# IEEE Systems, Man and Cybernetics Magazine - April 2020 - 15

1	Input-Output: A, B, E, Pn + 1, d n + 1, Fn + 1, G, H
2	Pn + 1 = " Pn + 1,w 2 ,;   d n + 1 = " d n + 1, z 2 ,;   Fn + 1 = " Fn + 1,v 2 ,
3	G = " G, Pos ^w 2 h,

4	if w 2 = A 1 then
5		 C =  LongestSubsequence ^Pn, Pn + 1 h (algorithm S11)
6		 B = Pn \C
7		 while length ^H h 2 length ^B h do
8			 delete H 1
9		 end
10		 E = Pn + 1 \ " n + 1 , \C
11	 else
12		 E = " E,w 2 ,
13	 end
14	 delete w 2 from A

Algorithm S14. Procedure M3.
Input : z 3 -  minimum distance from G3
w 3 -  closest point index from G3
v 3 -  MST connection index from G3
1	Input-Output: A, B, E, Pn + 1, d n + 1, Fn + 1, G, H
2	Pn + 1 = " Pn + 1,w 3 ,;   d n + 1 = " d n + 1, z 3 ,; Fn + 1 = " Fn + 1,v 3 ,
3	G = " G, Pos ^w 3 h,

4	if w 3 = A 1 then
5		 C =  LongestSubsequence ^Pn, Pn + 1 h (algorithm S11)
6		 B = Pn \C
7		 while length ^H h 2 length ^B h do
8			 delete H 1
9		 end
10		 E = Pn + 1 \ " n + 1 , \C
11	 else
12		 E = " E,w 3 ,
13	 end

Algorithm S16. Decremental VAT
(dec-VAT).
Input : D )n - n # n VAT reordered dissimilarity matrix for X n
Pn -  VAT reordering indices of D )n
d n -  MST cut magnitude order of D )n
Fn -  MST connection indices of D )n
x p -  point to remove
Output: D *n - 1 - ^n - 1h # ^n - 1 h  VAT reordered dissimilarity
matrix for X n - 1
Pn - 1 -  VAT reordering indices of D )n -1
d n - 1 - MST cut magnitude order of D )n -1
Fn - 1 - MST connection indices of D )n -1
1	Find the position i of x p in Pn
2	i = arg ^Pn = p h

3	Find the data points ^J h and their indices  ^ I h  in
Pn , that are connected to x p in the MST of D )n
4	I = arg ^Fn = i h; J = Pn
I

5	if J = 4  then
6			^D )n - 1, Pn - 1, d n - 1, Fn - 1 h = LeafNodeRemove ^D )n, Pn,
d n, Fn, i h 
(algorithm S17)
7	else
8			 if i = Pn then
9					 Pn - 1 = " Pn ,; d n - 1 = 4; Fn - 1 = " 1 ,
10					 A = " Pn , Pn ,f, Pn ,
11					 C = " Pn , Pn ,
12					 B = Pn \C
13					 E = 4
14					 G = {2}
15					 H = " Fn , Fn ,f, Fn ,
16					 k = arg ^J = Pn h; delete J k
17			 else
18					 Pn - 1 = " Pn , Pn ,f, Pn ,; d n - 1 = " d n , d n ,f, d n ,;
Fn - 1 = " Fn , Fn ,f, Fn ,
19					 A = " Pn , Pn ,f, Pn ,
20					 C = " Pn , Pn ,f, Pn ,
21					 B = Pn \C
22					 E = 4
23					 G = " 1, 2,f, i - 1 ,
24					 H = " Fn , Fn ,f, Fn ,
25			 end
1

2

3

4

1

2

3

Algorithm S15. Incremental iVAT
(inc-iVAT).
Input : D )n + 1 - ^n + 1h # ^n + 1 h  inc-VAT reordered
-dissimilarity matrix for X n + 1
D nl) - n # n  iVAT dissimilarity matrix for X n
i -  insertion index of the new data point x n+1
in Pn + 1
Output: D nl)+ 1 - ^n + 1h # ^n + 1 h inc-iVAT dissimilarity
matrix for X n + 1
1	 c = " 1, 2,f, i - 1 ,
2	 D nl)+ 1 = D nl )
cc

cc

3	for r ! i to n + 1 do
4		 j = argmin " D )n + 1 ,

4

n

2

1

2

1

i+1

i-1

2

i+1

1

14	 delete w 3 from A

n

i+2

2

i+2

1

2

i-2

i-1

n

i

n

26			 while A ! 4 do
27					 if  B 1 = J 1 then
28						 ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, J h =
SpecialInsert ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, J,
D )n, Pn, d n, Fn h (algorithm S18)

29					 else
30						 ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, h =
DecInsert ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, D n) , Pn,
d n, Fn h 

(algorithm S19)
31					 end
32			 end
33			 D )n - 1 = D )n
34	 end
G, G

rm

1 # m # r-1
)
)
n +1r j
n +1r j

5		 D l = D
6		 c = " 1, 2,f, r - 1 , \ " j ,
7		 D nl)+1 = max {D n) + 1 , D nl)+1 }
8		 D nl)+1 = D nl)+1
9	end
rc

rc

rj

jc

cr

Ap ri l 2020

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE

15

# 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
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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
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IEEE Systems, Man and Cybernetics Magazine - April 2020 - 11
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IEEE Systems, Man and Cybernetics Magazine - April 2020 - 13
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IEEE Systems, Man and Cybernetics Magazine - April 2020 - 15
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IEEE Systems, Man and Cybernetics Magazine - April 2020 - 27
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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
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