# IEEE Systems, Man and Cybernetics Magazine - April 2020 - 16

```Algorithm S17. LeafNodeRemove.

Algorithm S19. DecInsert.

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
i -  Position of leaf node x p in Pn
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

Input : D l)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
1	Input-Output: A, B, E, Pn - 1, d n - 1, Fn - 1, G, H

1	Initialize Pn -1, Fn -1, d n -1, and D n) -1
2	Pn - 1 = Pn
3	Fn - 1 = Fn
4	d n - 1 = d n
5	D )n - 1 = D )n
6	Delete the elements corresponding to x p
7	delete Pn - 1
8	delete Fn - 1
9	K = arg ^Fn - 1 2 i h
10	 Fn - 1 = Fn - 1 - 1
11	 delete d n - 1
12	 delete i th row and i th column of D )n -1
i

i

K

K

i-1

Algorithm S18. SpecialInsert.
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

1	Input-Output: A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, J
h
2	 z = min ^D )n
3	^ j, k h = argmin ^D )n
4	w = A j
5	v = arg ^Pn - 1 = G k h
6	Pn - 1 = " Pn - 1,w ,
7	d n - 1 = " d n - 1, z ,
8	Fn - 1 = " Fn - 1,v ,
9	G = " G, Pos ^w h,
G, Pos (A)

G, Pos (A)

h

10	 if w ! J then
11		 delete w from A
12		 if w = J 1 then
C = LongestSubsequence ^Pn, " Pn - 1, i ,h
13

(algorithm S11)
14
B = Pn \C
15			 while length ^H h 2 length ^B h do
16				 delete H 1
17			 end
18		 end
19		 delete w from J
20	 else
E = " E,w ,
21
22	 end

16

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2020

_ Minimum distance, closest
bb
point index, and MST
`
hb connection index from G1
a
_ Minimum distance,
)
h
z 3 = min ^D n
b
)
hb closest point index,
( j, k) = argmin ^D n
3
`
w3 = A j
b and MST connection
b
index from G3
v 3 = arg (Pn - 1 = E k )
a
z1 = dn
2	w 1 = B 1
v 1 = arg ^Pn - 1 = Pn
Pos (B 1) - 1

H1

Pos (A), Pos (E )

Pos (A), Pos (E )

4	 z = min ^z 1, z 3 h

5	switch z do
6		 case z 1 do
^A B, E, Pn - 1, d n - 1, Fn - 1, G, H h =

7			,
M1^A, B, E, Pn - 1, d n + 1, Fn - 1, G, H, z 1,w 1,v 1 h
8	
(algorithm S12)
9		 end
10		 case z 2 do
^A B, E, Pn - 1, d n - 1, Fn - 1, G, H h =

11			,
M3 ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, z 3,w 3,v 3 h
12	
(algorithm S14)
13		 end
14	 end

Algorithm S20. Decremental iVAT
(dec-iVAT).
Input : D )n - 1 - ^n - 1h # ^n - 1 h  dec-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 p
in Pn
Output: D nl)- 1 - ^n - 1 h # ^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 ,
rm

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

rc

rc

rj

cr

jc

```

# 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
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IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover3
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