNN depends on distance ✔ Manhattan = straight-line movement only ✔ Easy to compute ✔ Works well for grid-like data

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📚 Related Articles

• Gini Index
• Hamming Distance
• Linear Regression
• fit() Function
• Parameter Tuning

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🚀 Final Thought

Manhattan Distance is simple but powerful. It teaches an important idea: “How you measure distance changes your result.”