Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Course on Data Mining (581550-4)
Intro/Ass. Rules
7.11.
24./26.10.
Clustering
14.11.
Episodes
KDD Process
Home Exam
30.10.
Text Mining
21.11.
28.11.
Appl./Summary
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Course on Data Mining (581550-4)
Today 31.10.2001
•
Today's subject:
– Episodes and episode rules
•
Next week's program:
– Lecture:
– Exercise:
– Seminar:
Text mining
Episodes and episode rules
Episodes and episode rules
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Episodes and Episode Rules
Basics
WINEPI Approach
MINEPI Approach
Algorithms
Examples
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
• Association rules describe how things occur together in
the data
– E.g., "IF an alarm has certain properties, THEN it will
have other given properties"
• Episode rules describe temporal relationships between
things
– E.g., "IF a certain combination of alarms occurs within
a time period, THEN another combination of alarms
will occur within a time period"
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
Network Management System
MSC
MSC
MSC
BSC
BSC
BSC
Switched Network
Access Network
Alarms
BTS
BTS
BTS
MSC
Mobile station controller
BSC
Base station controller
BTS
Base station transceiver
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
• As defined earlier, telecom data contains alarms:
1234 EL1 PCM 940926082623 A1 ALARMTEXT..
Alarm type
Date, time
Alarming network element
Alarm number
Alarm severity class
• Now we forget about relationships between attributes
within alarms as with the association rules
• We just take the alarm number attribute, handle it here
as event/alarm type and inspect the relationships
between events/alarms
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
• Data:
– Data is a set R of events
– Every event is a pair (A, t), where
• A  R is the event type (e.g., alarm type)
• t is an integer, the occurrence time of the event
– Event sequence s on R is a triple (s, Ts, Te)
• Ts is starting time and Te is ending time
• Ts < Te are integers
• s =  (A1, t1), (A2, t2), …, (An, tn) 
• Ai  R and Ts  ti < Te for all i=1, …, n
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
• Example alarm data sequence:
D C A
0
10
B
20 30 40
D A B
C
A
D
C A
B
D A
50 60 70 80 90 100 110 120 130 140 150
• Here:
– A, B, C and D are event (or here alarm) types
– 10…150 are occurrence times
– s =  (D, 10), (C, 20), …, (A, 150) 
– Ts (starting time) = 10 and Te (ending time) = 150
• Note: There needs not to be events on every time slot!
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
• Episodes:
– An episode is a pair (V, )
• V is a collection of event types, e.g., alarm types
•  is a partial order on V
– Given a sequence S of alarms, an episode  = (V, )
occurs within S if there is a way of satisfying the event
types (e.g., alarm types) in V using the alarms of S so
that the partial order  is respected
– Intuitively: episodes consist of alarms that have certain
properties and occur in a certain partial order
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
• The most useful partial orders are:
– Total orders
• The predicates of each episode have a fixed order
• Such episodes are called serial (or "ordered")
– Trivial partial orders
• The order of predicates is not considered
• Such episodes are called parallel (or "unordered")
• Complicated?
– Not really, let's take some clarifying examples
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Basics
• Examples:
A
B
A
A
C
B
Serial episode
Parallel
episode
B
More complex
episode with
serial and parallel
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• The name of the WINEPI method comes from the
technique it uses: a sliding window
• Intuitively:
– A window is slided through the event-based data
sequence
– Each window "snapshot" is like a row in a database
– The collection of these "snapshots" forms the rows in
the database
• Complicated?
– Not really, let's take a clarifying example
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Example alarm data sequence:
D C A
0
10
B
20 30 40
D A B
C
50 60 70 80 90
• The window width is 40 seconds, last point excluded
• The first/last window contains only the first/last event
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Formally, given a set E of event types an event sequence
S = (s,Ts,Te) is an ordered sequence of events eventi such
that eventi  eventi+1 for all i=1, …, n-1, and Ts  eventi <
Te for all i=1, …, n
event1
event2
event3
…
…
eventn
Ts
t1
Te
t2
t3
…
…
tn
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Formally, a window on event sequence S is an event
sequence S=(w,ts,te), where ts < Te, te > Ts, and w consists of
those pairs (event, t) from s where ts  t < te
• The value ts  t < te is called window width, W
event1
event2
event3
…
…
eventn
Ts
t1
Te
t2
t3
ts W te
tn
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• By definition, the first and the last windows on a sequence
extend outside the sequence, so that the last window
contains only the first time point of the sequence, and the
last window only the last time point
event1
event2
event3
…
…
eventn
Ts
ts W tt1e
Te
t2
t3
tn
ts W te
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• The frequency (cf. support with association rules) of an
episode  is the fraction of windows in which the episode
occurs, i.e.,
fr(, S, W) =
|Sw  W(S, W) |  occurs in Sw |
|W(S, W)|
where W(S, W) is the set of all windows Sw of sequence S
such that the window width is W
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• When searching for the episodes, a frequency threshold
(cf. support threshold with association rules) min_fr is used
• Episode  is frequent if fr(, s, win)  min_fr, i.e, "if the
frequency of  exceeds the minimum frequency threshold
within the data sequence s and with window width win"
• F(s, win, min_fr): a collection of frequent episodes in s
with respect to win and min_fr
• Apriori trick holds: if an episode  is frequent in an event
sequence s, then all subepisodes    are frequent
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Formally, an episode rule is as expression   , where 
and  are episodes such that  is a subepisode of 
• An episode  is a subepisode of  (  ), if the graph
representation  is a subgraph of the representation of 
A
:
A
:
B
C
B
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• The fraction
fr(, S, W)
fr(, S, W)
= frequency of the whole episode
= frequency of the LHS episode
is the confidence of the WINEPI episode rule
• The confidence can be interpreted as the conditional
probability of the whole of  occurring in a window, given
that  occurs in it
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Intuitively:
– WINEPI rules are like association rules, but with an
additional time aspect:
If events (alarms) satisfying the rule antecedent (lefthand side) occur in the right order within W time units,
then also the rule consequent (right-hand side) occurs in
the location described by , also within W time units
antecedent  consequent [window width] (f, c)
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Algorithm
• Input: A set R of event/alarmtypes, an event sequence s over R, a set E
of episodes, a window width win, and a frequency threshold min_fr
• Output: The collection F(s, win, min_fr)
• Method:
1. compute C1 := {  E | || = 1};
2. i := 1;
3. while Ci  do
4.(*
compute F(s, win, min_fr) := {  Ci | fr(, s, win)  min_fr};
5.
i := l+1;
6.(** compute Ci:= {  E | || = I, and   F||(s, win, min_fr) for
all   E,   };
(* = database pass, (** candidate generation
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Algorithm
• First problem: given a sequence and a episode, find out
whether the episode occurs in the sequence
• Finding the number of windows containing an occurrence
of the episode can be reduced to this
• Successive windows have a lot in common
• How to use this?
– An incremental algorithm
– Same idea as for association rules
– A candidate episode has to be a combination of two episodes of
smaller size
– Parallel episodes, serial episodes
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Algorithm
• Parallel episodes:
– For each candidate  maintain a counter .event_count:
how many events of  are present in the window
– When .event_count becomes equal to ||, indicating
that  is entirely included in the window, save the
starting time of the window in .inwindow
– When .event_count decreases again, increase the field
.freq_count by the number of windows where 
remainded entirely in the window
• Serial episodes: use a state automata
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Example alarm data sequence:
D C A
0
10
B
20 30 40
D A B
C
50 60 70 80 90
• The window width is 40 secs, movement step 10 secs
• The length of the sequence is 70 secs (10-80)
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• By sliding the window, we'll get 11 windows (U1-U11):
…
U1
U2
U11
D C A
0
10
B
20 30 40
D A B
C
50 60 70 80 90
• Frequency threshold is set to 40%, i.e., an episode has
to occur at least in 5 of the 11 windows
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Suppose that the task is to find all parallel episodes:
– First, create singletons, i.e., parallel episodes of size 1 (A, B, C, D)
– Then, recognize the frequent singletons (here all are)
– From those frequent episodes, build candidate episodes of size 2:
AB, AC, AD, BC, BD, CD
– Then, recongize the frequent parallel episodes (here all are)
– From those frequent episodes, build candidate episodes of size 3:
ABC, ABD, ACD, BCD
– When recognizing the frequent episodes, only ABD occurs in more
than four windows
– There are no candidate episodes of size four
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• Episode frequencies and example rules with WINEPI:
D
C
A
B
DC
DA
DB
CA
CB
AB
DAB
: 73%
: 73%
: 64%
: 64%
: 45%
: 55%
: 45%
: 45%
: 45%
: 45%
: 45%
D  A [40] (55%, 75%)
D A  B [40] (45%, 82%)
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI: Experimental Results
• Data:
– Alarms from a telecommunication network
– 73 000 events (7 weeks), 287 event types
– Parallel and serial episodes
– Window widths (W) 10-120 seconds
– Window movement = W/10
– min_fr = 0.003 (0.3%), frequent: about 100 occurrences
– 90 MHz Pentium, 32MB memory, Linux operating
system. The data resided in a 3.0 MB flat text file
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Mika Klemettinen and Pirjo Moen
Nokia Research Center
TypeYourNameHere
University of Helsinki/Dept of CS
DOCUMENTTYPE
Autumn 2001
1 (1
TypeDateHere
WINEPI: Experimental Results
Window
width (s)
10
20
40
60
80
100
120
Serial episodes
Parallel episodes
#frequent time (s) #frequent time (s)
16
31
10
8
31
63
17
9
57
117
33
14
87
186
56
15
145
271
95
21
245
372
139
21
359
478
189
22
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
WINEPI Approach
• One shortcoming in WINEPI approach:
– Consider that two alarms of type A and one alarm of
type B occur in a window
– Does the parallel episode consisting of A and B appear
once or twice?
– If once, then with which alarm of type A?
D C A
0
10
B
20 30 40
D A B
C
50 60 70 80 90
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• Alternative approach to discovery of episodes
– No sliding windows
– For each potentially interesting episode, find out the
exact occurrences of the episode
• Advantages: easy to modify time limits, several time
limits for one rule:
"If A and B occur within 15 seconds, then C follows
within 30 seconds"
• Disadvantages: uses a lots of space
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• Formally, given a episode  and an event sequence S, the
interval [ts,te] is a minimal occurrence  of S,
– If  occurs in the window corresponding to the interval
– If  does not occur in any proper subinterval
• The set of minimal occurrences of an episode  in a
given event sequence is denoted by mo():
mo() = { [ts,te] | [ts,te] is a minimal occurrence of  }
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• Example: Parallel episode  consisting of event types A
and B has three minimal occurrences in s: {[30,40],
[40,60], [60,70]},  has one occurrence in s: {[60,80]}
A
:
:
B
D C A
0
10
A
C
B
B
20 30 40
D A B
C
50 60 70 80 90
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• Informally, a MINEPI episode rule gives the conditional
probability that a certain combination of events (alarms)
occurs within some time bound, given that another combination of events (alarms) has occurred within a time bound
• Formally, an episode rule is  [win1]   [win2]
•  and  are episodes such that    ( is a subepisode of
)
• If episode  has a minimal occurrence at interval [ts,te]
with te - ts  win1, then episode  occurs at interval [ts,t'e]
for some t'e such that t'e - ts  win2
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• The confidence of the rule  [win1]   [win2] is the
conditional probability that  occurs, given that  occurs,
under the time constraints specified by the rule:
|mo()| / |mo()|
where |mo()| is the number of minimal occurrences [ts,te]
of  such that te - ts  win1, and |mo()| is the number of
such occurrences where there is also an occurrence of 
within the interval [ts,ts+win2]
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• The frequency of the rule  [win1]   [win2] is |mo()|,
i.e., the number of times the rule holds in the database
• Let's take our example data again:
– Task: find all serial episodes by using maximum time
bound of 40 secs and window sizes 10, 20, 30 and 40
secs. Frequency threshold is set to one occurrence
D C A
0
10
B
20 30 40
D A B
C
50 60 70 80 90
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• Find all serial episodes (1/3):
– First, create singletons, i.e., episodes of size 1 (A, B, C,
D)
– While creating the singletons, we also create an
occurrence table for them. After this first database pass,
we do not have to scan the database anymore, but use
the created inverse tables
– Then, recognize the frequent singletons (here all are)
– From those frequent episodes, build candidate episodes
of size 2: AB, BA, AC, CA, AD, DA, BC, CB, BD, DB,
CD, DC
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• Find all serial episodes (2/3):
– Then, use the inverse table to create minimal
occurrences for the candidates. E.g., for AB take all
subepisodes, namely A and B, and compute mo(AB) as
follows:
• Read the first occurrence of A (30-30), and find the
first following B (40-40)
• Then take the second occurrence of A (60-60), and
find the first following B (70-70)
• Then continue with BA
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
• Find all serial episodes (3/3):
– In the recognition phase, we find all episodes frequent
and build the candidate episodes of size 3. Again,
almost all candidates are frequent
– Finally, the same procedure is repeated for candidates
of size 4, and episodes DCAB in 10-40, DABC in 50-80,
CABD in 20-50, CBDA in 20-60, and BDAC in 40-80
are found to occur
– Candidates of size 5 are not found, so the algorithm
terminates
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Minimal (serial) occurrences
+ frequencies in example data
MINEPI Approach
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
IF
D
THEN C
WITH [0] [10] 0.00 (0/2)
[0] [20] 0.50 (1/2)
[0] [40] 1.00 (2/2)
IF
D
A
THEN C
WITH [40] [40] 0.50 (1/2)
[20] [40] 1.00 (1/1)
IF
D
THEN A
C
WITH [0] [10] 0.00 (0/2)
[0] [40] 0.50 (1/2)
IF
D
C
THEN A
B
WITH [40] [40] 0.50 (1/2)
[30] [40] 1.00 (1/1)
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI Approach
IF
D
A
B
THEN C
WITH [40] [40] 0.50 (1/2)
[30] [40] 1.00 (1/1)
• Below are minimal
occurrences of the example
rules in the example data:
DAB, DCAB
DC
D C A
0
10
DC, DAC, DABC
B
20 30 40
DA
D A B
C
50 60 70 80 90
DA
DAB
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI: Experimental Results
• The same data set as with WINEPI:
– Alarms from a telecommunication network
– 73 000 events (7 weeks), 287 event types
– Serial MINEPI episodes
– Time bounds 15-120 seconds
– Window movement = W/10
– min_fr = 50-500
– 90 MHz Pentium, 32MB memory, Linux operating
system. The data resided in a 3.0 MB flat text file
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI: Experimental Results
• Number of episodes and rules:
Min_fr
50
100
250
500
15,30
1131
617
418
217
111
57
46
21
Time bounds (s)
30,60
60,120
2278 1982 5899 7659
739
642
1676 2191
160
134
289
375
59
49
80
87
15,30,60,120
5899 14205
1676 3969
289
611
80
138
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
MINEPI: Experimental Results
• Execution times:
Min_fr
50
100
250
500
15,30
158
80
56
50
Time bounds (s)
30,60
60,120
210
274
87
103
56
59
51
51
15,30,60,120
268
104
58
52
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Summary
• Episode rule mining:
– Based on association rule techniques
– Targeted for temporal data
• Two approaches:
– WINEPI with a sliding window
– MINEPI with the search for minimal occurrences
• The approaches can be used for different purposes
• In the seminar presentations, we will take a look at…
– some other approaches towards sequential pattern mining and
– incremental sequential pattern mining
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
References
• Mika Klemettinen, A Knowledge Discovery Methodology for
Telecommunication Network Alarm Databases. Report A-1999-1 (PhD
Thesis), University of Helsinki, Department of Computer Science,
January 1999. ISBN 951-45-8465-1, ISSN 1238-8645. See electronic
version at http://www.cs.helsinki.fi/u/mklemett/THESIS/, especially
pages 27-49
• H. Mannila, H. Toivonen, and A. I. Verkamo, Discovery of frequent
episodes in event sequences, Technical Report C-1997-15, Dept. of
Computer Science, University of Helsinki, 1997. See electronic
version at http://www.cs.helsinki.fi/research/fdk/datamining/pubs/C1997-15.ps.gz
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Course Organization
Next Week
•
Lecture 7.11.: Text mining
– Mika gives the lecture
•
Excercise 8.11.: Episodes and episode
rules
– Pirjo takes care of you! :-)
•
Seminar 9.11.: Episodes and episode
rules
– Mika gives the lecture
– 2 group presentations
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Seminar Presentations
• Seminar presentations:
– Articles are given on previous
week's Wed
– Presentation in an HTML page
(around 3-5 printed pages) due
to seminar starting:
• Can be either a HTML
page or a printable
document in
PostScript/PDF format
– 30 minutes of presentation
– 5-15 minutes of discussion
– Active participation
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Seminar Presentations
• Seminar presentations:
– Try to understand the
"message" in the article
– Try to present the basic ideas
as clearly as possible, use
examples
– Do not present detailed
mathematics or algorithms
– Test: do you understand your
own presentation?
– In the presentation, use
PowerPoint or conventional
slides
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Seminar Presentations/Groups 3-4
Sequential Patterns
R. Agrawal, R. Srikant:
"Mining Sequential
Patterns", ICDE 1995.
Incremental Mining
F. Masseglia, P. Poncelet and
M. Teisseire: "Incremental
Mining of Sequential
Patterns in Large
Databases", BDA'00.
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Mika Klemettinen and Pirjo Moen
University of Helsinki/Dept of CS
Autumn 2001
Episodes and Episode Rules
Thank you for
your attention!
Thanks to Heikki Mannila for his slides which greatly helped in
preparing this lecture!
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