The hierarchical agglomerative clustering with Gower index: A methodology for automatic design of OLAP cube in ecological data processing context

    The Hierarchical Agglomerative Clustering with Gower index: a methodology for automatic design of OLAP cube in ecological data processing context Lucile Sautot, Bruno Faivre, Ludovic Journaux, Paul Molin PII: DOI: Reference:

S1574-9541(14)00107-1 doi: 10.1016/j.ecoinf.2014.07.011 ECOINF 505

To appear in:

Ecological Informatics

Received date: Revised date: Accepted date:

29 November 2013 25 July 2014 29 July 2014

Please cite this article as: Sautot, Lucile, Faivre, Bruno, Journaux, Ludovic, Molin, Paul, The Hierarchical Agglomerative Clustering with Gower index: a methodology for automatic design of OLAP cube in ecological data processing context, Ecological Informatics (2014), doi: 10.1016/j.ecoinf.2014.07.011

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AC CE P

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"4* R+*+ *2C" O0.,"/

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&( "#$ "174$ .#)%# /$3/$*$!" "#$ !$. %14%+41"$, #)$/1/%#- )! "#$ ,1"171*$> G#+* "#$ !+27$/ &( 4$=$4* )* 1! $*")21")&! &( "#$ !$$,(+4 2$2&/- "& *1=$ "#$ #)$/1/%#->

SC

G#$ %14%+41")&! ")2$ 1!, "#$ !+27$/ &( 4$=$4* .$/$ 2$1*+/$, 1%%&/,)!: "& "#$ !+27$/ &( )!,)=),+14* 1!, "#$ !+27$/ &( =1/)174$* +*$, "& 7+)4, "#$ #)$/1/%#-> G#$ !+27$/ &( )!3+" ,1"1 )* /$J$%"$, )! "#$*$ ".& 31/12$"$/* 1!, .$ %1! $'3$%" "#1" "#$ )231%" &( "#$*$ 31/12$"$/* )* )!,$3$!,$!" "& "#$ %&23+"$/ %&!K:+/1")&!>

NU

C! "#$ L):+/$ @@ .$ *#&. "#$ !+27$/ &( 4$=$4* 1%%&/,)!: "& "#$ !+27$/ &( )!,)=),+14* 1!, "#$ !+27$/ &( 4$=$4* 1%%&/,)!: "& "#$ !+27$/ &( =1/)174$*> D7&+" "#$*$ :/13#*M .$ !&"$ "#1"H G#$ "#$&/$")%14 2)!)2+2 &( 4$=$4* 1%%&/,)!: "& "#$ !+27$/ &( )!,)=),+14* &7$-* "& 1 4&:1/)"#2)% (+!%")&!

MA

9N$=/&-$M @OPQA>

G#$ !+27$/ &( 4$=$4* 1%%&/,)!: "& "#$ !+27$/ &( )!,)=),+14* )* !$1/ "& "#)* 2)!)2+2H 1! 1*-23"&")% 7$#1=)&/> B- %&!"/1*"M "#$ !+27$/ &( =1/)174$* #1* !& $R$%" &! "#$ !+27$/ &( 4$=$4*>

D

G& 2&,$4 "#$ !+27$/ &( 4$=$4 1%%&/,)!: "& "#$ !+27$/ &( )!,)=),+14*M "#$ ".& 7$*" 2&,$4* 1/$ 1 3&.$/ (+!%")&! &/ 1 4&:1/)"#2)% (+!%")&!> N$*3)"$ "#$ (1%" "#1" "#$ 3&.$/ (+!%")&! #1* 1 %&//$41")&! %&$S%)$!" #):#$/ 9 R!

TE

"#1! "#$ %&//$41")&! %&$S%)$!" &( "#$ 4&:1/)"#2)% (+!%")&! 9 R!

= 0.47AM

= 0.54A

.$ 7$4)$=$ "#1" "#$ 4&:1/)"#2)% (+!%")&! )*

2&/$ /$4$=1!"M 7$%1+*$ .$ 0!&. "#1" "#$ 2)!)2+2 (&44&.* 1 4&:1/)"#2)% (+!%")&!> T&/$&=$/ "#$ 7$*" 2&,$4 (&/ "#$ !+27$/ &( 4$=$4* 1%%&/,)!: "& "#$ !+27$/ &( =1/)174$* )* 1 F+1,/1")% (+!%")&!> B+" "#$

x!

%&$S%)$!" 1!, "#$

x

%&$S%)$!" 1/$ =$/- !$1/ "& 6> U$ %1! $'%$3" "#1" "#$ !+27$/ &( =1/)174$* #1* 1

AC CE P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

=$/- 4)""4$ )231%" &! "#$ !+27$/ &( 4$=$4*> G#$ %&//$41")&! %&$S%)$!" (&/ "#)* 2&,$4 )* =$/- 4&. 9 R!

= 0.02A>

U$ !&"$ "#1" "#$ %&//$41")&! %&$S%)$!"* 1/$ 4&. (&/ $1%# $*")21")&! &( !+27$/ &( 4$=$4*> G#+* "#$ #)$/1/%#)%14 1::4&2$/1")=$ %4+*"$/)!: 3$/(&/2$, .)"# 1 I&.$/ )!,$' 1* ,)*"1!%$ 2$1*+/$2$!" 3/&,+%$* 7)!1/- "/$$* .#&*$ #$):#" ,$3$!,* &( "#$ !+27$/ &( )!,)=),+14*> G#$ 1=$/1:$ #$):#" &( "#$*$ 7)!1/- "/$$* )* =$/!$1/ "#$ 2)!)2+2 #$):#"> G#$ !$$,(+4 2$2&/- +*$, "& /$%&/, "#$ #)$/1/%#- )* *& !$1/ "#$ 2)!)2+2>

@Q

ACCEPTED MANUSCRIPT y = 2,3994x0,2943 R² = 0,5414

y = 2,1701ln(x) - 0,4112 R² = 0,4741

18 16

Height

12 Minimum of height Log. (Height)

10 8

PT

Number of levels

14

6 2 0

20 18 16 14 12 10 8 6 4 2 0

20

40

60

80 100 120 Number of individuals

160

180

200

NU

y = -0,0004x2 + 0,0516x + 9,8333 R² = 0,0247

140

Puissance (Height)

SC

0

RI

4

MA

Height

20

40

60 Number of variables

Poly. (Height)

80

100

120

TE

0

D

Number of levels

!"#$% &&' (%!")* +, *)% )!%$-$.)/ -..+$0!1" *+ 1#23%$ +, !10!4!0#-56 -10 -..+$0!1" *+ 1#23%$ +, 4-$!-35%6

! "#$ %&'()$ *+ ,$ -#., "#$ /01/(10"&.! "&2$ 0//.)3&!' ". "#$ !(24$) .5 &!3&6&3(01- 0!3 "#$ !(24$) .5 60)&041$-7 8$ !."$ "#0"9 :#$ /01/(10"&.! "&2$ 0//.)3&!' ". "#$ !(24$) .5 60)&041$- .4$;- ". 0 1&!$0) 5(!/"&.!7 :#$ /01/(10"&.! "&2$ 0//.)3&!' ". "#$ !(24$) .5 &!3&6&3(01- .4$;- ". 0 <(03)0"&/ 5(!/"&.!7 :#$ /.2=1$"$ 2.3$1> ,#&/# /0! $?=)$-- "#$ /01/(10"&.! "&2$ 0//.)3&!' ". 0 1&!$0) 5(!/"&.! .5 "#$ !(24$) .5 60)&041$0!3 0 <(03)0"&/ 5(!/"&.! .5 "#$ !(24$) .5 &!3&6&3(01-> &-9

AC CE P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

t(v, M ) = b1 M 2 + b2 M + b3 M 2 v + b4 M v + b5 v + b6

@! "#&- 5.)2(10> t &- "#$ $-"&20"$3 /01/(10"&.! "&2$> M &- "#$ !(24$) .5 &!3&6&3(01-> v &- "#$ !(24$) .5 60)&041$0!3 bi ,&"# i &! {1, 2, 3, 4, 5, 6} 0)$ /.$A/&$!"- "#0" 3$=$!3 .! "#$ /.!B'()0"&.! .5 "#$ /.2=("$) ,#&/# =$)5.)2 "#$ #&$)0)/#; /01/(10"&.!7 8$ =$)5.)2 0 -"$=,&-$ 1&!$0) )$')$--&.! ". B? "#$ /.$A/&$!"-7 :#$ /.$A/&$!"-> ,#&/# /0! 4$ -"0"&-/011; /.!-&3$)$3 $<(01 ". C$).> 0)$ )$2.6$37 8$ .4"0&! 0 5.)2(10 1&D$9 t(v, M ) = (b1 + b3 v)M 2 + b2 M + b6

8&"# "#$ /.2=("$)> "#0" ,$ (-$ 5.) "#$ =$)5.)20!/$- "$-"-> ,$ .4"0&! b1 = 1.83?10−3 > b2 = −1.06?10−6 > b3 = 1.51?10−5 0!3 b6 = 1.15 7 :#$ /.))$10"&.! /.$A/&$!" 4$",$$! "#&- 2.3$1 0!3 "#$ 2$0-()$3 /01/(10"&.! "&2$ &- $<(01 ". 99.7%7 ! "#$ %&'()$ *E ,$ -#., "#$ 2$0-()$3 /01/(10"&.! "&2$ 0!3 "#$ 2.3$1 "#0" ,$ -(''$-" 04.6$7 :#$ $-"&20"&.! -#.,- ,$11 "#$ /#0!'$- .5 /01/(10"&.! "&2$ 0//.)3&!' ". "#$ !(24$) .5 &!3&6&3(01- 0!3 "#$ !(24$) .5 60)&041$-7

*F

ACCEPTED MANUSCRIPT Number of individuals 30

50

5 4 3 2 1 0 0

20

40 60 80 Number of variables

10

20

30

50

100

NU

Time (s)

20

100

SC

Number of variables

30

PT

20

RI

Time (s)

10

10

MA

0 0

20

40 60 80 Number of individuals

100

23

18

13

AC CE P

TE

D

!"#$% &'( )*+,#+*-!./ -!0% *,,.$1!/" -. -2% /#03%$ .4 !/1!5!1#*+6 */1 -2% /#03%$ .4 5*$!*3+%6

Calculation time (s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

measured data

model 8

3

-2

10 20 30 50 100 10 20 30 50 100 10 20 30 50 100 10 20 30 50 100 10 20 30 50 100

10

20

30

50

100

Number of variables (first row) & number of individuals (second row)

!"#$% &7( )*+,#+*-!./ -!0% *,,.$1!/" -. /#03%$ .4 5*$!*3+%6 89$6- $.: .4 ; *
ACCEPTED MANUSCRIPT !"#" $"%&'%()*+" ,"#,# !)-" .""* $"%&'%("/ '* ,!" &'00'12*3 +'*435%),2'*6 !" +'($5,"% !)# ) 7*,"0! 8'%"" 9:5' $%'+"##'% )*/ ;<' =>?@ !" A$"%),2*3 BC#,"( DABE 2# ) F2*/'1# GH I9J.2, D # ?2+%'#'&, 8'%$'%),2'*E@ !" $%',',C$" %5*# '* ,!" #'&,1)%" ?> K>L ! 9MNN D# ?),!F'%O#E@

PT

!"#$""!%&

SC

RI

!"#$""!%& '(%$) )*+ ",")+- )*') .+ *'/+ 01%0%"+2 7* ,!2# $)%,H 1" /2#+5## ).'5, ,!" #C#,"( ,!), 2# $%'$'#"/ )*/ 1" #533"#, $"%#$"+,2-"# ,' 2($%'-" ,!" $%',',C$"@ P2%#,H 1" /2#+5## ).'5, ,!" +05#,"%2*3 (",!'/@ B"+'*/0CH 1" /2#+5## ).'5, ,!" 5#" '& ,!" <'1"% 2*/"Q@ !2%/0CH 1" /2#+5## ).'5, ) $"%#$"+,2-" '& +05#,"% +!)%)+,"%2R),2'*@

D

MA

NU

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

TE

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

AC CE P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

N^

ACCEPTED MANUSCRIPT

MA

NU

SC

RI

PT

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

p

D

0,30

significance level of p

TE

0,25

AC CE P

0,20

0,15

0,10

0,05

qualitative

!"#$% &'( )*+,-#%. /0 .1,1!.1!2,- 1%.1. 0/$ %,23 +,$!,4-%5 63!23 ,$% #.%7 1/ 4#!-7 13% 3!%$,$238

!

VALI

SALI

quantitative

URBA

PRAI

ROCH

PENT

NLIN

NMIL

MIAQ

LDIV

LARV

LARI

LARR

LARB

IURB

HARI

HMAX

FORP

FORB

DVIL

DFOR

ALTI

CULT

SUBS

VEAQ

GRVL

STRAT

FRAG

CONF

0,00 COUR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

RI SC NU

!"#$% &'( )*+#%, -. /0% 1*2!1#1 0%!"0/ -. $!3*$!*4 .-$%,/ 56789: !4 1%/%$,; *<<-$=!4" /- /0% <+#,/%$!4" $%,#+/,

MA

!"#$""!%& '(%$) )*+ ",")+- .+/0%/-'&#+"

! "#$% &'(") *+ ,$%-.%% '/0." "#+ &+(10(2'!-+% 01 "#+ %3%"+2 "#'" $% &(0&0%+, '!, *+ %.44+%" &+(%&+-"$5+% "0 $2&(05+ "#+ &(0"0"3&+ &+(10(2'!-+%6

! 1'-") *+ #'5+ 2',+ -#0$-+% '/0." "#+ ,'"' 2$!$!4 2+"#0,) *#$-# $% .%+,

"0 -'7-.7'"+ "#+ !+* #$+('(-#36 8." "#+%+ -#0$-+% #'5+ ' %"(0!4 $2&'-" 0! "#+ -'7-.7'"$0! "$2+ 01 ' !+* #$+('(-#36 9$(%") "#+ #$+('(-#$-'7 '44702+('"$5+ -7.%"+($!4 &+(2$"% "0 0/"'$! ' -02&7+"+ #$+('(-#3 01 "#+ ,'"'6 8." *+ -'!

D

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