Statistical Learning Theory and Applications Lecture 10 Unsupervised Learning Instructor:Quan Wen SCSE@UESTC Fall 2021
Statistical Learning Theory and Applications Lecture 10 Unsupervised Learning Instructor: Quan Wen SCSE@UESTC Fall 2021
Outline (Level 1) DK-Means Clustering Algorithm ②PageRank 1/32
Outline (Level 1) 1 K-Means Clustering Algorithm 2 PageRank 1 / 32
Outline (Level 1) K-Means Clustering Algorithm PageRank 2/32
Outline (Level 1) 1 K-Means Clustering Algorithm 2 PageRank 2 / 32
1.K-Means Clustering Algorithm In the clustering problem,we are given a training set {x(),...x(,x()ER", and want to group the data into a few cohesive"clusters."No labels(are given. The k-means clustering algorithm is as follows: Initialize cluster centroidsE R",j=1,2,...,k,randomly. 2 Repeat until convergence: For each training samplex(),set c0=argmin|lr0-马l2 2 For every cluster centroid i,set ∑l(c0=r0 ∑1I(c0=) } I()is the indicator function. 3/32
1. K-Means Clustering Algorithm ▶ In the clustering problem, we are given a training set {x (1) , . . . , x (m)}, x (i) ∈ R n , and want to group the data into a few cohesive “clusters.” No labels y (i) are given. ▶ The k-means clustering algorithm is as follows: 1 Initialize cluster centroids µj ∈ R n , j = 1, 2, . . . , k, randomly. 2 Repeat until convergence: { 1 For each training sample x (i) , set c (i) = arg min j ∥x (i) − µj∥2 2 For every cluster centroid µj , set µj = Pm i=1 I(c (i) = j)x (i) Pm i=1 I(c (i) = j) } • I(·) is the indicator function. 3 / 32
Outline (Level 1-2) K-Means Clustering Algorithm 。Explanation Convergence of K-Means o Matrix Modelling of K-Means 4/32
Outline (Level 1-2) 1 K-Means Clustering Algorithm Explanation Convergence of K-Means Matrix Modelling of K-Means 4 / 32