ST-Spli VFL: Spa io-Tempo al Spli Ve ical
Fede a ed Lea ning
Ani a G ase 1[0000−0001−5361−2885], Jose An onio
Lo encio-Ab il1[0009−0005−9127−4844], Axel Weissen eld1[0000−0002−7246−2744],
and Anahid Wachsenegge 1[0000−0002−8889−0735]
AIT Aus ian Ins i u e o Technology, 1210 Vienna, Aus ia
[email p o ec ed]
Abs ac . The inc easing demand o accu a e spa io- empo al o e-
cas ing in domains such as mobili y and u ban managemen is o en
cons ained by da a p i acy egula ions and ins i u ional eluc ance o
sha e sensi i e in o ma ion. Fede a ed Lea ning (FL) o e s a p omising
pa adigm by enabling collabo a i e model aining wi hou cen alized
da a agg ega ion. This pape in oduces ST-Spli VFL, a no el ame-
wo k o Spa io-Tempo al Spli Ve ical Fede a ed Lea ning, which ex-
ends e ical FL wi h spli lea ning and spa ial g aph cons ain s. In
his se ing, clien s main ain hei local da a while selec i ely exchang-
ing encoded in e media e ep esen a ions wi h geog aphically o logically
connec ed pee s. We e alua e ST-Spli VFL on wo da ase s and demon-
s a e ha ST-Spli VFL consis en ly ou pe o ms locally ained models
and achie es p edic i e pe o mance close o cen alized and ully con-
nec ed FL baselines, while subs an ially educing model size and commu-
nica ion o e head. By p ese ing da a locali y, minimizing ne wo k con-
ges ion, and suppo ing mul i- a ge o ecas ing, ST-Spli VFL p o ides
an e icien and p i acy-p ese ing solu ion o spa io- empo al lea ning
ac oss dis ibu ed s akeholde s.
Keywo ds: GeoAI ·Mobili y Da a Science ·Spa io- empo al Fo ecas -
ing
1 In oduc ion
The apid p og ess o A i icial In elligence (AI) and i s b oad up ake ac oss
indus y ha e mo i a ed public au ho i ies and companies o deploy da a-d i en
se ices o ci izens and end use s. Fo ecas ing models, based on his o ical ime
se ies a e one popula op ions since hey ha e he po en ial o enable be e
planning and p epa edness o u u e condi ions. Howe e , AI sys em aining
ypically equi es access o la ge, high-quali y da ase s ha many o ganiza ions
do no possess [19]. E en when da a exis s, egula o y equi emen s and eluc-
ance o disclose p op ie a y in o ma ion o en cons ain da a sha ing. These
ac o s hinde he implemen a ion o AI solu ions ha equi e cen alized da a
agg ega ion.
2 A. G ase e al.
Fede a ed Lea ning (FL) add esses hese challenges by enabling collabo a i e
model aining wi hou cen alizing aw da a [15]. Ins ead o uploading da a o a
se e , clien s compu e local upda es o in e media e ep esen a ions and sha e
only hese wi h a coo dina o . This decen aliza ion mi iga es p i acy isks and
educes he a ack su ace associa ed wi h single poin s o ailu e.
Two p ima y FL pa adigms a e Ho izon al Fede a ed Lea ning (HFL) and
Ve ical Fede a ed Lea ning (VFL) [7] (also known as Sample-based FL o C oss-
silo FL and Fea u e-based FL, espec i ely). HFL applies when pa ies hold he
same ea u e space o disjoin se s o en i ies; VFL applies when pa ies hold
complemen a y ea u e spaces o (pa ially) o e lapping en i ies. VFL is espe-
cially ele an when di e en o ganiza ions main ain ea u e-speci ic da a ha
should emain p i a e – o example, clinical eco ds a a hospi al and demo-
g aphic eco ds a a municipali y o he same pa ien . Such se ings equen ly
a ise in spa io- empo al o ecas ing, whe e mul iple s akeholde s collec geo-
g aphically dis ibu ed da a o e ime and wish o ob ain join insigh s wi hou
exposing aw da a.
GeoAI combines machine lea ning wi h geog aphy and GIScience o sup-
po geospa ial analysis and o ecas ing [6,23]. While FL and GeoAI a e na u al
complemen s, hei in e sec ion emains unde explo ed; ea ly s udies ne e he-
less poin o s ong syne gies [5,24]. Spa io- empo al da a in oduce addi ional
complexi y: hey couple empo al dynamics wi h spa ial dependence and aise
speci ic p i acy isks [20]. When such da a a e agmen ed ac oss o ganiza ions,
e ec i e lea ning wi hou cen aliza ion is pa icula ly challenging.
This wo k in oduces a Spa io-Tempo al Spli Ve ical Fede a ed Lea ning
amewo k (ST-Spli VFL) ailo ed o o ecas ing o space– ime se ies. The ame-
wo k ex ends VFL by inco po a ing spa ial ela ions among clien s ia a spa ial
g aph, enabling join use o empo al his o ies and spa ial con ex while keep-
ing aw da a local. In ou se ing, clien s hold dis inc o ecas ing asks and
in e ela ed da ase s. ST-Spli VFL le e ages hese in e connec ions o imp o e
p edic i e pe o mance wi hou comp omising da a locali y. The main con ibu-
ions a e:
–We in oduce ST-Spli VFL, a spli VFL app oach o space– ime se ies o e-
cas ing ha connec s spa ially ela ed clien s h ough a spa ial g aph. The
g aph de ines a Spli NN in which each clien pe o ms local o ecas ing wi h
LSTM-based modules while selec i ely exchanging in e media e embeddings
wi h geog aphically o logically adjacen clien s.
–We conduc comp ehensi e expe imen s showing ha ST-Spli VFL ou pe -
o ms locally ained models and app oaches he pe o mance o cen alized
models, while educing model complexi y and ne wo k conges ion.
–We p o ide a heo e ical a gumen ha g aph-cons ained sha ing yields
smalle models whose size g ows linea ly in he numbe o clien s, and em-
pi ical e idence ha his educ ion does no deg ade pe o mance.
The emainde o his pape is o ganized as ollows: Sec ion 2 e iews ela ed
wo k on spa io- empo al o ecas ing and ede a ed lea ning. Sec ion 3 p esen s
ST-Spli VFL: Spa io-Tempo al Spli Ve ical Fede a ed Lea ning 3
he ST-Spli VFL amewo k. Sec ion 5 desc ibes he expe imen al se up and
esul s, and discusses implica ions and applica ions. Sec ion 6 concludes.
2 Rela ed Wo k
Bo h p e ious wo ks on spa ial ime se ies o ecas ing as well as on spa io-
empo al ede a ed lea ning esea ch a e ele an o he de elopmen o ST-
Spli VFL. A de ailed su ey o Spa io- empo al ML is p esen ed in [23], wi h he
au ho s e iewing how NNs ha e been made spa ially-awa e o di e en asks.
In he ollowing subsec ion, we ocus on hose pape s ha add ess speci ically
spa ial ime se ies.
2.1 Spa ial Time Se ies Fo ecas ing
When p edic ing ime se ies a di e en spa ial loca ions, making models spa ially-
explici can imp o e o ecas esul s. Table 1 p o ides an o e iew o exis ing
neu al ne wo k app oaches o spa io- empo al o ecas ing and how hey ap-
p oach modeling he spa ial and empo al dimensions.
Con olu ional NNs (CNNs) a e a common app oach o build spa ial models
by pe o ming a con olu ion ope a ion on he spa ial dimension. This ep esen s
he assump ion ha he spa ial ela ionships should be simila in di e en lo-
ca ions, i.e., simila pa e ns in di e en a eas should ha e simila e ec s. Fo
example, [28][8] p ocess each loca ion’s ime se ies independen ly using em-
po al con olu ions and ime segmen a ion. Then he esul s a e p ocessed o
ex ac spa ial ela ionships h ough a spa ial con olu ion. Asadi e al. [1] e-
place he empo al CNN wi h ecu en NNs (RNNs). CNNs a e also common
in app oaches ha model spa ial da a as images [14,26].
Spa ial Modeling Tempo al Modeling Re e ence
CNN [28,8]
CNN on empo al
modeling ou pu RNN [1]
CNN on images ha
ep esen spa ial da a RNN [14,26]
GNN on
spa ial g aph RNN [18,10]
GNN on
spa io- empo al g aph [2]
Global a en ion on
empo al modeling ou pu
Local a en ion
mechanism [3,25]
Table 1. Classi ica ion o he app oaches o spa io- empo al o ecas ing.
G aph NNs (GNNs) p esen a di e en way o model spa ial co ela ions
by encoding he spa ial in o ma ion using a spa ial g aph. GNNs can p ocess
4 A. G ase e al.
he spa ial g aph ep esen ing he spa ial in o ma ion, while empo al da a is
p ocessed wi h RNNs [18,10]. Ins ead o sepa a ing he p ocessing o spa ial
and empo al ea u es, GNNs can also be applied o uni ied spa io- empo al
g aphs [2], ex ac ing spa ial and empo al ela ionships simul aneously.
T ans o me s [21] can also be used o ackle spa io- empo al o ecas ing, by
using he a en ion mechanism on he spa ial and empo al dimensions [3,25].
As his summa y shows, in mos wo ks, he spa io- empo al dependencies
a e analyzed sepa a ely as empo al dependencies and spa ial dependencies, and
combined a some poin o e ec i ely model he mixed na u e o he da a. This
app oach can educe he complexi y o he model bu could miss possibly ele-
an in e ac ions. On he o he hand, he comple ely spa io- empo al app oach
enables o ake in o accoun di e en dependencies, bo h spa ial and empo al
and acili a es mul i-g anula analysis, howe e , he model can become qui e
in ol ed.
Fo ede a ed lea ning, he wo-s ep app oach is mo e app op ia e, since each
FL clien holds only local empo al da a, and spa ial dependencies can only be
de ec ed wi h access o mul iple clien s’ da a. We de ail how we deal wi h he
spa io- empo al dependencies in Sec ion 3, and con inue now o e iew how FL
has been made spa ially-explici in he exis ing li e a u e.
2.2 Spa io-Tempo al Fede a ed Lea ning
FL can be adap ed o cope wi h spa ial ela ionships in di e en ways. Some o
hese a e e y na u al, e.g. each local model is adap ed o he local speci ici ies
o he da a, while o he s equi e an in ol ed p ocess o cons uc ing a g aph o
an a en ion mechanism. Table 2 summa izes di e en app oaches o spa ially-
explici FL.
An ea ly spa ially-explici HFL se ing was p oposed in [4], enabling he
global model o lea n gene al pa e ns in he da a while allowing local mod-
els o cus omiza ion o he local egional cha ac e is ics. A simila app oach
is ollowed in [16]. In hese wo HFL app oaches, he global model is an ag-
g ega ion o he local models, and he e o e he cus omiza ion depends on he
local upda ing o he local da a. Al e na i ely, GNNs can be used o model he
in e dependencies [22].
VFL app oaches p ocess each da a sou ce wi h a di e en NN module, which
is locally ained a each cell [27,11]. The model pa ame e s a e sha ed wi h
o he clien s and locally agg ega ed. The e o e, his app oach le e ages spa ial
in o ma ion by looking a local con ex ual spa ial in o ma ion (wea he condi-
ions and POIs, sha ed by Spli VFL) and by sha ing model pa ame e s aking
in o accoun he spa ial componen .
In he nex chap e , we de elop ou p oposed solu ion, which ollows he
na u al idea o he spli lea ning se ing o local models coping wi h local speci-
ici ies, bu adding an ex a le el o locali y by sha ing only embeddings ac-
co ding o he opology o a spa ial g aph ep esen ing he spa ial ela ionships
be ween clien s. In addi ion, ou p oposed amewo k copes wi h a mul i- a ge
en i onmen , whe e each clien may ha e di e en p edic ion needs, while o he
ST-Spli VFL: Spa io-Tempo al Spli Ve ical Fede a ed Lea ning 5
Spa ial Modeling
FL Type Global Local Re e ence
Local aining [4,16]
HFL Th ough GNNs [22]
Mix
Local models
agg ega ion A en ion mechanism
be ween clien embeddings [27]
VFL Cen aliza ion
o embeddings
Spli lea ning local
models [11]
Table 2. Classi ica ion o he app oaches o spa ially-explici FL.
bes o ou knowledge, he e is no p e ious esea ch ackling his p oblem in a
spa ially-awa e ede a ed se ing.
3 Spa io-Tempo al Spli Ve ical Fede a ed Lea ning
Building on insigh s om ou p e ious wo k-in-p og ess a icle [13] and he ap-
p oach p oposed by Lie e al. [12], we de elop a a ian ha we deno e ST-
Spli VFL. I enables collabo a i e model aining ac oss mul iple clien s by con-
s uc ing a global model capable o gene a ing p edic ions locally a each clien
si e. The model inco po a es in o ma ion om o he clien s h ough secu e agg e-
ga ion mechanisms, ensu ing ha aw da a emains con ined o local da abases
and ha p i acy is p ese ed h oughou he aining p ocess.
Fo a se o clien s C={C1, ..., Cn}, each clien holds a local da a se
Xci, i = 1, ..., n and is placed in a loca ion lci∈ L (which could possibly e-
pea ). Clien s a e ei he ac i e i hey ha e a o ecas ing ask o passi e i hey
do no ha e a o ecas ing ask (and hus only se e as da a p o ide s). Ac i e
clien s hold wo neu al modules: 1) mul i-head encode Ei,j wi h i= 1, ..., n and
j∈ N(Ci), whe e N(Ci)a e he neighbo s o clien Ciin he spa ial g aph (de-
ined in he ollowing pa ag aph), including i sel ; 2) o ecas e Fi, i = 1, ..., n,
esponsible o gene a ing p edic ions ˆ
Yi. In con as , passi e clien s se ing as
co a ia es main ain only he encode module and do no pe o m o ecas ing
asks hemsel es. This app oach is exempli ied in Fig. 1, which depic s wo ac i e
clien s and one passi e clien . The illus a ion highligh s how da a exchange is
s uc u ed based on spa ial ela ionships among he clien s. In pa icula , only
encoded ep esen a ions a e exchanged be ween clien s—no he o iginal aw
da a—which is a key aspec in ensu ing da a p i acy h oughou he p ocess.
Fi s ly, we build a spa ial g aph o he sys em, G= (C,E), whe e Eis he se
o edges connec ing hose clien s. The spa ial g aph encodes he spa ial ela ion-
ships be ween he clien s, de e mined by hei loca ions. E.g. clien s Ciand Cj
a e connec ed in he g aph, i he dis ance be ween lciand lcjis smalle han
some p e-de ined h eshold.
Secondly, he opology o he spa ial g aph de e mines he a chi ec u e o he
Spli NN o he sys em. Each clien adds one head o he encode o each neigh-
bo ing clien , and he in e media e esul s will be sen only o hese neighbo ing
6 A. G ase e al.
Fig. 1. Illus a ion o he Spli VFL app oach, wi h ac i e clien s A and B, and passi e
clien C. Clien C is only connec ed o clien B. Do ed a ows ep esen in o ma ion
ansmi ed h ough he ne wo k, and con inuous a ows ep esen local da a low.
ST-Spli VFL: Spa io-Tempo al Spli Ve ical Fede a ed Lea ning 7
clien s. Tha is, each clien Cip oduces
Zi,j =Ei,j(Xi),
and ecei es
Z′
i= [Zj,i : (j, i)∈ E].
Finally, he o ecas e module o each clien ecei es all in e media e esul s
om neighbo ing clien s, conca ena ed, and uses hem and he local da a o
make o ecas s ˆ
Yi=Fi(Z′
i).
To p ocess he empo al da a, bo h he encode and he o ecas e a e LSTM
ne wo ks, while he spa ial componen is aken in o accoun by de ining he
opology o he ne wo k acco ding o he spa ial g aph, G.
We illus a e his ST-Spli VFL amewo k in Figu e 1, whe e we show how
he numbe o heads a ies acco ding o he connec i i y o he g aph, as well
as he di e en oles o ac i e and passi e clien s.
To ain he sys em, a wo-phase app oach is ollowed:
1. Encode s p e- aining: each clien ains an encode wi h i s local da a in
an encode -decode ashion. Once i is ained, i makes as many copies as
neighbo ing clien s i has. These encode s a e upda ed du ing he second
phase.
2. Fede a ed aining: each ba ch is encoded by each clien , and sen o i s
neighbo s. All incoming encoded da a a e conca ena ed and inpu o he
o ecas e , which makes p edic ions. The loss is compu ed and he o ecas e
is upda ed ia backp opaga ion. The g adien s a e sen o he app op i-
a e clien s o ine- une each head o he encode o he associa ed o ecas -
ing ask, ollowing he in e se pa h ha he da a ollowed in he o wa d
pass, as shown in Figu e 2. Fo mally, i encoded ep esen a ions om clien
Ci, head Ei,j,Zi,j =Ei,j(Xi), a e used by clien Cj o make o ecas s,
ˆy=Fj([..., Zi,j, ...]), hen we compu e he loss o clien Cjas Lj(yj,ˆyj), up-
da e Fjacco ding o ∂Lj
∂WFj
, whe e WFja e he weigh s o Fj, and ansmi
∂Lj
∂WFj,Zi,j
o clien Ci, so ha his clien can compu e ∂Lj
∂WEi,j
and upda e he
local encode Ei,j associa ed o clien Cj.
4 Expe imen al Se up
4.1 Da ase s
Expe imen s we e pe o med on wo di e en da ase s: he public Po o da ase
om Kaggle (o iginally eleased as pa o he ECML/PKDD 2015 Disco e y
Challenge [17]) and a p op ie a y da ase om Sche eningen (Ne he lands) ha
was pa o ou p ojec . The basic da ase s a is ics a e summa ized in Table 3.
The Sche eningen da ase consis s o six a eas wi h c owd da a and an ad-
di ional da a sou ce p o iding wea he o ecas s. Each clien has 22,202 eco ds.
8 A. G ase e al.
Fig. 2. Illus a ion o he backp opaga ion p ocess in Spli VFL, ocusing on he loss
o clien B, and how he di e en g adien s low backwa d, ep esen ed as ed a ows.
The numbe o connec ions o he spa ial g aph is ei he ou o i e (depending
on he loca ion o he a ea).
The Po o da ase p o ides he oppo uni y o es on a la ge geog aphic
egion. I encompasses axi ajec o y da a collec ed wi hin he ci y o Po o,
Po ugal. To align he da ase wi h ou amewo k, we p ep ocess i by agg e-
ga ing spa ial and empo al in o ma ion. Spa ially, we pa i ion he ci y using
he H3 g id sys em [9], esul ing in 78 dis inc hexagonal a eas and 8,760 eco ds
pe clien . Tempo ally, he da a is segmen ed in o hou ly in e als. Wi hin each
a ea, we compu e he hou ly coun o ac i e axis. Fo he p edic i e ask, we
use da a om he p eceding ou days o o ecas axi ac i i y o e he nex ou
hou s. To model spa ial ela ionships, we cons uc a g aph by connec ing each
hexagon o i s six nea es neighbo s.
Table 3. Cha ac e is ics o he da ase s a e p e-p ocessing: numbe o clien s, eco ds
pe clien , and inpu /ou pu sizes.
Use case Types o clien s No. clien s Recs./clien Inpu size Ou pu size
Sche eningen C owd a eas 6 22202 168 ×3 168
Wea he 1 168 ×6-
Po o Taxi coun s a eas 78 8760 96 ×3 4
ST-Spli VFL: Spa io-Tempo al Spli Ve ical Fede a ed Lea ning 9
4.2 T aining
Each o he da a se s is p ocessed wi h a window unc ion ha c ea es inpu
and ou pu sequences o aining and alida ion, wi h an 80/20 empo al spli
( i s 80% o he da a used o aining, and inal 20% o alida ion). As de-
sc ibed in Sec ion 3, ST-Spli VFL clien s ha e a o ecas ing model and mul iple
encode s. We used a wo-laye LSTM encode and a wo-laye LSTM decode ,
each wi h a hidden s a e size o 16. The o ecas e is implemen ed as a bidi-
ec ional LSTM wi h a hidden s a e size o 64. The model is op imized using
Adam op imize , wi h a d opou a e o 0.1, an ini ial lea ning a e o 1 x 10−2,
and a lea ning a e schedule ha educes he a e by hal e e y 20 epochs. The
ba ch size is 64 o Sche eningen and 32 o he Po o da ase . We used he
s anda d loss unc ion MSE (mean squa e e o ) and ained o 200 epochs. To
imp o e aining s abili y, he encode s a e i s p e- ained on local da a. We
hen pe o m join aining, whe e he o ecas e models a e ained, and he
encode s a e ine- uned simul aneously. Ou ne wo ks we e ained om sc a ch
using PyTo ch. All expe imen s we e conduc ed on a sys em equipped wi h an
NVIDIA TITAN RTX GPU wi h 24GB RAM. The aining was epea ed o e
11 independen uns in o de o p o ide a sound, s a is ically eliable es ima e
o he model pe o mance.
4.3 Baseline Models
Fo compa ison, we ained wo baselines: local LSTM models and Spli VFL.
Fo he i s baseline, we ained models whe e each clien independen ly using
only i s local da a, wi hou any communica ion o in o ma ion exchange wi h
o he clien s. Hence, clien s do no ha e any encode s bu only a o ecas e wi h
bidi ec ional LSTM as desc ibed in Sec. 4.2 and whe e he inpu size adop ed
acco dingly. We e e o his se up as he Local LSTM model.
Fo he second baseline, he Spli VFL model is based on he ST-Spli VFL
model bu wi hou he spa ial g aph, which de ines he connec ions be ween
clien s. The clien connec ions o he Spli VFL models sligh ly di e depending
on he da ase (Sche eningen o Po o) hey a e ained on. The clien s o he
Spli VFL model ained on he Sche eningen da ase main ain ull in e connec-
i i y wi h one ano he . Since he e a e only a ew clien s in he Sche eningen
da ase , he di e ence be ween ull in e connec i i y and he spa ial g aph is
small - se en connec ions in he case o ull in e connec i i y e sus ou o i e
connec ions using he spa ial g aph. In con as , he Po o da ase has 78 clien s.
In his case, he clien s o he Spli VFL model we e andomly connec ed wi h 39
o he clien s. No e, ha he numbe o connec ed clien s needed o be es ic ed
o 39 because o he limi ed GPU capaci y o aining he models. The ain-
ings o all models we e ca ied ou in he same way as desc ibed in he p e ious
sec ion.
