Outline (Level 1-2) K-Means Clustering Algorithm Explanation Convergence of K-Means Matrix Modelling of K-Means 10/32
Outline (Level 1-2) 1 K-Means Clustering Algorithm Explanation Convergence of K-Means Matrix Modelling of K-Means 10 / 32
1.3.Matrix Modelling of K-Means Let cluster center matrix be HE RxP,data matrix be A E R"xp,define the distortion function W as: mS,S2,…,S用=∑∑la-h i=1 alES where h∈Rlxp,a'∈RIXP are rows of matrix H and A S;stands for the clustering result. Represent the cluster of af as one-hotE Rixk: {收 11/32
1.3. Matrix Modelling of K-Means ▶ Let cluster center matrix be H ∈ R k×p , data matrix be A ∈ R n×p , define the distortion function Wb as: Wb (S1, S2, · · · , Sk , H) = X k i=1 X a T∈Si a T − h T i 2 where h T i ∈ R 1×p , a T ∈ R 1×p are rows of matrix H and A Si stands for the clustering result. ▶ Represent the cluster of a T i as one-hot ϕ T i ∈ R 1×k : ϕ T i j = ( 1, a T i ∈ Sj , 0, a T i ∈/ Sj , 11 / 32