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KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
h ps://doi.o g/10.1007/s42489-021-00072-5
Dis o ion E ec s inEqual A ea Uni Maps
JochenSchiewe1
Recei ed: 5 Decembe 2020 / Accep ed: 7 Janua y 2021 / Published online: 1 Feb ua y 2021
© The Au ho (s) 2021
Abs ac
Maps ha co ec ly ep esen he geog aphic size and shape o egions, aking in o accoun scaling and gene aliza ion, ha e
he disad an age ha small egions can easily be o e looked o no seen a all. Hence, o some map use asks whe e small
egions a e o impo ance, al e na i e map ypes a e needed. One op ion is he so-called equal a ea uni maps (EAUMs),
whe e e e y enume a ion uni has he same a ea size, possibly also he same basic shape such as squa es o hexagons. The
geome ical dis o ion o EAUMs, howe e , leads o a mo e di icul sea ch o egions as well as a alsi ica ion o opological
ela ionships and spa ial pa e ns. To desc ibe hese dis o ions, a se o analy ical measu es is p oposed. Bu i u ns ou ha
he exp essi eness o hese measu es is a he limi ed. To be e unde s and and o model he in luence o dis o ions, wo
use s udies we e conduc ed. The s udy on he sea ch in EAUMs (also wi h he aim o econs uc he sea ch s a egies o
he use s) e ealed how impo an i is o conside he local opology (e.g. co ne o bo de posi ions o egions) du ing he
gene a ion p ocess. Wi h ega d o pa e n iden i ica ion, i could be shown ha EAUMs signi ican ly inc ease he de ec ion
a e o local ex eme alues. On he o he hand, global la e al g adien s o geos a is ical ho spo s o en ge blu ed o e en
los . As a consequence, a ask-o ien ed selec ion o map ypes and u he de elopmen s a e ecommended.
Keywo ds Equal a ea uni maps· Cho ople h maps· Pa e n iden i ica ion· Usabili y
Ku z assung
Ka en, die un e Beach ung des Maßs abes und de Gene alisie ung die geog aphische G öße und Fo m on Regionen ko -
ek wiede geben, haben den Nach eil, dass kleine Regionen leich übe sehen ode ga nich gesehen we den. Dahe we den
ü einige Ka ennu zungsau gaben, bei denen kleine Regionen on Bedeu ung sind, al e na i e Ka en ypen benö ig . Eine
Op ion sind sogenann e Equal A ea Uni Maps (EAUMs), bei denen jede Einhei dieselbe Flächeng öße und zumeis auch
dieselbe G und o m wie Quad a e ode Hexagone besi z . Die geome ische Ve ze ung on EAUMs üh jedoch zu eine
schwie ige en Suche nach Regionen sowie zu eine Ve älschung opologische Beziehungen und äumliche Mus e . Um
diese Ve ze ungen zu besch eiben, wi d ein Sa z on analy ischen Maßzahlen o geschlagen. Es zeig sich jedoch, dass
die Aussagek a diese Maßzahlen ehe beg enz is . Um den Ein luss on Ve ze ungen besse e s ehen und modellie en
zu können, wu den zwei Anwende s udien du chge üh . Die S udie zu Suche in EAUMs (auch mi dem Ziel, die Such-
s a egien de Benu ze nachzu ollziehen) e gab, wie wich ig es is , die lokale Topologie (z. B. Eck- ode Randposi ionen
on Regionen) wäh end des Gene ie ungsp ozesses zu be ücksich igen. In Bezug au die Iden i ika ion äumliche Mus e
konn e gezeig we den, dass EAUMs die E kennungs a e lokale Ex emwe e signi ikan e höhen. Ande e sei s e schwim-
men globale la e ale G adien en ode geos a is ische Ho Spo s häu ig ode gehen soga e lo en. In olgedessen we den eine
au gabeno ien ie e Auswahl on Ka en ypen sowie wei e e En wicklungen emp ohlen.
Schlüsselwo e Equal A ea Uni Maps· Cho ople henka en · Mus e e kennung· Geb auchs auglichkei
1 In oduc ion
Maps gene ally ollow he p inciple o co ec ly ep esen ing
he geog aphic size and shape o egions, o cou se, unde
conside a ion o scale and gene aliza ion. Howe e , due o
* Jochen Schiewe
jochen.schiew[email p o ec ed]
1 Lab o Geoin o ma ics andGeo isualiza ion (g2lab),
Ha enCi y Uni e si y Hambu g, Henning-Vosche au-Pla z 1,
20457Hambu g, Ge many
72 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
1 3
he he e ogeneous di e ences in he size o he enume a ion
a eas, his o en leads o a e y small egions appea ing so
small ha hey can be o e looked o no seen a all (e.g.
Singapo e is shown in a wo ld map a a scale o 1: 90 million
as an a ea o 0.3mm by 0.5mm). In cho ople h maps, he e
a e also he cogni i ely caused e ec ha la ge egions a e
pe cei ed as mo e dominan , al hough hey ha e he same
colo alue compa ed o he small egions, which leads o
misin e p e a ions and w ong decisions (Slocum e al. 2009).
Empi ical s udies ha e con i med ha he de ec ion a es in
he o de o 60% o global ex eme alues in small a eas
wi hin cho ople h maps a e signi ican ly wo se han hose o
la ge a eas, which a e in he o de o 90% (Schiewe 2019).
As an al e na i e o he ue-scale ep esen a ion, Equal
A ea Uni Maps (EAUMs) ha e gained an inc easing pop-
ula i y in he ecen pas , especially in he news media.1
EAUMs ep esen each enume a ion a ea in he same size
and possibly use uni o m basic shapes (e.g. squa es, ec an-
gles, hexagons, o mul i-hexagons—see Fig.1). Chap e 2
gi es a deepe insigh in o e minology ela ed o EAUMs
and me hods o gene a ing hem.
The ad an age o EAUMs is ha o a a ie y o map use
asks all enume a ion a eas a e shown wi h equal p omi-
nence. This makes i easy o look-up and compa e alues
and o a oid he a ea size-bias. Assuming a ce ain size o
he basic uni s, EAUMs can accommoda e no only one
colo o hachu e o e e y egion, bu also ex , symbols o
small diag ams, which enables he display o mul i a ia e
da a. EAUMs a e also mo i a ing o use because hey ep-
esen an unusual depic ion o egions and p oduce a ce ain
su p ise e ec due o he alse-scale ep esen a ion. I can
also be a gued ha he consis en use o clea shapes such as
squa es o hexagons is aes he ically pleasing.
Looking a he disad an ages, he gene a ion o EAUMs
leads o dis o ions conce ning he dis ances be ween
egional uni s, a ea sizes, shapes and opological ela ion-
ships (such as loss and addi ion o neighbo hoods and mem-
be ships) compa ed o he o iginal geog aphical da a. As
a esul , he sea ch o speci ic egions and he in e p e a-
ion o spa ial dis ibu ions o pa e ns in he o iginal da a
becomes mo e di icul and mo e e o -p one. To desc ibe
he dis o ions in a mo e objec i e and quan i a i e man-
ne , Chap e 3 p esen s selec ed geome ical and opological
measu es. F om his, i can be concluded ha hese meas-
u es show a la ge a ia ion wi hin a map and do no p o-
duce a clea o e all imp ession o dis o ions. Fu he mo e,
he qui e la ge se o analy ical measu es is no sui able o
pu poses such as compa ing map designs o con olling an
EAUM gene a ion algo i hm.
To be e unde s and he ele ance o dis o ions, his
con ibu ion also ollows an empi ical app oach. While o
some map ypes, such as alue-by-a ea maps (Sun and Li
2010), s udies on he e ec s o he dis o ions on he in e -
p e abili y exis , he e is s ill no empi ical e idence o he
cogni i e e ec o EAUMs.
A i s use s udy (Chap e 4) deals wi h he e ec i eness
o he sea ch in EAUMs bu also wi h he de i a ion o ypi-
cal sea ch s a egies ha can be o in e es o con olling he
EAUM gene a ion p ocess. The second s udy (Chap e 5)
ocuses on he iden i ica ion o pa e ns in EAUMs: i s ly,
he hypo hesis is examined ha pa e ns ela ed o indi idual
egions (such as local ex eme alues) a e well ecognized
wi hin EAUMs. The second hypo hesis is ela ed o he iden-
i ica ion o o he pa e ns such as No h–Sou h g adien s o
ho spo s, which is much mo e di icul due o he inhe en
geome ical dis o ions. Chap e 6 summa izes he esul s
o he wo s udies and gi es ecommenda ions o u u e
de elopmen s in he EAUM en i onmen .
Fig. 1 Example o equal a ea
uni maps (EAUMs), composed
o egula g id cells (middle) o
hexagons ( igh ), in compa ison
o o iginal geog aphical egions
(le )
1 Examples o EAUMs in news media [las access Dec 1, 2020]:
NY Times: h ps ://a chi e.ny im es.com/www.ny im es.com/in e
ac i e/2013/06/26/us/sco u s-gay-ma i age.h ml
abc News: h ps :// i e hi y eigh .com/ ea u es/whe e -you -s a e -ge s-
i s-money /
Bloombe g: h ps ://www.bloom be g.com/g aph ics/2015-pace-o -
socia l-chang e/
The Gua dian: h ps ://www. hegu a dia n.com/us-news/ng-in e ac i
e/2014/oc /22/-sp- o in g- igh s-iden i ica ion-how- ien dly-is-you -
s a e .
73KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
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2 Equal A ea Uni Maps
2.1 Te minology
In he ollowing I de ine an equal a ea uni map (EAUM)
as a base map whe e e e y enume a ion uni (geog aphic
en i y) is gi en he same size, possibly also he same shape
(such as squa es, ec angles o hexagons). O e lapping uni s
a e no allowed; howe e , gaps a e possible. The a ange-
men o uni s is done acco ding o one o mo e op imiza ion
c i e ia (e.g. minimizing he posi ional shi o cen oids
be ween geog aphic o iginal and esul ing EAUM).
I should o be no ed ha he e is no common e minology
in li e a u e o his ype o ep esen a ion. One op ion is he
e m “equal a ea ca og am” (B ai h 2015; O dnance Su ey
2020). S ic ly speaking, a ca og am is no app op ia e he e,
since a modi ica ion o shapes and sizes o uni s is no based
on da a alues as de ined by Slocum e al. (2009). On he
o he hand, he e m “equal a ea ca og am” lea es ou he
e m “map”—as Raisz (1934) does, who s a es ha he “ ec-
angula s a is ical ca og ams” in his wo k a e no maps.
I one akes he s ic de ini ion by Hake e al. (2002) in o
accoun , an EAUM does no ul ill he condi ion o a co ec
o hogonal p ojec ion; ins ead, i could be ca ego ized as a
map-alike p oduc . On he o he hand, aking in o accoun
he less s ic de ini ion o he In e na ional Ca og aphic
Associa ion (ICA 2003), i is applicable o use he e m
“map” since he p ima y ele ance o spa ial ela ionships
is s ill gi en.
Some imes, his map ype is associa ed o he e m “ ile
map” (e.g. McNeill and Hale 2017). Howe e , he e is also
ano he (and mo e dominan ) meaning ha ile maps cu
geog aphical space—wi hou explici ly conside ing admin-
is a i e egions—in o egula elemen s o allow as e and
indi idualized access (Pe e son 2012). O he au ho s such
as Epps ein e al. (2015) o Wongsuphasawa (2016) use he
e m “g id map”. This sugges s a egula as e , neglec ing
o he uni ep esen a ions such as hexagons.
Finally, EAUMs should no be con used wi h alue-by-
a ea maps (Den 1999) o a ea ca og ams (Slocum e al.
2009), in which he a eas o each enume a ion uni a e
scaled o sized p opo ionally o an a ibu e alue (e.g.
popula ion).
2.2 Gene a ion o EAUMs
The gene a ion o EAUMs can be iewed as a so-called
assignmen p oblem, which is known om g aph heo y:
gi en is a bipa i e g aph, which consis s o wo subse s wi h
he same numbe o nodes, one pa i ion o he o iginal geo-
g aphic inpu si ua ion and he o he o he ou pu EAUM.
While he nodes ep esen egion cen oids, he edges model
he ac ual neighbo hood o egions. The g aph ma ching is
now a combina o ial op imiza ion p oblem ha looks o a
unique assignmen be ween nodes o he wo pa i ions, in
which he o e all cos s o edge weigh s (e.g. he dis ances
o cen oids) mus be minimized.
The con en ional algo i hm o weigh ed ma chings in
bipa i e g aphs is he Hunga ian me hod, also called he
Kuhn-Munk es algo i hm (Kuhn 1955; Munk es 1957). I
sol es he assignmen p oblem in O(n3) ime (whe e n is he
numbe o nodes). This algo i hm was also used o gene a -
ing map examples o he ollowing s udy.2 The e a e se e al
specialized o ex ended o ms o his algo i hm as well as
o he app oaches such as he simplex me hod (Ba e al.
1977). Howe e , i is beyond he scope o his pape o gi e
a comp ehensi e o e iew o he a ie y o hese me hods.
3 Dis o ions inEAUMs
To enable an objec i e and nume ical desc ip ion o dis-
o ions in EAUMs o absolu e o ela i e compa ison
pu poses, a ious measu es a e p esen ed in he ollowing
(Sec .3.1). These measu es a e hen applied o h ee exam-
ple maps in o de o assess hei exp essi eness (Sec .3.2).
3.1 Measu es
The dis o ion e ec be ween wo maps can be desc ibed
by se e al measu es. Fo example, Nus a and Kobou o
(2016) use he ca ego ies s a is ical accu acy (p ese a-
ion o hema ic alues), con igui y (p esence o o e laps
o gaps), geog aphy (p ese a ion o shape and size), and
opology (especially p ese a ion o neighbo hoods). Alam
e al. (2016) e e o dis o ions o geome y, opology and
complexi y. EAUMs a e no deal wi h in hese publica ions.
Fo ou pu poses, he ollowing geome ical and opological
measu es ha e been de ined:
Geome ical dis o ions:
• Dis ance dis o ion (G_DD): mean alue o all dis ances
be ween egion cen oids in geog aphical and EAUM
map ha co espond o each o he ’s (no malized by
dis ance o longes ex ension o o al map, i.e. ei he in
No h–Sou h o Eas –Wes di ec ion).
• Single enume a ion a ea size a iance (G_SA): s anda d
de ia ion o a ea sizes o geog aphical egions (no mal-
ized by di ision by mean alue o a ea sizes). The la ge
he s anda d de ia ion is, he la ge he dis o ion wi hin
an EAUM (wi h a ea s anda d de ia ion o Ze o) will be.
2 PyEAC so wa e: h ps ://gi la b.com/g2lab /pyeac .
74 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
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• To al enume a ion a ea size a iance (G_TA): di e ence
o o al a eas be ween geog aphical and EAUM ep esen-
a ion (no malized by o al a ea o geog aphical a ea).
• Di e ence A ea o pe ime e (G_DP): sum o p o uding
and clipped a eas o EAUM in compa ison o geog aphi-
cal a ea (no malized by o al geog aphical a ea).
Topog aphical dis o ions:
• Omission o neighbo s (T_ON): numbe o neighbo -
hood ela ionships ha a e missing a e ans o ma ion
o EAUM (no malized by o al numbe o neighbo hoods
in map)
• Commission o neighbo s (T_CN): numbe o neigh-
bo hood ela ions ha a e added a e ans o ma ion o
EAUM (no malized by o al numbe o neighbo hoods
in map).
• To al numbe o neighbo hood e o s (T_TN): sum o
T_ON and T_CN.
• P opo ion o islands (T_PI): numbe o islands (which
by de ini ion canno be p ese ed in EAUMs) in ela ion
o o al numbe o egions.
In all cases he measu es a e designed in such a way ha
he alue ange is limi ed o [0; 1] and he ideal case (i.e., no
dis o ion) is e lec ed by he alue 0.
3.2 Example
The a o emen ioned measu es ha e been applied o h ee
EAUMs ha ha e been de i ed om gi en base maps
wi h co ec geog aphical appea ance—showing he s a es
o Aus alia, Ge many, and he Uni ed S a es. Using he
PyEAC so wa e men ioned in chap e 2.2, wo ypes o uni
shapes ha e been c ea ed, namely egula squa es (REG)
and hexagons (HEX). Table1 summa izes he esul s o all
gi en measu es.
Compa ing he indi idual measu es be ween he wo basic
EAUM shapes (REG and HEX) o one and he same a ea, no
signi ican di e ences wi h ega d o geome ical dis o ions
can be obse ed (e.g. in he case o Aus alia: G_DD = 0.19
o HEX and G_DD = 0.20 o REG). On he o he hand, he e
a e clea di e ences be ween REG and HEX in opological
measu es, howe e , wi h no clea ends. The di e en maxi-
mum numbe o neighbo s (REG: eigh , HEX: six) oge he
wi h he ac ual dis ibu ion o egions is p obably esponsible
o hese di e ences.
When looking a he di e ences be ween a eas (wi h he
same basic EAUM shape), Aus alia shows la ges dis o ions,
which is due o he small numbe o egions and he speci ic
loca ion o Tasmania. Compa ed o he Ge man map, he US
example shows (wi h one excep ion) sligh ly smalle geome i-
cal dis o ions. Rega ding opological changes, again no clea
ends can be de i ed.
Figu e2 shows o an exempla y measu e (D_GG) and a
selec ed basic shape (REG) ha he e a e la ge spa ial a i-
ances wi hin he measu es lis ed in Table1. The speci ied
mean alues, he e o e, show a s ong smoo hing e ec and
do no c ea e a clea o e all imp ession o dis o ions o a
speci ic da a se .
All in all, due o he in many cases unclea ends, he
egional a ia ion o he measu es and he a he la ge se o
analy ical measu es, his analy ical app oach is no easible
o pu poses such as compa ing maps o e en con olling an
EAUM gene a ion algo i hm. As a consequence, his con i-
bu ion will ollow an empi ical app oach in he nex chap e s
o be e unde s and he impo ance and ele ance o hese
measu es.
Table 1 Geome ical and
opological dis o ions o
EAUMs o h ee example a eas
A ea Aus alia Ge many USA
No. o egions 7 16 49
EAUM basic shape HEX REG HEX REG HEX REG
Geome ical dis o ions
G_DD 0.19 0.20 0.01 0.01 0.15 0.16
G_SA 0.91 0.91 0.81 0.81 0.77 0.77
G_TA 0.11 0.08 0.05 0.08 0.04 0.02
G_DP 0.37 0.43 0.27 0.25 0.18 0.18
Topological dis o ions
T_ON 0.00 0.10 0.34 0.16 0.50 0.45
T_CN 0.19 0.48 0.48 0.60 0.54 0.81
T_TN 0.19 0.57 0.83 0.76 1.04 1.27
T_PI 0.00 0.00 0.13 0.13 0.00 0.00
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4 Empi ical S udy: Sea ch o Regions
inEAUMs
4.1 Resea ch Ques ion
Fo many map usage asks ha a e o be sol ed wi h he help
o hema ic maps wi h a ea e e ence (e.g. mosaic o cho o-
ple h maps), he sea ch o egions is an essen ial ope a ion.
In his case ei he he name o he egion o he loca ion on
ano he map o compa ison pu poses is gi en. Since geo-
me ical dis o ions a e ine i able wi h EAUMs, he ques ion
a ises how e ec i e he sea ch can be. Fo u he de elop-
men s o EAUMs and o he map ypes, i is also in e es ing
o know which sea ch s a egies he use s a e using.
4.2 Hypo heses
Based on he knowledge o cogni i e psychology and isual
pe cep ion (e.g. op-down objec ecogni ion; Biede man
1981), i is assumed ha opological ela ionships a e key
c i e ia o sea ching o speci ic egions in maps. This leads
o he ollowing hypo heses:
• [H1.1] Use s apply di e en sea ch s a egies o egions
depending on hei opological si ua ion (e.g. co ne , bo -
de , cen e , and island).
• [H1.2] Algo i hms o gene a ing EAUMs can p ese e
he espec i e opological ela ionships only o a ce ain
deg ee and hus in luence he sea ch e ec i eness.
4.3 S udy Design
Conside ing he a ious opological cases wi h dis inc
solu ions ha allow single o mul iple choice ques ions, a
quan i a i e, web-based s udy has been gene a ed. Because
no use g oup-speci ic cha ac e is ics a e assumed,
socio-demog aphic we e no ga he ed. In o de no o le he
s udy p ocessing ime become oo long, only map examples
o Ge many and he USA we e shown.
The s udy used he wo mos common basic geome ical
shapes o EAUMs, namely egula squa es (REG) and hexa-
gons (HEX). The egion o be sea ched o was ma ked on
a map wi h he “co ec ” geog aphical shape (GEO). Righ
o i an EAUM—ei he in REG o HEX layou —was p e-
sen ed and a single choice selec ion om ou sugges ed
a ge egions was eques ed; in all cases he ques ion was:
“Please loca e he ma ked egion in he igh map. Choose
he bes solu ion o you” (Fig.3).
“Please loca e he ma ked egion in he igh map. Choose
he bes solu ion o you” (Fig.3). Wi h ha app oach, a pos-
sible lack o knowledge abou he names o he egions was
bypassed. A o al o 11 cases we e gi en—conside ing com-
bina ions o possible opologies (co ne , bo de , cen e , and
island) and di e en base maps ( ede al s a es o Ge many
and USA). When applying hese cases o he wo EAUM
shapes (REG, HEX), a o al o 22 asks had o be sol ed.
Fig. 2 Spa ial dis ibu ion o measu e D_GG o h ee EAUM da a se s wi h basic REG shape (no e: maps use di e en da a classi ica ion
schemes because absolu e alue anges di e oo much be ween examples)
Fig. 3 Exempla y ask o sea ching gi en egion in map wi h geo-
g aphical shape (GEO; le ) in he EAUM map (he e: REG; igh )

76 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
1 3
The map examples we e no p esen ed in a sys ema ic o de
in o de o a oid lea ning e ec s. As e iciency is no in he
ocus o his su ey, ime measu emen s we e no conduc ed.
4.4 Resul s
A o al o 222 pa icipan s ook pa in he su ey. While
Fig.4 shows he espec i e loca ions o he cases men-
ioned, Table2 gi es an o e iew o he esul s. The col-
umn “use p e e ence” shows he pe cen age o use s who
selec ed he mos common solu ion, ega dless o whe he
his solu ion was iden ical wi h he algo i hmic assignmen
o he espec i e s a e. This measu e e alua es he pu e
sea ch s a egy. The column “calcula ed s a e de ec ed”
shows he pe cen age a which use s selec ed he egion
wi h a name ma ch be ween geog aphical and EAUM ep-
esen a ion. Only in 9 o 22 cases (ma ked wi h “Y” in
he column “compa ison”) did use p e e ence ac ually
e e ed o he egion wi h he calcula ed s a e.
No consis en s a egies and esul s could be obse ed
o he sea ch o co ne egions. In case 1.1 ( egion in
an uppe igh co ne ; Fig.5), 91% o he egions we e
assigned in he REG ep esen a ion and 87% in he HEX
ep esen a ion. In con as , he localiza ion in case 1.2
(lowe igh co ne ; Fig.6) shows signi ican ly poo e al-
ues. The lowe igh co ne was selec ed in REG only by
48% ( hough he majo i y) and in HEX by 41% o he pa -
icipan s. The sea ch c i e ion o a co ne (in his example
he lowes and igh mos ) was ob iously no p edominan ,
bu he pe iphe al loca ion in combina ion wi h he imagi-
na y o e lap o he EAUM egion wi h he o iginal egion.
Case 1.2 is also an example o a misma ch be ween solu-
ions ha we e p e e ed by use s and he one ha was
gene a ed by he algo i hm. I is he e o e no su p ising
ha only 4% ( o REG and HEX) o he pa icipan s iden i-
ied ha algo i hmic solu ion as Ba a ia.
Also o bo de egions, de ec ion esul s di e ed
s ongly be ween examples. No h Rhine-Wes phalia (case
1.3) shows e y good de ec ion a es o 98% (REG) and
Fig. 4 Localiza ion o cases 1 o 11 in s udy 1
Table 2 Resul s o s udy 1 conce ning egion sea ch in EAUMs
Topological
si ua ion
Case S a e EAUM Use p e e ence Calcula ed s a e
de ec ed
Compa ison
Co ne 1.1 Mecklenbu g-Wes e n Pome ania REG 91% 91% Y
HEX 87% 87% Y
1.2 Ba a ia REG 48% 48% Y
HEX 49% 4% N
Bo de 2.3 No h Rhine-Wes phalia REG 98% 98% Y
HEX 90% 90% Y
1.4 B andenbu g REG 59% 59% Y
HEX 60% 38% N
1.5 Texas REG 45% – –
HEX 65% 1% N
Cen e 1.6 Hesse REG 63% 36% N
HEX 78% 78% Y
1.7 Saxony-Anhal REG 40% 32% N
HEX 55% – –
1.8 U ah REG 41% 41% Y
HEX 95% – –
1.9 Neb aska REG 70% 1% N
HEX 79% 6% N
Island 1.10 B emen REG 52% 46% N
REG 50% 50% Y
1.11 Be lin REG 62% 34% N
REG 79% 18% N
77KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
1 3
90% (HEX). The s a egy he e was ob iously o ei he
coun along he edge om op o bo om, o o selec
he egion a abou he same heigh as in he o iginal. In
case 1.4 (B andenbu g), he esul is signi ican wo se
(59%/38%), which is appa en ly due o he unclea posi ion
o he s a e B andenbu g ela i e o he island Be lin in
he EAUMs. In he case o Texas (case 1.5; Fig.7) i was
no he bulge a he lowe edge, bu he i s a eal o e lap
wi h he o iginal egion ha was selec ed mos equen ly
(65%)—using he eading o de om he le o igh . The
HEX-algo i hm has Texas placed o a a he dis an loca-
ion, which, unsu p isingly, was only ecognized by 1%
o use s.
Also o cen e egions, a s ong de ia ion be ween exam-
ples can be obse ed— he use p e e ence alues ange
be ween 40 and 70% (REG) and 55% and 95% (HEX). Ob i-
ously, mos use s sol ed hese asks by coun ing enume a-
ion uni s. Howe e , he coun ing as such was no always
Fig. 5 Case 1.1: Sea ch o
Mecklenbu g-Wes e n Pome a-
nia (le , geog aphical shape)—
use alloca ions (in pe cen ) in
REG (middle) and HEX ( igh )
ep esen a ions; g een column
indica es alloca ion o ha
egion by algo i hm
Fig. 6 Case 1.2: Sea ch o
Ba a ia (le , geog aphical
shape)—use alloca ions (in
pe cen ) in REG (middle) and
HEX ( igh ) ep esen a ions;
g een column indica es alloca-
ion o ha egion by algo i hm
Fig. 7 Case 1.5: Sea ch
o Texas (le , geog aphi-
cal shape)—use alloca ions
(in pe cen ) in HEX ( igh )
ep esen a ion; g een column
indica es alloca ion o ha
egion by algo i hm
78 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
1 3
co ec —in pa icula , i mo e han h ee egions had o be
conside ed like in he USA example. Fu he mo e, he mis-
alignmen o spa ial uni s in he geog aphical and ( o some
ex en ) in he HEX- ype hampe s he coun ing. In gene al,
HEX has highe ecogni ion a es han REG in he gi en
examples.
Island egions ep esen a p oblem wi h he ep esen a ion
in EAUMs as he e is pe se no pe ec solu ion. Acco d-
ingly, he de ec ion a es a e also no sa is ying. In 50–79%
o he cases, he island and he su ounding polygon we e
a anged in he o de in which hey we e ead (usually om
le o igh ; e.g. Be lin is assumed o be o he igh o
B andenbu g, Fig.8). No HEX solu ion was o e ed o he
sea ch o island egions bu one and he same REG a ian
had o be p ocessed wice by he pa icipan s in he s udy
wi h a ce ain ime lag. While he de ec ion a e emained
he same in he case o B emen, he a e o Be lin luc-
ua ed e y s ongly (62% s. 79%), which sugges s low
in ui i eness.
4.5 In e p e a ion
Hypo hesis [H1.1]—assuming di e en sea ch s a egies
o di e en opological si ua ions—could be pa ially con-
i med. In pa icula , co ne and bo de posi ions we e aken
in o conside a ion du ing he sea ch. Essen ially, he ela i e
loca ion was es ima ed o spa ial uni s we e coun ed— he
le – igh o op-down sea ch sequences clea ly domina ed.
In he case o la ge geog aphic egions, hose EAUM
egions we e o en selec ed ha show an imagina y o e lap
wi h he geog aphical egion (e.g. in case 1.2).
Due o he sca e ed esul s and he unsa is ying mean o
66% o he use p e e ence nei he a clea no a success ul
s a egy can be de i ed. Ne e heless, he iden i ied basic
opological sea ch p e e ences should be aken in o accoun
when gene a ing he EAUM. I can be concluded ha he e-
quen ly used pa ame e “minimizing dis ances o cen oids”
(see Chap e 2.2) does no coincide wi h use ’s expec a ions.
Hypo hesis [H1.2] could be con i med: dis o ions in
EACMs lead o signi ican de ia ions ha use s canno eas-
ily compensa e o . Compa ed o he a o emen ioned mean
alue o 66% o he use p e e ence, he de ec ion a e o
he egions wi h a name ma ch is only 43%. Fu he mo e,
only in 9 ou o 22 asks did he use ’s majo choice ag ee
wi h he algo i hmic solu ion.
5 Empi ical S udy: Pa e n Iden i ica ion
inEAUMs
5.1 Resea ch Ques ion
Cho ople h maps a e p ima ily used o iden i y spa ial pa -
e ns. In he ollowing, egions wi h local ex eme alues
(LE), global la e al g adien s (GLG; i.e. No h–Sou h o
Eas –Wes g adien s) as well as ho spo s (HS) a e consid-
e ed. The al e na i e use o EAUMs ha bo s he isk ha he
inhe en spa ial dis o ion lead o he ac ha pa e ns a e
no longe ecognized well o no a all. On he o he hand,
EAUMs should ha e he po en ial o a be e ecogni ion o
local ex emes o small enume a ion a eas, hus a oiding he
a ea size-bias.
5.2 Hypo heses
I is assumed ha due o geome ical dis o ions also he
iden i ica ion o spa ial pa e ns in EAUMs is a ec ed in
a nega i e manne wi h he excep ion o he iden i ica ion
o local ex eme alue egions. This leads o he ollowing
hypo heses:
• [H2.1] The iden i ica ion o LE akes place in EAUMs
wi h g ea e e ec i eness, because he a ea size bias
is a oided. Since neighbo hoods a e i ele an in his
con ex , no di e ence be ween REG and HEX is o be
expec ed.
• [H2.2] The iden i ica ion o GLG and HS is bes done in
he o iginal geog aphical layou (GEO) due o po en ial
neighbo hood dis o ions in REG and HEX.
5.3 S udy Design
Conside ing he a ious pa e n cases wi h dis inc solu-
ions ha allow single o mul iple choice ques ions, a
Fig. 8 Case 1.11: sea ch o Be lin (le , geog aphical shape)—use
alloca ions (in pe cen ) in REG ( igh ) ep esen a ion; g een column
indica es alloca ion o ha egion by algo i hm
79KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82
1 3
quan i a i e, web-based s udy has been gene a ed. Because
no use g oup-speci ic cha ac e is ics a e assumed, socio-
demog aphic we e no ga he ed. In o de no o le he
s udy p ocessing ime become oo long, only map exam-
ples o Ge many and he USA we e shown.
The ask was o iden i y pa e ns in di e en map ypes
(GEO/REG/HEX). Fo each ask, one map wi h one o mo e
pa e ns was p esen ed; in o al, eigh maps we e gi en
(examples a e gi en in Figs.9, 10, 11). Pa icipan s we e
asked o a mul iple choice-selec ion wi h he op ions o one
locale ex eme alue egion (LE), wo LE, No h–Sou h and
Eas –Wes g adien s, and HS (while he la e was desc ibed
as, high alue su ound by o he qui e high alues “ o be -
e unde s anding”). In all cases he ques ion was: “Please
name he spa ial pa e n ha you iew in his map. Mul iple
op ions a e possible. No e ha da ke colo s mean highe
alues”. By pu pose, he espec i e loca ions (i.e., he s a es)
should no be named in o de o a oid localiza ion e o s
(see s udy 1).
Fig. 9 Case 2.3: Rep esen a ion
o he same single LE in small
enume a ion a ea (he e: B emen
in he No h–Wes ) in GEO,
REG and HEX maps ( om le ;
he da ke he colo he la ge
he alue)
Fig. 10 Rep esen a ion o he
same Eas –Wes pa e ns in
GEO, REG and HEX maps
( om le ; he da ke he colo
he la ge he alue)
Fig. 11 Rep esen a ion o he
same ho spo in GEO, REG
and HEX maps ( om le ; he
da ke he colo he la ge he
alue)