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Discovering RFM Sequential Patterns From Customers’ Purchasing Data
中央大學資管系陳彥良 教授
Date: 112/04/21
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Agenda
• Introduction
• Related Work
• Problem Definition
• Algorithm
• Performance Evaluation
• Conclusion
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Sequential Pattern Mining1
• Sequential pattern mining – To find the relationships between occurrences of
sequential events– To find if there exist any specific order of the
occurrences.
• Example– Every time Microsoft stock drops 5%,
IBM stock will also drops at least 4% within three days.
Introduction1
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Sequential Pattern Mining2
• Applications of sequential pattern mining– Customer shopping sequences:
• First buy computer, then CD-ROM, and then digital camera, within 3 months.
– Medical treatments, natural disasters (e.g., earthquakes), science & eng. processes, stocks and markets, etc.
– Telephone calling patterns, Weblog click streams– DNA sequences and gene structures
Introduction2
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Sequential Patterns v.s. Association Rules
Correlation between transactions
Correlation between transactions
Relationships intra transaction
Relationships intra transaction
CID Purchased Items
1
1
1
2
2
Which items are bought together?
( , )
Which items are bought in a certain order?
< , >
Introduction3
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What Is Sequential Pattern Mining?
• Given a set of sequences, find the complete set of frequent subsequences
A sequence database
A sequence : < (ef) (ab) (df) c b >
An element may contain a set of items.Items within an element are unorderedand we list them alphabetically.
<a(bc)dc> is a subsequence of <<a(abc)(ac)d(cf)>
Given support threshold min_sup =2, <(ab)c> is a sequential pattern
SID sequence
10 <a(abc)(ac)d(cf)>
20 <(ad)c(bc)(ae)>
30 <(ef)(ab)(df)cb>
40 <eg(af)cbc>
Introduction4
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A SPM Example and the Problems
• Since traditional SPM methods discover only frequencies of the maximal sequential patterns
– In a real-life situation the environment may change constantly and users’ behavior may also change over time
– A lot of patterns are of little value
Introduction5
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RFM Definition in Marketing by Bult and Wansbeek
• R (Recency): period from the last purchase to now– R↓: higher possibility the customer makes a repeated purchase
• F (Frequency): number of purchases made in a certain period– F↑: the customer has higher loyalty
• M (Monetary): the amount of money spent during a certain period– M↑: the customer is more important
Introduction6
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The Proposed Algorithm: RFM-SPM
• Frequency constraint (traditional SPM) Frequency, Recency and Monetary constraints (RFM-SPM)
• Each constraint has two thresholds– Upper threshold and lower threshold– Ensure considered factor can be restricted within a
specified range
• By setting these three factors to different intervals, we can discover those patterns which we feel interested
Introduction7
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Recency Constraint
• Specified by giving a range from Rtime_min to Rtime_max, which are the number of days away from the starting date of the sequence database.
Starting date Ending dateRtime_min = 200 Rtime_max = 270
200
270
Introduction8
Sequence DB
2002/12/312001/12/27 2001/12/27+200 2001/12/27+270
Ensuring that the last transaction of the pattern occurred in this interval
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Monetary Constraint
• Given by a range from M_min to M_max. It ensures that the value of the discovered pattern must be between the M_min and M_max.
• Suppose the pattern is <(a), (bc)>. Then we say a sequence satisfy this pattern with respect to the monetary constraint, if we can find an occurrence of pattern <(a), (bc)> in this data sequence whose value is within this range.
Introduction9
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Frequency Constraint
• The frequency of a pattern is the percentage of sequences in database that satisfy the recency constraint and monetary constraint.
• A pattern could be output as an RFM-pattern if its frequency falls within the interval of minsup_min and minsup_max.
Introduction10
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A Example of RFM-Pattern
• 30% of customers who bought a computer
would recently come back buying a scanner
and a microphone and the total amount of these
products is greater than NT 55,000 dollars.
Introduction11
• 30% of customers who bought a computer
would recently come back buying a scanner
and a microphone and the total amount of these
products is greater than NT 55,000 dollars.
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Related Work• Cluster
– Similar needs and/or characteristics that are likely to exhibit similar purchasing behaviors
• Classification– Classifying customers to different categories of customer value and
they are also used to classify unseen cases• Association rule
– Extracting Share Frequent Itemsets with Infrequent Subsets• SPM
– Constraint-Based Sequential Pattern Mining: the Consideration of Recency and Compactness
– Discovering RFM sequential patterns from customers’ purchasing data
Introduction Related work1
R F M
R F M
M
R F
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Data-Sequence in RFM-SPMIntroduction Related work Problem def1
Sid Sequence
10 <(a) (c) (ab) (a) (c)>
20 <(b) (c) (a), (b), (c) >
30 <(ab) (b) (c)>
40 <(b) (bc)>
50 <(c) (b) (ab) (bc)>
Traditional sequence DB
Sid Sequence
10 <(a, 1, 10), (c, 3, 40), (a, 4, 30), (b, 4, 70), (a, 6, 50), (c, 10, 70)>
20 <(b, 3, 30), (c, 5, 50), (a, 7, 20), (b, 7, 70), (c, 14, 20) >
30 <(a, 8, 40), (b, 8, 50), (b, 16, 20), (c, 20, 100)>
40 <(b, 15, 30), (b, 22, 20), (c,22, 120)>
50 <(c, 5, 30), (b, 6, 40), (a, 10, 30), (b, 10, 60), (b, 19, 90), (c, 19, 70)>
Transferred sequence DB
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An Overview of Program Definition
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Containment of itemsetContainment of itemset
SubsequenceSubsequence Recent SubsequenceRecent Subsequence
Recent Monetary Subsequence
Recent Monetary Subsequence
Introduction Related work Problem def2
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Example 3.1. (subsequence)
• Data-sequence A = – < (a, 1, 10), (c, 3, 40), (a, 4, 30), (b, 4, 70), (a, 6, 50), (e, 6, 90),
(c, 10, 70) >
Itemset (ab) - be contained in A [ ]
Sequence B <(ab)(ae)> - a subsequence of A [ ]
Introduction Related work Problem def3
Yes
Yes
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An Overview of Program Definition
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Containment of itemsetContainment of itemset
SubsequenceSubsequence Recent SubsequenceRecent Subsequence
Recent Monetary Subsequence
Recent Monetary Subsequence
Introduction Related work Problem def4
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Example 3.2. (recent subsequence)
• Data-sequence A = <(a, 1, 10), (c, 3, 40), (a, 4, 30), (b, 4, 70),
(a, 6, 50), (e, 6, 90), (c, 10, 70)>
• Rtime_min = 5 and Rtime_max = 8.
Sequence B <(ab)(ae)> - is a recent subsequence of A [
] Sequence B <(ab)(ae)> is a subsequence of A
The occurring time of itemset (ae)= 6 ≥ Rtime_min and 6 < Rtime_max
Introduction Related work Problem def5
Yes
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An Overview of Program Definition
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Containment of itemsetContainment of itemset
SubsequenceSubsequence Recent SubsequenceRecent Subsequence
Recent Monetary Subsequence
Recent Monetary Subsequence
Introduction Related work Problem def6
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Example 3.3. (recent monetary subsequence )
• Data-sequence A =
– <(a, 1, 10), (c, 3, 40), (a, 4, 30), (b, 4, 70), (a, 6, 50), (e, 6, 90), (c, 10, 70)>
• Rtime_min = 5, Rtime_max = 8 , M_min = 200, M_max = 250.
• Sequence B <(ab)(ae)> - is a recent monetary subsequence of A [
] Sequence B <(ab)(ae)> is a recent subsequence of A
The total money of this subsequence = 240 ≥ M_min and 240 < M_max.
Introduction Related work Problem def7
Yes
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Definition 3.1. (f-pattern, rf-pattern, rfm-pattern)• Let B = <I1I2...Is> be a sequence of itemsets.
Call B an Contain B as a Denote Thresholdf-pattern Subsequence f-support or B.supf no less than minsup_min
rf-pattern recent subsequence
rf-support or B.suprf
no less than minsup_min
rfm-pattern recent monetary subsequence
rfm-support or B.suprfm
between minsup_min and minsup_max
Introduction Related work Problem def8
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Example 3.4. (RFM pattern) • Given a data-sequence DB and six thresholds • R: Rtime_min=10 ≤ < Rtime_max = 21• M: M_min = 150 ≤ < M_max = 250• F: Minsup_min = 2 ≤ < Minsup_max = 4• The RFM-patterns are listed as follows:
– Containing 1 itemset = { }– Containing 2 itemsets ={<(ab)(c)> }– Containing 3 itemsets ={<(c)(b)(c)>, <(c)(ab)(c)> }– Containing 4 itemsets ={<(c)(b)(a)(c)>}
Sid Sequence
10 <(a, 1, 10), (c, 3, 40), (a, 4, 30), (b, 4, 70), (a, 6, 50), (c, 10, 70)>
20 <(b, 3, 30), (c, 5, 50), (a, 7, 20), (b, 7, 70), (c, 14, 20) >
30 <(a, 8, 40), (b, 8, 50), (b, 16, 20), (c, 20, 100)>
40 <(b, 15, 30), (b, 22, 20), (c,22, 120)>
50 <(c, 5, 30), (b, 6, 40), (a, 10, 30), (b, 10, 60), (b, 19, 90), (c, 19, 70)>23
Introduction Related work Problem def9
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RFM-Apriori Algorithm
• The RFM-Apriori algorithm is developed by modifying the well-know Apriori (GSP) algorithm
• GSP
– Put all items into C1, the set of candidate f-patterns with length 1, and then scans the database to find the frequent 1-patterns (L1)
– Assume we already have the set of frequent (k-1)-patterns Lk-1. Then it generates the set of candidate f-patterns Ck by joining Lk-1 with Lk-1
– Afterwards, it scan the database to determine the supports of the patterns in Ck, and then find out Lk
Introduction Related work Problem def RFM-Apriori Algorithm1
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RFM-Apriori AlgorithmIntroduction Related work Problem def RFM-Apriori Algorithm2
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C1 L1 C2 L2 Lk-1… Ck
CI1(LI1
f)
LI1(LI1
f, LI1rf, LI1
rfm)
CI2 LI2(LI2
rf, LI2rfm)
LIk-1(LIk-1
rf, LIk-1rfm)
… CIk
LI1f x LI1
rf
L1 x L1
LIk-1rf x LIk-1
rfApriori
All items Lk-1 x Lk-1
1
2 3 4
Candidate Generation
Support Counting
Let CIk denote the set of candidate rf-patterns with length k in RFM-Apriori
Count B.supf
CountB.Suprf
B.suprfm
1InverseCandidateTree
Lk
LIk(LIk
rf, LIkrfm)
2
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Example 4.1. (Candidate generation- CI2)
• Suppose LI1f= {<a>, <b>, <c>, < (ab)>, < (bc)>} and
LI1rf= {<b>, <c>}, the CI2 is as follows:
– CI2={<(a)(b)>, <(a)(c)>, <(b)(b)>, <(b)(c)>, <(c)(b)>, <(c)(c)>, (ab)(b)>, <(ab)(c)>, (bc)(b)>, <(bc)(c)> }
illustrationLI1
f LI1rf
b c
…….
abcabbc
Introduction Related work Problem def RFM-Apriori Algorithm3
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Example 4.2. (Candidate generation- CIk, k>2)
• Suppose LI3rf={<(b)(a)(c)>, <(c)(a)(c)>, <(b)(b)(c)>,
<(c)(b)(c)>, <(b)(ab)(c)>, <(c)(ab)(c)> }, the CI4 is as follows:– CI4={<(b)(c)(a)(c)>, <(c)(b)(a)(c)>, <(b)(b)(a)(c)>,
<(c)(c)(a)(c)>,<(b)(b)(b)(c)>, <(b)(c)(b)(c)>, <(c)(b)(b)(c)>,<(c)(c)(b)(c)>,<(b)(b)(ab)(c)>,<(b)(c)(ab)(c)>, <(c)(b)(ab)(c)>,<(c)(c)(ab)(c)> }
<(b)(ab)(c)> <(c)(ab)(c)>LI3rf:
{<(b)(c)(ab)(c)>, <(c)(b)(ab)(c)>}CI4:
illustration
Introduction Related work Problem def RFM-Apriori Algorithm4
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RFM-Apriori Algorithm – Example• Given a data-sequence DB and six thresholds
Rtime_min=10, Rtime_max=21, M_min=150,
M_max=250, Minsup_min=2 and Minsup_max=4, try to
find the patterns that satisfy RFM constrains
Introduction Related work Problem def RFM-Apriori Algorithm5
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CI1
LI1
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Synthetic data parameters
Introduction Related work Problem def RFM-Apriori Algorithm Experiment1
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Synthetic data parameters settings
|S| = 4, |I| = 1.25, NS = 5000, NI = 25,000, N = 10000, TI = 10, H_price = 1000, M_price = 500, L_price = 100, H_quantity = 1, M_quantity = 3 and L_quantity = 1.
Introduction Related work Problem def RFM-Apriori Algorithm Experiment2
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Real-life dataset – SC-POS
• The sales data of a chain supermarket in Taiwan.• The SC-POS dataset recorded all transactions from
twenty branches between 2001/12/27 and 2002/12/31.
• Each transaction in SC-POS dataset is the shopping list of a customer’s transactions, each transaction of which recorded the purchased date and time and the purchased items.
• A series of data preprocessing and cleaning tasks were performed, the final dataset contained 17685 items and 33500 customers’ data-sequences.
Introduction Related work Problem def RFM-Apriori Algorithm Experiment3
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Test 4.1. Comparing the runtimes and number of patterns of the two algorithms
• Varying minsup_min from 1.25% to 0.5% in synthetic datasets
• Varying minsup_min from 3.5% to 2.5% in real-life dataset.
Introduction Related work Problem def RFM-Apriori Algorithm Experiment4
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0
50
100
150
200
0.005 0.008 0.01 0.013
minsup_min
Run
time(
sec)
GSPRFM
0
500
1000
1500
2000
2500
3000
0.005 0.008 0.01 0.013
minsup_min
num
ber o
f patt
erns
GSPRFM
0
5000
10000
15000
20000
0.025 0.03 0.035
minsup_min
Run
time(
sec)
GSPRFM
0100200300400500600700
0.025 0.03 0.035
minsup_min
num
ber of
pat
tern
sGSPRFM
SYN-DS1
SC-POS
Introduction Related work Problem def RFM-Apriori Algorithm Experiment5
More complicated procedure to generate candidate pattern and compute supports
Generates fewer candidate and frequent patterns
>
<
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Test 4.2. Scalability test• During this test, we vary the value of a selected
parameter and keep all the other parameters constant.
• In each test, a parameter is increased to determine how the algorithms scale-up as the parameter increases.
– The first test varies the number of customers, lDl; from 250,000 to 750,000;
– The second varies the average number of transactions per customer, lCl; from 10 to 20
– The final one varies the average number of items bought per transaction, lTl; from2.5 to 4.5
Introduction Related work Problem def RFM-Apriori Algorithm Experiment6
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0
100200
300
400500
600
250K 500K 750K
| D|
Run
time(
sec)
GSPRFM
0
5001000
1500
20002500
3000
250K 500K 750K
| D|
num
ber of
pat
tern
s
GSPRFM
Introduction Related work Problem def RFM-Apriori Algorithm Experiment7
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Introduction Related work Problem def RFM-Apriori Algorithm Experiment8
0200400600800
100012001400
10 15 20
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Longer sequences would result in more patterns
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Test 4.3. Testing the reaction of runtime and number of patterns by varying following parameters
• Varying the Rtime_min from 75 to 115
• Varying the M_min from 1000 to 5000
Introduction Related work Problem def RFM-Apriori Algorithm Experiment9
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Introduction Related work Problem def RFM-Apriori Algorithm Experiment10
CIK=LIK-1rf x LIK-1
rf
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Test 4.4. Comparing the number of three kinds of interesting patterns
• (*F*)
• (RF*)
• (RFM)
Introduction Related work Problem def RFM-Apriori Algorithm Experiment11
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Introduction Related work Problem def RFM-Apriori Algorithm Experiment12
C10-T2.5-S4-I1.25 RF* RFM *F*
Name # of patterns
% # of patterns
% # of patterns
%
D=25, minsup_min=0.075 186 22 48 6 835 100%
D=50, minsup_min=0.075 189 24 23 3 796 100%
D=75, minsup_min =0.075 187 24 23 3 793 100%
C=10, minsup_min =0.015 4 4 0 0 99 100%
C=15, minsup_min =0.015 78 22 5 1 360 100%
C=20, minsup_min =0.015 293 29 36 4 1001 100%
T=2.5, minsup_min =0.008 152 22 43 6 700 100%
T=3.5, minsup_min =0.008 639 28 204 9 2273 100%
T=4.5, minsup_min =0.001 1122 25 455 10 4554 100%
SC-POS,minsup_min =0.015
168 10 14 1 1704 100%
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Test 4.5. Segment the discovered patterns by RFM constraints as following
Divisions R F M
1 0-75 0.007-0.008
0-100
2 75-150 0.008-0.009
100-200
3 150-225 0.009-0.01 200-300
4 225-300 0.01-0.02 300-400
5 300-360 0.02-1 400-
RFM-segmentation # of patterns
1-1-1(R-F-M) 50
3-3-3 0
5-5-5 3
1-5-1 40
5-1-1 97
1-1-5 0
5-1-5 17
1-5-5 0
5-5-1 22
5-3-5 4
3-5-5 0
5-5-3 3
Introduction Related work Problem def RFM-Apriori Algorithm Experiment13
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Managerial Applications
• Growing patterns: (RFM)– A(BC) in segments 122, 233, 334, 445, 555
• Weakening patterns– A(BC) in segments 134, 233, 322, 421, 511
• Dead patterns: – A(BC) in segments 123, 211
• Emerging patterns– A(BC) in segments 412, 523
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Introduction Related work Problem def RFM-Apriori Algorithm Experiment14
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Managerial Applications
• Stable patterns – A(BC) in segments 132, 232, 332, 432, 532
• Sort all patterns with R=3 according to M
• Sort all patterns with R=3 according to F
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Introduction Related work Problem def RFM-Apriori Algorithm Experiment14
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Conclusion
• We have developed an efficient algorithm for mining frequent patterns with consideration of Recency and Monetary.
• These two factors can help users identify those patterns which are active recently and have high monetary value
• Besides, the experiments showed our approach is more efficient than the traditional GSP algorithm.
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Thanks for your attention!!!!!