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
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_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