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Clustering (K-means Algorithm (Lloyd's Algorithm) (Algorithm (Step 0…
Clustering
K-means Algorithm (Lloyd's Algorithm)
Why
NP Hard
Alternate assumptions
Assume \(\mu_x\) is known
Assume \(r_{nk}\) is known
Algorithm
Step 0
Initialize \(\mu_k\)
Step 1
Assume \(\mu_k\) is known
Assign \(r_{nk}\)
\(r_{nk}\) is assigned if date point is close to cluster's center
\(r_{nk} = argmin_j \mid \mid x_n - \mu_j \mid \mid_2^2\)
Step 3
Assume k is fixed
Look at data points assigned to k
Where is the average of this cluster \(\to\) new \(\mu_k\)
Step 4
Repeat this process until objective function doesn't change
Go to Step 1 if it does change
Properties
Improves each iteration
Intuition
Data points assigned to cluster k should be close to \(\mu_k\) which is its prototype
Steps
Terms
Protype \(\mu_k\)
Center of cluster
Properties
Application
Compresion
Reduce K(Number of clusters) = transformation to smaller dimensions
