🧑‍🤝‍🧑 K-Nearest Neighbors (KNN): Effect of Neighbors and Feature Scaling on Decision Boundaries

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🔹 Introduction

K-Nearest Neighbors (KNN) is a simple, non-parametric, and intuitive algorithm used for classification and regression.
Its decision boundaries depend on two main factors:

  1. The number of neighbors (n_neighbors).

  2. The scale of the input features.

Let’s break this down.

🔹 Decision Boundaries and Number of Neighbors

KNN classifies a new sample based on the majority vote of its nearest neighbors.

  • Low n_neighbors (e.g., k = 1, 3):

    • Very sensitive to noise.

    • Decision boundaries are complex and jagged.

    • High variance, low bias.

  • High n_neighbors (e.g., k = 15, 30):

    • Each prediction considers more neighbors.

    • Decision boundaries become smoother.

    • Lower variance, higher bias.

✅ Correct statement:

“KNeighborsClassifier with high values of n_neighbors produces smooth decision boundaries.”

❌ Wrong assumption:

“High values of n_neighbors produce complex decision boundaries.”

🔹 Impact of Feature Scaling

KNN relies on distance metrics (Euclidean, Manhattan, etc.).
If features are on different scales (e.g., age in years vs. income in dollars), the feature with larger values dominates the distance.

👉 Therefore, scaling features (standardization or normalization) is essential.

✅ Correct statement:

“In KNeighborsClassifier, the scale of the features (columns) can impact the decision boundaries.”

🔹 Final Takeaways

  • Small k → More complex, flexible, but noisy decision boundaries.

  • Large k → Smoother, more stable, but less flexible decision boundaries.

  • Always scale features before applying KNN.

👉 Pro Tip: Use cross-validation to tune the best value of k. Typically, odd numbers are preferred in binary classification to avoid ties.

Would you like me to also add a visual plot of decision boundaries for small vs large k (with code in sklearn + matplotlib) to make your blog more engaging?

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