Source Of Summary:

Handout 6 - unsupervised learning.pdf

1. Clustering Algorithms 🧩

• Hierarchical Algorithms: Create a hierarchical decomposition of the set of objects using some criterion while … 🔄
• Partitional Algorithms: Construct various partitions and then evaluate them by some criterion (e.g., k-means, k-medoids) ✅
  • Nonhierarchical: Each instance is placed in exactly one of K nonoverlapping clusters 🐍
  • User Input: Must specify desired number of clusters K in advance ❗

2. Partitional Clustering: k-means 🔍

2.1 Algorithm Steps

1. Decide on k: Choose the number of clusters. 🎯
2. Initialize centers: Randomly (if necessary) pick k cluster centers. 🎲
3. Assign memberships: For each of the N objects, assign to nearest center. 📏
4. Re-estimate centers: Compute new centroids from current memberships. ↺
5. Convergence Check: If no object changed cluster in last iteration, stop; otherwise, go to 3. 🔁

2.2 Objective Function 🎯

• Goal: Minimize

  $$ J = \sum_{i=1}^k \sum_{j=1}^n w_{ij}\,d(x_j, z_i) $$

• Definitions:

  • $w_{ij}$: 1 if object $x_j$ assigned to cluster $i$, else 0. ✅
  • $d(x_j, z_i)$: Distance (Euclidean) between $x_j$ and centroid $z_i$. 📐