机器学习笔记 ---- K-Means Algorithm

1. K-Means Algorithm

• Randomly choose x$x$ points as centroids, i-th is μi${\mu }_i$
• Divide all points into x$x$ groups by determining the minimum distance they have from all x$x$ centroids
• Change the centroids into the average of each groups
• Repeat until all centroids do not change

2. Obtimization Objective of K-Means

Let c(i)$c_{(i)}$ denote the group i-th point belongs to, then our task is

minc,μJ(c,μ)=∑(x(i)−μc(i))2$$mi{n}_{c,\mu }J(c,\mu )=\sum (x^{(i)}-{\mu }_{c_{(i)}}{)}^2$$

3. Random Initialization

Randomly pick k$k$ examples in which k$k$ is the number of centroids
May be stuck in local optima: Init and Run K-Means for many times, pick the solution with lowest J$J$

4. Choose the Number of Clusters

Elbow method / Depending on later purpose