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Distance measurement

KNN measures distance between examples using Euclidean or Manhattan distance.

Euclidean distance

KNN's default distance is Euclidean distance: the square root of the sum of squared differences, i.e. the straight-line length between two points.

a = np.array([1, 2])
b = np.array([4, 6])
print(np.sqrt(((a - b) ** 2).sum()))   # 5.0
print(np.linalg.norm(a - b))           # 5.0

All features enter the sum with the same weight, so features with different units must be scaled first.

Manhattan and metric

Manhattan distance is the sum of the absolute differences, like walking city blocks. In KNN it is chosen with the metric parameter:

print(np.abs(a - b).sum())   # 7  Manhattan
m = KNeighborsClassifier(n_neighbors=3, metric="manhattan")

With outliers or many dimensions, Manhattan sometimes does better; which one fits is chosen by validation.

Practice Compute the distances

Compute the Euclidean distance from the query point q to every point in X using broadcasting (np.sqrt(((X - q) ** 2).sum(axis=1))) and print it. Then print the index of the nearest point with argmin.

Starter code

model.py
import numpy as np

X = np.array([[0, 0], [3, 4], [1, 1], [6, 8]])
q = np.array([1, 0])

# buraya yaz

Sample solution

model.py
import numpy as np

X = np.array([[0, 0], [3, 4], [1, 1], [6, 8]])
q = np.array([1, 0])

d = np.sqrt(((X - q) ** 2).sum(axis=1))
print(d)
print(d.argmin())

Expected output

[1.         4.47213595 1.         9.43398113]
0

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 What is the Euclidean distance between (0, 0) and (6, 8)?

  • 14
  • 48
  • 100
  • 10 Correct answer

Explanation: ��(6² + 8²) = √100 = 10.

2 Use the Manhattan distance.

Question 
m = KNeighborsClassifier(n_neighbors=3, metric=____)
Answer 
m = KNeighborsClassifier(n_neighbors=3, metric="manhattan")

Explanation: The default metric is minkowski (p=2), i.e. Euclidean.

3 Match the distances with the formulas.

Term Meaning
Euclidean √Σ(a-b)²
Manhattan Σ|a-b|
np.linalg.norm(a-b) Euclidean length
metric= KNN distance choice

All lessons in Beginner

1 What is ML?

  1. What is machine learning?
  2. Supervised and unsupervised
  3. Data and model
  4. Training and testing
  5. Feature and label notation
  6. Summary - ML fundamentals

2 NumPy basics

  1. What is NumPy?
  2. Creating arrays
  3. Array properties
  4. Array indexing
  5. Reshaping arrays
  6. Summary - NumPy basics

3 Pandas basics

  1. What is Pandas?
  2. Creating a DataFrame
  3. Column operations
  4. Selecting and filtering data
  5. Viewing first rows
  6. Summary - Pandas basics

4 Data preprocessing

  1. Data cleaning
  2. Missing data
  3. Data types
  4. Label encoding
  5. Data splitting
  6. Summary - Data preprocessing

5 Statistics basics

  1. Mean
  2. Median
  3. Standard deviation
  4. Variance
  5. Correlation
  6. Summary - Statistics

6 Linear algebra

  1. Vectors
  2. Matrices
  3. Matrix multiplication
  4. Transpose
  5. Identity matrix
  6. Summary - Linear algebra

7 Project: Data analysis

  1. Loading data
  2. Cleaning data
  3. Computing statistics
  4. Printing results

8 Regression

  1. What is regression?
  2. Linear regression
  3. Model training
  4. Prediction
  5. Error measurement
  6. Summary - Regression

9 KNN

  1. What is KNN?
  2. The K parameter
  3. Distance measurement
  4. Classification
  5. Model training
  6. Summary - KNN

10 Decision trees

  1. What is a decision tree?
  2. Splitting criterion
  3. Depth
  4. Classification
  5. Overfitting
  6. Summary - Decision trees

11 Classification

  1. What is classification?
  2. Binary classification
  3. Multi-class
  4. Accuracy
  5. Confusion matrix
  6. Summary - Classification

12 Model evaluation

  1. Train-test split
  2. Accuracy
  3. Precision
  4. Recall
  5. F1 score
  6. Summary - Model evaluation

13 Project: Classification

  1. Preparing data
  2. Training model
  3. Prediction
  4. Evaluation

14 Scaling

  1. What is scaling?
  2. StandardScaler
  3. MinMaxScaler
  4. When to use?
  5. Pipeline
  6. Summary - Scaling

15 Feature engineering

  1. What is a feature?
  2. Feature selection
  3. Feature extraction
  4. Categorical features
  5. Numerical features
  6. Summary - Feature engineering

16 Model selection

  1. What is model selection?
  2. Cross-validation
  3. Grid search
  4. Score comparison
  5. Hyperparameter
  6. Summary - Model selection

17 Project: Regression

  1. Preparing data
  2. Training model
  3. Prediction
  4. Error measurement

18 Metrics

  1. What is a metric?
  2. Accuracy
  3. Precision
  4. Recall
  5. F1 score
  6. Summary - Metrics

19 Data visualization

  1. What is visualization?
  2. Scatter plot
  3. Histogram
  4. Line plot
  5. Box plot
  6. Summary - Visualization

20 Beginner final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4