机器学习笔记 ---- K-Means Algorithm

版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/sinat_35406909/article/details/82291094

1. K-Means Algorithm

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

2. Obtimization Objective of K-Means

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

$$min_{c,\mu} \quad J(c,\mu)=\sum (x^{(i)}-\mu_{c_{(i)}})^2$$

3. Random Initialization

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

4. Choose the Number of Clusters

Elbow method / Depending on later purpose