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Iterative Clustering
i-th cluster
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j-th cluster
1-st cluster
2-nd cluster
J_e = \displaystyle \sum_{j=1}^c J_j
J_1 = \displaystyle \sum_{\mathbf{x} \in \mathcal{D}_1} \Vert \mathbf{x} – \mathbf{m}_1 \Vert^2
J_2 = \displaystyle \sum_{\mathbf{x} \in \mathcal{D}_2} \Vert \mathbf{x} – \mathbf{m}_2 \Vert^2
J_i = \displaystyle \sum_{\mathbf{x} \in \mathcal{D}_i} \Vert \mathbf{x} – \mathbf{m}_i \Vert^2
J_j = \displaystyle \sum_{\mathbf{x} \in \mathcal{D}_j} \Vert \mathbf{x} – \mathbf{m}_j \Vert^2
J_i^* = J_i – \frac{n_i}{n_i – 1} \Vert \hat{\mathbf{x}} – \mathbf{m}_i \Vert^2
J_j^* = J_j + \frac{n_j}{n_j + 1} \Vert \hat{\mathbf{x}} – \mathbf{m}_j \Vert^2
Iterative Clustering
3-rd cluster
i-th cluster
1-st cluster
2-nd cluster
J_3 = \displaystyle \sum_{\mathbf{x} \in \mathcal{D}_3} \Vert \mathbf{x} – \mathbf{m}_3 \Vert^2
\hat{\mathbf{x}}
\rho_1 = \frac{n_1}{n_1 + 1} \Vert \hat{\mathbf{x}} – \mathbf{m}_1 \Vert^2
\rho_2 = \frac{n_2}{n_2 + 1} \Vert \hat{\mathbf{x}} – \mathbf{m}_2 \Vert^2
\rho_3 = \frac{n_3}{n_3 + 1} \Vert \hat{\mathbf{x}} – \mathbf{m}_3 \Vert^2
\rho_i = \frac{n_i}{n_i – 1} \Vert \hat{\mathbf{x}} – \mathbf{m}_i \Vert^2
Iterative Optimisation
Pseudo Code: Algorithm for Basic iterative minimum-squared-error clustering
begin initialise n, c, m1, m2, . . ., mc
do randomly select a sample x̂;
i � argmin
kx̂�mi0 k (classify x̂)
if ni 6= 1 (do not destroy a singleton cluster)
compute r j =
kx̂�m jk2 j 6= i
kx̂�m jk2 j = i
, j = 1,2, . . . ,c
k � argmin
r j (find the minimum r j)
transfer x̂ to Dk from Di
recompute Je, mi, mk
until no change in Je in n attempts
return m1, m2, . . ., mc
Table 3: Pseudo Code: Algorithm for basic iterative minimum-squared-error clustering.
Dr H.K. Lam (KCL) Unsupervised Learning & Clustering Pattern Recognition 2017-18 24 / 57
IterativeOptimisationPseudoCode:AlgorithmforBasiciterativeminimum-squared-errorclustering
begininitialisen,c,m
dorandomlyselectasample
k(classify
6=1(donotdestroyasingletoncluster)
,j=1,2,…,c
(findtheminimumr
recomputeJ
untilnochangeinJ
innattempts
Table3:PseudoCode:Algorithmforbasiciterativeminimum-squared-errorclustering.
DrH.K.Lam(KCL)UnsupervisedLearning&ClusteringPatternRecognition2017-1824/57
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