An ex ended ch onicle disco e y app oach o ind empo al pa e ns be ween
sequences
Al a ez, M.A.a; Subias, A.b,c; T a ´
e-Massuy`
es, L.b,c; Gonzalez-Ab il, L.d; O ega, J.A.a
aDepa men o Compu e Science, Uni e si y o Se ille, 41500 Se ille, Spain
bCNRS, LAAS, 7, a enue du Colonel Roche, F-31400 Toulouse, F ance
cUni de Toulouse, INSA, LAAS, F-31400 Toulouse, F ance
dDepa men o Applied Economics I, Uni e si y o Se ille, 41500 Se ille, Spain
maal [email p o ec ed], {subias, louise}@laas. , {luisgon, jo ega}@us.es
Abs ac
Sequences o e en s desc ibing he beha io and
ac ions o use s o sys ems can be collec ed in se -
e al domains. An episode is a collec ion o e en s
ha occu s ela i ely close o each o he in a gi en
pa ial o de . Also, ch onicles a e a special ype o
empo al pa e ns, whe e empo al o de s o e en s
a e quan i ied wi h nume ical bounds and e lec
he empo al e olu ion o he sys em o e he ime.
In his pape , he p oblem o inding ules o de-
sc ibing o p edic ing he beha io o he sequences
wi h he in en ion o cha ac e izing some in e es -
ing asks is conside ed. Ob aining hese pa e ns is
he main objec i e o his wo k, whe e an au oma ic
me hod o lea n ele an and disc imina ing ch on-
icles is p oposed. The me hod ex ends exis ing al-
go i hms ha ha e been p oposed o ind equen
episodes/ch onicles in a single e en sequence o
he case o mul iple sequences.
1 In oduc ion
In some applica ion a eas o knowledge like da a mining o
machine lea ning, he da a o be analyzed is made up o a se-
quence o e en s. So, he da a can be iewed as a sequence
o e en s, whe e each e en has an associa ed ime o occu -
ence. An example o an e en sequence is shown in Figu e
1. He e A o F a e e en s and hey a e ep esen ed on a ime
line. In he las yea s, he e ha e been many au ho s in e -
es in knowledge disco e y om sequen ial da a [Dousson e
al., 2008; Le Guillou e al., 2008; Pencol´
e and Subias, 2009;
Be and e al., 2009; Saddem e al., 2010; Baue e al., 2011]
because he echnology ha e been applied in a lo o a eas.
Analysing human ac i i ies is equi ed in many domains,
like e gonomics, sa e y diagnosis, p ocess design, and mo e
gene ally o unde s anding cogni i e and social p ocesses.
In his a icle, we p opose an app oach o suppo he p ocess
o ac i i y analysis wi h he help o in e ac i e disco e y o
empo al pa e ns named ch onicles.
The i s ask o desc ibing he beha io o sys ems om
sequences o e en s is o ind equen episodes, i.e., collec-
ions o e en s occu ing equen ly oge he . In he Figu e 1,
he e en E is ollowed by F se e al imes and i is an episode,
and o de ed se o e en s. F om he same sequence in he ig-
u e, he obse a ion ha whene e A and B occu , in ei he
o de , C occu s soon can be done.
Taking in o accoun he las de ini ion, a se o maximum
episode ules can be ob ained om a e en sequence. The
main mo i a ion o his pape is o ind a minimal se o ules
om some e en sequences. This se mus con ain he maxi-
mum episode ules ha ha e been ound in all sequences, i.e.
he se is an in e sec ion o he se o each one.
In his pape he ollowing p oblem is conside ed. Gi en
some inpu sequences o e en s, ind all episodes ha occu
equen ly in all sequences. To achie e his goal some ex-
ended echniques om [Mannila e al., 1997],[Mannila and
Ronkainen, 1997]and [C am e al., 2011]a e p oposed.
The es o his pape is o ganized as ollows: i s , he
main p oblem and he mo i a ion o his pape a e p esen ed
in Sec ion 2. La e , he de ini ion o he p oblem is p esen ed
in Sec ion 3 o es ablish he no a ion o he es o he pape .
In Sec ion 4, he exis ing algo i hms o disco e ch onicles in
a sequence a e explained. Sec ion 5 con ains he Mannila’s
app oach o ge ch onicles and Sec ion 6 p esen s a me hod-
ology o disco e ch onicles ha mus be exis in all e en
sequences. Sec ion 7 epo s he ob ained esul s o apply-
ing he me hodology. The pape is inally concluded wi h a
summa y o he mos impo an poin s in Sec ion 8.
2 P oblem and mo i a ion
This wo k aims o each an es ima ion o he s a e o a ne -
wo k om ch onicle ecogni ion. The ch onicles desc ibe be-
ha io s o si ua ions o be ecognized om empo al pa e ns.
The main di icul y o his app oach ocuses on how o
de elop ch onicles. One o he possible solu ions can be
ob ained om lea ning, so in his pape , one o he p inci-
pal ch onicle lea ning app oaches exis ing in he li e a u e is
s udied. F om his app oach, a solu ion o he p oblem o
he adap a ion o he communica ion p o ocols is p oposed.
These p oblems can be ne wo k conges ions o packe loss.
These pa e ns a e based on gene a ed signals om ou e s.
3 De ini ions
An inpu as a sequence o e en s is conside ed whe e each
e en has a ag and a ime s amp ep esen ed by an in ege .
Gi en a se Eo e en ypes, an e en eis a pai (A, )whe e
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Figu e 1: A sequence o e en s
A∈Eis an e en ype and is he ime o he e en .
e=(A, |A∈E)
A sequence sis a lis o e en s be ween an in e al o ime
s amps
s(Ts,T
e)=((A1,
1),(A2,
2),...,(An,
n))(1)
whe e
Ai∈E,∀i=1,2,...,n
i≤ i+1,∀i=1,2,...,n
Ts≤ i<T
e,∀i=1,2,...,n
A e en sequence s(29,68) is ep esen ed in Figu e 1.
s(29,68) =((E,31),(D,32),(F,33),(A, 35),(B,37),
(C, 38),...,(D,67))
A window ωon a sequence is de ined as a se o e en s
be ween an in e al o ime s amps
ω( s,
e)={(A, )∈s| s≤ <
e}(2)
whe e s<T
eand e>T
s.
Also, wo windows ωaand ωba e simila i |ωa|=|ωa|
and |(Ai,
i)|=|(Aj,
j)|whe e Ai=Aj,∀Ai∈ωa,∀Aj∈
ωb.
A wid h can be de ined as he di e ence be ween wo ime
s amps. In Figu e 1, he wid h o he sequence is he di e -
ence be ween he s a ime s amp and he end ime s amp:
wid h(s)=Te−Ts= 68 −29 = 39
Also, he wid h o a window ωcan be de ined as
wid h(ω)= e− s.
Now, om 1 and 2, he se o all windows wi h he same
wid h in a sequence is ep esen ed below:
W(s, win)={ω( s,
e)∈s|wid h(ω)=win}
Fo example, in Figu e 1, he numbe o windows wi h
he wid h equals o 5 is 43, |W(s, 5)|= 43, and (∅,25,30)
and (((D,67)),25,30) a e he i s and he las windows o
W(s, 5).
Finally, an episode αis a se o nodes wi h a pa ial o de
and a ela ion be ween hem:
α=(V,≤,g:V→E)
Also, an episode βis a subepisode o αi he ollowing
condi ions a e ull iled:
β=(V!,≤!,g!:V!→E)!α=(V,≤,g:V→E)(3)
∃ :V!→V|g!(ν)=g( (ν)),∀ν∈V!
ν≤!%,∀ν,%∈V!
(ν)≤ (%),∀ν,%∈V!
In he o he hand, an episode αis a supe episode o β, i
and only i β!α.
F om 3, an episode ule is de ined as β⇒αi β!α.
In Figu e 2, α,βand γa e episodes and γis a subepisode
o β.
Figu e 2: Th ee di e en episodes
4 S a e o he a on disco e ing ch onicles
[Dousson and Ghallab, 1994]de ines ch onicle as a empo al
pa e n in ended o ep esen a pa e n o e olu ion o a sys-
em, i is mainly composed o a se o e en s and empo al
cons ain s be ween hei da es o occu ences. A ch onicle
Cis p esen ed as C=S, T whe e S ep esen s all he e en s
and T ep esen s all he cons ain s.
In Figu e 3, he e3e en occu s be ween 3and 6 ime uni s
a e he e1e en o be ween 3and 9 ime uni s a e he e2
e en . This ch onicle is ep esen ed below:
C={S, T}
S={e1,e
2,e
3}
T={ 1<
3∧ 2<
3|3≤ 3− 1≤6∧3≤ 3− 2≤9}
Some conside a ions a e needed o aking in o accoun o
ecognize a ch onicle:
iA se o da ed e en s: his se is he inpu o he ecogni ion
sys em.
ii A se o cons ain s: hese cons ain s a e ime in e als
be ween he da es o occu ences o e en s.
iii A se o o mulas o a gene al scheme: i is he ch onic
pa e ns wi hou conside ing iming cons ain s be ween
hei da es o occu ence.
Recognizing is o explain he inpu e en s (i) using he em-
po al pa e ns (iii) while espec ing he cons ain s o he ield
(ii). So, a ch onicle is a se o cons ain s on e en s wi h hei
da es o occu ence, whe e each cha ac e is ic o a ch onicle
si ua ion is based on he obse ed consequences.
In ou con ex , an abno mal communica ion sys em is cha -
ac e ized by a se o ch onicles, whe e each ch onicle de-
sc ibes he si ua ion o in e es acco ding o he e olu ion o
he sys em. Fo example, a si ua ion o da a loss has many
causes, such as ne wo k conges ion, loss o connec i i y o
changing access in e ace. Each o hese si ua ions o s a es
mus be ep esen ed by a leas one ch onicle.
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1
2
3
[3, 6]
[3, 9]
Figu e 3: A ch onicle wi h h ee e en s
5 Mannila’s app oach
Mannila’s app oach inds all episodes ha occu equen ly in
a e en sequence. I is based on he idea o i s inding small
equen episodes and hen p og essi ely looking o la ge
equen episodes.
Apa om he de ini ions in Sec ion 3, Mannila de ines
he equency o an episode as he ac ion o windows in
which he episode occu s. Tha is, gi en an e en sequence s
and a window wid h win, he equency o an episode αin s
is
(α, s, win)=|w∈W(s, win)|αoccu s in w|
|W(s, win)|
Fu he mo e, αis equen i (α, s, win)≥min
whe e min is a equency h eshold.
The main objec i e is o disco e all equen episodes
om a se o episodes. Mannila deno es he collec ion o
equen episodes wi h espec o s,win and min by
F(s, win, min ).
F om episode ule, he con idence is de ined as (γ,s,win)
(β,s,win).
The nex Mannila algo i hm desc ibes how ules and
hei con idences can be compu ed om he equencies o
episodes whe e he inpu is a se Eo e en ypes, a sequence
s, a se o Eo episodes, a window wid h win, a equency
h eshold min and a con idence h eshold min con ; and
he ou pu is he episode ules ha hold in swi h espec o
win,min and min con .
/*Find equen episodes */
compu e F(s, win, min )
/*Gene a e ules */
o all α∈F(s, win, min )do
o all β≺αdo
i (α)/ (β)≥min con hen
ou pu he ule β→αand
he con idence (α)/ (β);
6 Disco e ing episodes common o se e al
sequences
In his sec ion, a me hodology o disco e episodes in some
sequences is de eloped. I is based on Mannila’s app oach
because i inds he episode wi h he maximum wid h ha oc-
cu s in all sequences.
The simila i y be ween wo windows is necessa y o un-
de s and he de eloped app oach. Two windows a e simila i
he numbe o all exis ing e en ypes in he windows is equal.
Fo example, in he nex sequences, he windows ω(0,2) o e
sequences s1and s2a e no simila , bu ω(1,4) yes.
s1=((A, 0),(B,1),(B,2),(C, 3),(C, 4),(B,5),(D,6))
s2=((A, 0),(C, 1),(B,2),(C, 3),(B,4),(B,5),(D,7))
s3=((A, 1),(B,2),(B,3),(C, 4),(C, 6),(D,8))
Le Sa se o sequences, lan in ege and Wa se o
episodes.
/*Se a iables */
S={s1,s
2,...,s
n};
l=min{wid h(s1),wid h(s2),...,wid h(sn)};
W=∅;
/*Ge maximum simila windows */
while |W|=0and l>0do
W={ω( s,
e)∈s|∀s∈S, wid h(ω)=l};
l=l−1;
i |W|=0 hen
he e is no a common episode
else
/*Cons uc ch onicle */
k=wid h(ω0);
nodes =∅;
while k>0do
nodes =∅;
o all ω∈Wdo
nodes =nodes ∩e en (ω, k);
episode =episode ∩nodes;
k=k−1;
In he abo e code, nodes =nodes ∩e en (ω,k)adds
e en s o exis ing in se ial and episode =episode ∩nodes
adds e en s o exis ing in pa allel. Fu he mo e, e en (ω,k)
ge s he e en in he i h posi ion.
No e ha he ime cons ain s be ween wo ela ed e en s is
he minimum be ween all simila pai s o e en s in he same
posi ion.
7 Expe imen a ion
The algo i hm does no been applied o e a eal da a se , bu
i has been p o en o e he sequences s1,s2and s3in Sec ion
6.
The maximum simila windows a e below:
ω1(0,4) = {(A, 0),(B,1),(B,2),(C, 3),(C, 4)}
ω2(0,4) = {(A, 0),(C, 1),(B,2),(C, 3),(B,4)}
ω3(1,6) = {(A, 1),(B,2),(B,3),(C, 4),(C, 6)}
Finally, he ch onicle can be iewed in Figu e 4.
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1
2
1
1
1
1
Figu e 4: The gene a ed ch onicle
8 Conclusions
We ha e s udied a me hod o ind all episodes ha occu e-
quen ly in a e en sequence, Mannila’s app oach, whose ob-
jec i e is o ind small equen episodes a i s and hen p o-
g essi ely looking o la ge equen episodes. A e ha , we
ha e de eloped a me hodology o disco e episodes in some
sequences based on Mannila’s app oach. Thus, a new simila -
i y be ween wo windows has been de ined o de e mine he
maximum ch onicle. To es he de elopmen o he me hod-
ology, i has been applied o h ee sample sequences o ob ain
he maximum common ch onicle. Ne e heless, we hink ha
his app oach can be sa is ac o ily applied o da a se s ha i
is he nex s ep o complemen his de elopmen .
Acknowledgmen s
This esea ch is pa ially suppo ed by he p ojec s o
he Spanish Minis y o Economy and Compe i i eness
ARTEMISA (TIN2009-14378-C02-01) and Simon (TIC-
8052) o he Andalusian Regional Minis y o Economy, In-
no a ion and Science.
Re e ences
[Baue e al., 2011]A. Baue , A. Bo ea, A. G as ien,
P. Haslum, and J. Rin anen. Ala m p ocessing wi h model-
based diagnosis o e en disc e e sys ems. In P oceedings
o he AI o an In elligen Plane , page 2. ACM, 2011.
[Be and e al., 2009]O. Be and, P. Ca le, and C. Choppy.
Modelling ch onicle ecogni ion o dis ibu ed simula ion
p ocessing wi h colou ed pe i ne s. In P oceedings o
he 2nd In e na ional Con e ence on Simula ion Tools and
Techniques, page 42. ICST (Ins i u e o Compu e Sci-
ences, Social-In o ma ics and Telecommunica ions Engi-
nee ing), 2009.
[C am e al., 2011]D. C am, B. Ma he n, and A. Mille. A
comple e ch onicle disco e y app oach: applica ion o ac-
i i y analysis. Expe Sys ems, 2011.
[Dousson and Ghallab, 1994]C. Dousson and M. Ghallab.
Sui i e econnaissance de ch oniques. Re ue din elligence
a i icielle, 8(1):29–61, 1994.
[Dousson e al., 2008]C. Dousson, F. Cle o , and F. Fessan .
Me hod o he machine lea ning o equen ch onicles
in an ala m log o he moni o ing o dynamic sys ems,
June 17 2008. US Pa en 7,388,482.
[Le Guillou e al., 2008]X. Le Guillou, M.O. Co die ,
S. Robin, and L. Roz´
e. Ch onicles o on-line diagnosis o
dis ibu ed sys ems. In P oceeding o he 2008 con e ence
on ECAI 2008: 18 h Eu opean Con e ence on A i icial
In elligence, pages 194–198. IOS P ess, 2008.
[Mannila and Ronkainen, 1997]H. Mannila and
P. Ronkainen. Simila i y o e en sequences. In Tem-
po al Rep esen a ion and Reasoning, 1997.(TIME’97),
P oceedings., Fou h In e na ional Wo kshop on, pages
136–139. IEEE, 1997.
[Mannila e al., 1997]H. Mannila, H. Toi onen, and
A. Inke i Ve kamo. Disco e y o equen episodes in
e en sequences. Da a Mining and Knowledge Disco e y,
1(3):259–289, 1997.
[Pencol´
e and Subias, 2009]Y. Pencol´
e and A. Subias. A
ch onicle-based diagnosabili y app oach o disc e e
imed-e en sys ems: Applica ion o web-se ices. Jou -
nal o Uni e sal Compu e Science, 15(17):3246–3272,
2009.
[Saddem e al., 2010]R. Saddem, A. Toguyeni, and M. Tag-
ina. Consis ency’s checking o ch onicles’ se using ime
pe i ne s. In Con ol & Au oma ion (MED), 2010 18 h
Medi e anean Con e ence on, pages 1520–1525. IEEE,
2010.
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