IEEE Systems, Man and Cybernetics Magazine - April 2020 - 13
Algorithm S5. Dark Block Extraction [54].
Input : D - n # n dissimilarity matrix
a - minimum cluster size as a fraction of n
Output: k - the number of dark blocks
1 Transform D to Dl with d ij = 1- e -d /v, where v is a
scale parameter obtained by applying Otsu's
-algorithm [184] on D
2 Apply VAT to Dl to generate RDI I (1)
3 Threshold I (1) using Otsu's algorithm [184] to generate
binary image I (2)
4 Filter I (2) using morphological operator with directional
"line" structuring elements of size l 1 = an to obtain
filtered binary image I (3)
5 Perform distance transformation on I (3) to obtain a
new grayscale image I (4) and scale the pixel values
to [0, 1]
6 Project pixel values of I (4) onto the main diagonal
axis of the image to form a projection signal H (1)
7 Smooth H (1) using simple average filter h of length
l 2 = 2an to obtain the filtered signal H (2)
8 Compute first-order derivative of H (2) to obtain
signal H (3)
9 Find peak position p i (positive-to-negative zero-crossing
points) and valley position (negative-to-positive zerocrossing points) in H (3)
10 Select major peaks by removing minor peaks and
valleys using a filter size of length l 3 = 2an
11 k = number of major peaks
ij
16 for t ! 1 to kl do
n #|S t|
m
nt = c
17
N
18 Draw n t unique random indices Su t from S t
19 end
kl
20 Su = ' Su t ; D n = dist " x Su , x Su ,
t=1
21 Apply VAT to D n returning D )n, P and d
22 Apply iVAT to D )n returning D l)n
Algorithm S7. Clustering Using
Scalable iVAT (clusiVAT) [79]-[81].
Input : X = " x 1, x 2,f, x N , - N p -dimensional data points
k l - overestimate of actual number of clusters
n - approximating sample size
Output: D l)n - n # n iVAT reordered dissimilarity matrix of D n
u : X " " 1, 2,f, k , - cluster membership
1 Apply siVAT on X returning D l)n, Su, P, d
2 Choose the number of clusters k using siVAT image
3 t = argmax d i
1# i # k
4 Form the aligned partition:
5 u ) = " t 1 : t 2 - t 1 :f: t k - t k - 1 ,
6 u Su = u P) ; 1# i # k
7 for xt ! Xt = X - X Su do
8 j = argmin " dist " x st , x i ,,
Pi
i
i ! Su
9 u st = u j
10 end (nearest prototype rule)
Algorithm S6. Asymmetric iVAT [13].
Input : X = " x 1, x 2,f, x N , - N p -dimensional data points
k l - overestimate of actual number of clusters
n - approximating sample size
Output: D l)n - n # n iVAT reordered dissimilarity matrix
of D n
Su - indices of samples in D n
P - VAT reordering indices of D n
d - ordering of MST cut magnitudes
1 Select the indices m of kl distinguished objects
2 m 1 = 1
3 y = " dist " x 1, x 1 ,,f, dist " x 1, x N ,,
4 for t ! 2 to kl do
5 y = ^min " y 1, dist " x m , x 1 ,,f,
6 min " y N , dist " x m , x N ,,h
7 m t = argmax {y j}
t-1
t-1
8 end
1#j#N
9 Group objects in X = " x 1, x 2,f, x N , with their
-nearest distinguished objects
10 S 1 = S 2 = f = S k l = 4
11 for t ! 1 to N do
l = argmin " dist " x m , x t ,,
12
j
1#j#k
Sl = Sl , " t ,
13
14 end
Algorithm S8. InsertPosition.
Input : Pn - VAT reordering indices of D )n
d n - MST cut magnitude order of D )n
Fn - MST connection indices of D )n
V = " v 1,v 2,f,v n , Distance of x n+1 from
" x 1, x 2,f, x N ,
Output: i - insertion position of x n+1
Pn + 1 - initialization of VAT reordering indices of D )n +1
d n + 1 - initialization of MST cut magnitude order
of D )n +1
Fn + 1 - initialization of MST connection indices
of D )n +1
1 Y = VP = " v P ,v P ,f,v P ,
2 i = n + 1
3 j = argmin (V )
n
1
n
4 for t ! 1 to n - 1 do
5 if min ^" Y1,Y2,f,Yt ,h 1 d n then
6 i = t + 1
j = argmin ^" Y1,Y2,f,Yt ,h
7
8 break
9 end
10 end
t
11 Pn + 1 = " Pn , Pn ,f, Pn , n + 1 ,
12 d n + 1 = " d n , d n ,f, d n , min^Y1,Y2,f,Yi -1 h,
13 Fn + 1 = " Fn , Fn ,f, Fn , j ,
1
15 Randomly select data near each distinguished
object to form D n
2
2
1
1
Ap ri l 2020
i-1
2
2
i -2
i-1
IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE
13
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_202310
https://www.nxtbook.com/nxtbooks/ieee/smc_202307
https://www.nxtbook.com/nxtbooks/ieee/smc_202304
https://www.nxtbook.com/nxtbooks/ieee/smc_202301
https://www.nxtbook.com/nxtbooks/ieee/smc_202210
https://www.nxtbook.com/nxtbooks/ieee/smc_202207
https://www.nxtbook.com/nxtbooks/ieee/smc_202204
https://www.nxtbook.com/nxtbooks/ieee/smc_202201
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