# 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

## Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - April 2020

Contents
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover1
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover2
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Contents
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 2
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 3
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 4
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 5
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 6
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 7
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 8
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 9
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 10
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 11
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 12
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 13
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 14
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 15
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 16
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 17
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 18
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 19
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 20
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 21
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 22
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 23
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 24
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 25
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 26
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 27
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 28
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 29
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 30
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 31
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 32
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 33
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 34
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 35
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 36
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 37
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 38
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 39
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 40
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 41
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 42
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 43
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 44
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 45
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 46
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 47
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 48
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 49
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 50
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 51
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 52
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 53
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 54
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 55
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 56
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 57
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 58
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 59
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 60
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover3
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/smc_202110
https://www.nxtbook.com/nxtbooks/ieee/smc_202107
https://www.nxtbook.com/nxtbooks/ieee/smc_202104
https://www.nxtbook.com/nxtbooks/ieee/smc_202101
https://www.nxtbook.com/nxtbooks/ieee/smc_202010
https://www.nxtbook.com/nxtbooks/ieee/smc_202007
https://www.nxtbook.com/nxtbooks/ieee/smc_202004
https://www.nxtbook.com/nxtbooks/ieee/smc_202001
https://www.nxtbook.com/nxtbooks/ieee/smc_201910
https://www.nxtbook.com/nxtbooks/ieee/smc_201907
https://www.nxtbook.com/nxtbooks/ieee/smc_201904
https://www.nxtbook.com/nxtbooks/ieee/smc_201901
https://www.nxtbook.com/nxtbooks/ieee/smc_201810
https://www.nxtbook.com/nxtbooks/ieee/smc_201807
https://www.nxtbook.com/nxtbooks/ieee/smc_201804
https://www.nxtbook.com/nxtbooks/ieee/smc_201801
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1017
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0717
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0417
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0117
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1016
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0716
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0416
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0116
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1015
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0715
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0415
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0115
https://www.nxtbookmedia.com