在商業環境裡，客戶是整個產品價值鏈最後付錢購買的人，因此對於客戶的理解，以及對於顧客價值管理與顧客貢獻度的研究，是企業獲利分析的最重要環節之一。消費品市場的特色包括產品項目多、顧客數目多、消費筆數多、在一定時間間隔內持續購買、消費金額不大、重複購買相同產品等；而且，不同的顧客群體，因為購買力不同，使用習慣不同，購買金額、購買間隔也會不同。因此，時間軸的資訊，是分析顧客消費行為的關鍵要素之一。本研究以時間性資料探勘技術(Temporal Data Mining)，建立重複購買序列型樣的數學模型，將序列型樣中各事件的次序、間隔、頻率轉換為一個離散數值的數學結構。藉著分析函數的數學特性，找出實際消費行為的規律與變化關係，包括：是否有重複購買現象、重複購買是否有週期、反覆購買同一項目次數、特定消費行為的延續時間等。透過數學模型的建構，結合產業知識 (industry know-how) ，得到更豐富、準確的關於顧客的知識。根據顧客消費行為的知識，企業經營者可以採取更有效率、更即時、更有針對性的行銷策略，以獲得最佳收益。

Consumer market has several characteristics in common such as repeat-buying over the relevant time frame, a large number of customers, and a wealth of information detailing past customer purchases. Analyzing the characterizations of repeat-buying is necessary to understand and adapt to dynamics of customer behavior for company to survive in a continuously changing environment. The aim of this research is to develop a methodology to detect the existence of repeat-buying behavior and discover the potential period of the repeat-buying behavior. A mathematical model to capture the characteristics of repeat-buying behavior is devised. The algorithms based on our previous works then proposed to provide a scheme to discover periodicity and trends of the purchase. Two fundamental repeat-buying types has been identified and analyzed. Any repeat-buying scenarios can be expressed as the combination of the two fundamental types. The proposed mathematical model coupled with our works on repeat-buying modeling form a process to uncover the characteristics of repeat-buying phenomenon. Coupled with industry domain knowledge and marketers’ expertise, the constructed model helps to predict likely buying behavior, then the corresponding actions can be taken to maximize enterprise's revenue.

Table of Contents
1. Introduction	1
1.1 Background	1
1.2 Motivation and Research Objectives	4
1.3 Organization of this Dissertation	6
2. Literature Review	7
2.1 Temporal Data Mining	7
2.2 Pattern Discovery	10
2.2.1 Sequential Patterns	13
2.2.2 Frequent Episode	20
2.2.3 Patterns with explicit time constraints 	22
2.3 Periodic Mining	25
3. Repeat-Buying Analysis	30
3.1 Repeat-Buying Sequence	30
3.2 Repeat-Buying Distribution Function	34
3.3 General Periodicity Detection (GPD)	36
3.4 Repeat-Buying Sequence Analyzer (RBSA)	41
3.5 Repeat-Buying Modeler (RBM)	45
4. Experimental Results	49
4.1 Data Sources	49
4.2 Experiment Setup	50
4.3 Comparison between RBM and CMA	51
4.3.1 Comparing RBDF and TDF	51
4.3.2 Applying RBM on 2-rb-sequence	53
4.4 Repeat-Buying Phenomenon in Consumer Market 	55
4.4.1 Repeat-Buying of physical goods	55
4.4.2 Repeat-Buying of digital services	58
4.5 Lessoned learned from repeat-buying analysis	62
4.5.1 Histogram as a helper 	62
4.5.2 Study on segmentation	64
4.5.3 RBM as a descriptive model	67
5. Conclusions	70
6. References	72

List of Figures
Fig. 1 Overview of Temporal Patterns	12
Fig. 2 The Apriori-based algorithm GSP takes the breadth-first approach (Source: Pei et al., 2004)	16
Fig. 3 Projection-based algorithm takes the depth-first approach (Source: Dong, 2009)	16
Fig. 4 An example of event sequence	20
Fig. 5 Types of episodes	21
Fig. 6. A sample of timed finite automata with granularities (Source: Bettini, Wang & Jajodia, 1996 )	23
Fig. 7 Universal Formulation of Sequential Patterns (Source: Joshi, Karypis & Kumar, 2001)	24
Fig. 8 A time-interval sequential pattern (a, i1, b, i2, c)	27
Fig. 9 Pseudocode for computing TDF	28
Fig. 10 Two fundamental types of repeat-buying sequences	31
Fig. 11. The plot of  f(x) = (sin(x)+ 1.5)(24 - x)/18.	37
Fig. 12 The pseudocode of GPD	39
Fig. 13 Vertical dotted line drawn at an interval 2π, solid lines drawn at an interval of 6.39	40
Fig. 14. The pseudocode of RBSA	42
Fig. 15 The plot the sequence <108510> is a linear decreasing function	43
Fig. 16 The domain is divided into two sub-domains at the point Xmax = 112  	44
Fig. 17 The plot of the RBDF f1(x) defined on [1, 111]	44
Fig. 18 The plot of the RBDF f2(x) defined on [112, 360]	45
Fig. 19. The pseudocode of algorithm RBM	46
Fig. 20 There are 3889 transactions in which product 3103 and 3801 are purchased together	47
Fig. 21. The output of modified AprioriAll Algorithm	51
Fig. 22 Analysis result <3301, 3304> based on CMA (Chiang, Wang, Chen & Chen, 2009)	53
Fig. 23 The plot of the model of <3301, 3304> established by RBSA	53
Fig. 24 There 10,323 transactions such that customers purchase 3301 and 3304 simultaneously	54
Fig. 25 The counts of interval between 3302 and 3103 in year 2000	56
Fig. 26 The counts of interval between 3302 and 3103 in year 2001	56
Fig. 27 The plot of repeat-buying sequence <3302, 3103> in year 2000	57
Fig. 28 The plot of repeat-buying sequence <3302, 3103> in year 2001	57
Fig. 29  The plot of RBDF of <1004> obtained from 2007 database	59
Fig. 30 The repeat-buying models of  <1004> obtained during 2007-2009	59
Fig. 31 The plot of RBDF of <67466> obtained from 2007 database	60
Fig. 32 The repeat-buying models of  <67466> obtained during 2007-2009	60
Fig. 33 The plot of RBDF of <72175> obtained from 2007 database	61
Fig. 34 The repeat-buying models of  <72175> obtained during 2007-2009	61
Fig. 35 The number of points of <58089> are too little to plot a curve	63
Fig. 36 The sequence <81624> obtained from 2009 database is similar to <58089>	63
Fig. 37 The plot of <2001> obtained from Company A's 2001 database	65
Fig. 38 The result of GPD applied to Group A	66
Fig. 39 The result of GPD applied to Group A	66
Fig. 40 Each year, the sales of <1004> slumps steeply	68
Fig. 41 Stacked bar chart of <1004>'s acquisition channels	69

List of Tables
Table 1 Transactions conducted by five customers in two months	14
Table 2 Multi-dimensional sequence database	18
Table 3 Company A's Database Size	49
Table 4 The transactions conducted by Company B's members during 2007-2009	50
Table 5 The acquisition channels of <1004>	68

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