EBU6504_smart_arch_notes/tutorials.md

# Tutorials

## Week1 tutorial

- Calculation: (formulas are given from test paper)
    - $Accuracy = \frac{Correct Classifications}{Total Classification} = \frac{TP + TN}{TP + TN + FP + FN}$
    - $F1 = \frac{2}{recall^{-1} + precision^{-1}} =  \frac{2 \times TP}{2 \times TP + FP + FN}$
- Accuracy vs. F1:
    - Accuracy: TP and TN are more important
    - F1: FP and FN are more important, used for imbalanced classes

## Week2 tutorial

- IQR: difference between the 25% (Q1) and the 75% (Q3) in a dataset
    - The spread of 50% of values
    - Popular method of defining observation:
    - Finding median, Q1, Q3, Upper bound, Lower bound
    - Method: https://www.scribbr.com/statistics/interquartile-range/

## Week 3 tutorial

- K-means clustering:
    - Initialize K
    - Assign random K points to be centroids
    - Assign each data point to closest centroid
    - Calculate the mean, and place a new centroid (doesn't have to be on a
      point) to each cluster
    - Repeat, until centroid doesn't change anymore

## Week 4 tutorial

- Euclidean distance
- Cosine similarity
    - Useful for applications with sparse data, since even if the objects are
      far in euclidean distance, they can still have a small angle between.
        - Word documents (NLP)
        - Market transaction data
        - Recommendation system
        - Image on computer
    - Because 0, 0 data will be ignored
    - Values:
        - Cos close to 1: similar
        - Cos close to 0: orthogonal, not related
        - Cos close to -1: opposite
    - Calculation:
      $Similarity(A,B) = cos(\theta) = \frac{A \cdot B}{||A||\times||b||}$
        - $\theta$ is the angle between vectors
        - $A \dot B$ is the dot product, $A_1 B_1 + A_2 B_2 + ... + A_n B_n$
        - $||A||$ is the magnitude of vector,
          $\sqrt{A^2_1 + A^2_2 + ... + A^2_n}$
    - Calculate the angle with $arccos(\theta)$