IEEE Systems, Man and Cybernetics Magazine - April 2020 - 18
13 for t = 1 N do
l = )argmin 1 # i # k l " rm t ,
14
Zl = Zl , " t ,
15
16 end
17 Randomly select data near each distinguished point to obtain the n number of samples
18 n i = ^n #u Z iu/N h i = 1, 2,f, k l
19 Draw n i unique random indices from Z i to build sample Z il
i
kl
20 S d = ' Z il
i=1
21 % % Ensemble method to obtain a reliable iVAT image % %
22 Generate Q , down-space data sets " S d,i ,Qi = 1 1 R q from S u 1 R p ^S d " S u h, using random matrices " Ti ,Qi = 1 ! R q # q,
uS uu =uS du = n
23 Compute distance matrices " D d,i ,Qi = 1 from " S d,i ,Qi = 1
24 D n,d ! 0 (Initialize a n # n distance matrix)
25 for t = 1 Q do
W i = NormalizeRows ^D d,i h
26
Vi = 1/2 ^W i + W Ti h
27
28
D n, d = D n, d + V i
29 end
30 Apply VAT/iVAT on D n,d returning D l )n,d , P, c
31 Choose the number of clusters k using image of D l )n,d
32 % % Clustering % %
33 Find indices u of k largest values in MST cut magnitudes c
34 Form the aligned partition, U ) = " u 1 :u 2 - u 1 :f:u k - u k - 1 ,, U S = U )P , 1# i # k
35 Generate down-space data sets " Yi ,Qi = 1 1 R q using RP, uYiu = N
36 for each Yi do
37 Consider sample Y (Si ) 1 R q and Yi - Y (Si ) 1 R q, where uY (Si )u = n, and uYi - Y (Si )u = N - n for each data point, yt ! Yi - Y (Si ) do
38 l = argmin i ! S " dist " yt, y i ,,
(i )
39 U yt = U l
40 end
41 end
(i )
42 U = Mode of labels for each data points U yt
u
d
d
d
i
d
d
d
Algorithm S23. Coclustering VAT (coVAT) [94].
Input : D - m # n rectangular dissimilarity matrix
Output: D ), Dt r , Dt c, and Dt r , c - reordered dissimilarity matrices
1 Build estimates of D r and D c by interpreting the m rows and n columns of D as the feature vector representing m row
objects and n column objects, respectively
Dr D
E
2
D r ,c = ; T
D Dc
3 Apply VAT to D r ,c generating permutation array Pr ,c = " P ^1h, P ^2h f, P ^m + nh,
4 Initialize rc = cc = 0; RP = CP = 0
5 for t ! 1 to m + n do
6 if P ^ t h # m then
7 rc = rc + 1, rc is row component
8 RP ^rc h = P ^ t h, RP are row indices
9 else
10 cc = cc + 1, cc is column component
11 CP ^cc h = P ^ t h - m, CP are column indices
12 end
13 end
14 for p ! 1 to m do
15 for q ! 1 to n do
16 D )p,q = D RP ,CP
17 end
18 end
19 Create I ^D ) h
p
18
q
IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2020
IEEE Systems, Man and Cybernetics Magazine - April 2020
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