REPORT

1. What are the common distance metrics used in distance-based classification algorithms?

1. Euclidean Distance: Represents the shortest distance between two vectors.
2. Manhattan Distance: Measures the distance between two points by adding up the absolute differences of their coordinates.
3. Mahalanobis Distance: Represents the distance between a point P and a distribution D by measuring how many standard deviations away P is from the mean of D.

2. What are some real-world applications of distance-based classification algorithms?

• Anomaly and Fraud Detection
• Face Recognition
• Malware Categorization
• Disease Classification

3. Explain various distance metrics.

1. Chebyshev Distance: Also known as Chessboard distance, because in Chess it equals the minimum number of moves needed by a king to go from one square to another.
2. Minkowski Distance: A generalized distance metric which can be modified by substituting the value of ‘p’ to calculate the distance between two points:
   • If p = 1, Manhattan Distance (L1 norm)
   • If p = 2, Euclidean Distance (L2 norm)
   • If p = ∞, Chebyshev Distance (L∞ norm)
3. Cosine Distance: Measures the degree of angle between two vectors (often used for word frequency comparisons in documents). It is used when the magnitude does not matter, but their orientation does.

4. What is the role of cross-validation in model performance?

• Prevents overfitting by testing on different subsets of data.
• K-fold cross-validation: Splits data into k parts, trains on k-1 parts, tests on the remaining, and repeats k times.
• Improves reliability by averaging performance across multiple splits.
• Reduces bias & variance compared to a single train-test split.
• Essential for model selection and hyperparameter tuning.

5. Explain variance and bias in terms of KNN.

• Bias: The error due to overly simplistic assumptions in the model.

  • Small k: Low bias (follows training data closely).
  • Large k: High bias (overly smooth decision boundary).

• Variance: The error due to excessive sensitivity to training data.

  • Small k: High variance (sensitive to noise).
  • Large k: Low variance (more stable but may underfit).

SCREENSHOTS