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Vectors

A vector is a 1-D array of numbers with magnitude and direction.

Vectors

A vector is an ordered list of numbers. In ML each example is a feature vector: [height, weight, age]. In NumPy it is a one-dimensional array; addition and scalar multiplication are element-wise:

u = np.array([1, 2, 3])
v = np.array([4, 5, 6])
print(u + v)       # [5 7 9]
print(2 * u)       # [2 4 6]

The length (norm) of a vector is found with np.linalg.norm(u): √(1² + 2² + 3²) ≈ 3.742.

Dot product

The dot product of two vectors is the sum of the products of corresponding elements. That is exactly a linear model's prediction: weights · features + intercept.

w = np.array([0.5, 2.0])
x = np.array([4, 3])
print(np.dot(w, x))   # 0.5*4 + 2.0*3 = 8.0
print(w @ x)          # the same

The dot product also measures how much two vectors point the same way; for perpendicular vectors the result is 0.

Practice Linear prediction

The weight vector w, feature vector x and intercept b are given. Compute the prediction with w @ x + b and print it.

Starter code

model.py
import numpy as np

w = np.array([2.0, -1.0, 0.5])
x = np.array([3, 4, 10])
b = 1.5

# buraya yaz

Sample solution

model.py
import numpy as np

w = np.array([2.0, -1.0, 0.5])
x = np.array([3, 4, 10])
b = 1.5

print(w @ x + b)

Expected output

8.5

Questions and answers

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

1 What is <code>np.linalg.norm([3, 4])</code>?

  • 5.0 Correct answer
  • 7.0
  • 25.0
  • 12.0

Explanation: ��(3² + 4²) = √25 = 5.

2 Take the dot product of the two vectors.

Question 
skor = np.____(w, x)
Answer 
skor = np.dot(w, x)

Explanation: np.dot or the @ operator gives the dot product; * is element-wise multiplication.

3 Match the operations (u = [1, 2], v = [3, 4]).

Term Meaning
u + v [4 6]
u * v [3 8]
u @ v 11
2 * u [2 4]

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