From 8a233ffa970441afd400ad42483a4d37b0b11c2a Mon Sep 17 00:00:00 2001
From: Ryan <ryan@alien.gov>
Date: Wed, 8 Jan 2025 20:20:25 +0800
Subject: [PATCH] Add tutorial

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+# 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:
+      $Similarity(A,B) = cos(\theta) = \frac{A \dot B}{||A||\times||b||}$
+        - $\theta$ 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 $arccos(\theta)$