Draw Influence Diagram From Decision Tree

Influence Diagram

Spreadsheets

Shashidhar Kaparthi , Daniel J. Power , in Encyclopedia of Information Systems, 2003

III.H.3. Visual Spreadsheeting Using Influence Diagrams

An influence diagram provides a graphical presentation of the relationships in a model. Arrows are used to depict the influence of certain variables on other variables. The direction of the arrow indicates the direction of the influence. Typically, rectangles are used to represent independent or decision variables, circles are used to represent uncontrollable or intermediate variables, and ovals are used to represent dependent or outcome variables. An influence diagram can be drawn using the drawing toolbar that allows users to superimpose geometric shapes on a worksheet. Such diagrams allow the visualization of relationships between variables in a model that would normally be hidden inside formulas. An influence diagram for the car loan analysis previously discussed is presented in Fig. 9.

Figure 9. Influence diagram of a car loan analysis model.

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Quantitative and Systemic Methods for Modeling Sustainability

Amin Hosseinian-Far , Hamid Jahankhani , in Green Information Technology, 2015

Influence Diagram vs. Decision Tree

Influence diagrams can construct a decision problem, but the fact is that only the surface of the decision problem is covered. However, decision trees (DT) reveal more details about the decision problem. Each route in a DT represents probability branches ( Burton, 2014).

According to DECIDE-IT user manual (2011), the order of nodes in an ID is not as important as it is in a DT. This flexibility gives preference to using IDs rather than DTs. According to Decision IT, this suppleness gives the decision maker the opportunity to adjust decision variables accordingly at different stages of modeling.

IDs and DTs can be converted into each other. There is slight difference in constructions because the DTs cannot be constructed with the chance node in the beginning of the diagram. For instance, chance node alpha should not precede the decision node beta because the decision variable in a DT cannot depend on a chance node. Similarly, adding nodes would become problematic because the addition of decision nodes, which depend on an uncertain chance, are not valid (DecideIT, 2011).

The majority of DTs and IDs can be interchangeable; therefore, the consideration and selection of a specific tool might not be an issue for all problem domains; both DT and ID can capture the logic of the decision scenario and develop the DSS.

IDs are perfect for showing a decision's organization but encapsulate some details. A DT reveals more details of the decision scenario compared with an ID. The expansion of the decisions can lead to a probability tree (Howard and Matheson, 2005).

Unlike the nodes in a DT, the nodes in an ID do not require being totally ordered, nor do they require depending directly on all predecessors. This freedom from total ordering allows for convenient probabilistic assessment and computation. This ability gives the possibility of rescheduling the observation of some variables to the decision maker. It also provides the possibility of adding extra nodes without interrupting some of the orders.

Lastly, IDs have power in both deterministic and probabilistic cases. In the deterministic cases, the relationships between nodes mean that one variable can depend in a general way on several others. For example, profit is a function of revenue and cost. At the level of function, we specify the relationship; namely, that profit equals revenue minus cost. At number level, we specify the numerical values of revenue and cost, and hence determine the numerical value of profit. In probabilistic cases at the level of relation, we mean that given the information available, one variable is probabilistically dependent on certain other variables and probabilistically independent of even more variables. At the level of function, the probability distribution of each variable is assigned conditionally on the values of the variables on which it depends. Finally, at the number level, unconditional distributions are assigned on all variables that do not depend on any other variable and hence determine all joint and marginal probability distributions. As an example of the probabilistic case, we might assert at the level of relation that income depends on age and education and that education depends on age. Next, at the level of function we would assign the conditional distribution of income given age and education as well as the distribution of education given age. Different individuals can make the successive degrees of specification. Thus, an executive may know that sales depend in some way on price but may leave to others the probabilistic description of the relationship. Because of its generality, the ID is an important tool not only for decision analysis but also for any formal description of relationship and thus for all modeling work.

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Venture Capital Decision Making

Richard E. Neapolitan , Xia Jiang , in Probabilistic Methods for Financial and Marketing Informatics, 2007

9.1 A Simple VC Decision Model

A simple influence diagram modeling the decision of whether to invest in a start-up firm appears in Figure 9.1. The influence diagram was developed using Netica. The following report, produced by Netica, shows the conditional distributions and utilities in the diagram:

Figure 9.1. A simple influence diagram modeling the decision of whether to invest in a start-up firm.

We see that only three variables directly affect the utility of the investment. These variables are the Likely_Risk_Adjusted_Return, Dilution_Risk, and V C_Risk_Adj_Return_Exp. The first of these variables concerns the likely return of the investment, the second concerns the risk inherent in the firm's ability to repay the loan, while the third concerns the risk-adjusted expectation concerning how soon the firm will repay the loan. The utilities are not actual returns. The utility can be thought of as a measure of the potential of the firm, with 0 being lowest and 1 being highest. An investment with a value of 1 can be thought of as the perfect investment. If Likely_Risk_Adj_Return is high, VC_Risk_Adj_Return_Exp is low, and Dilution_Risk is false, then the firm has the most possible potential the model can provide, and a utility of 95 is assigned. So even when the variables directly related to the value node have their most favorable values, the utility is still only 95. We compare the investment choice to a utility of 50. If the utility of the investment is less than 50, it would not be considered a good investment, and we would choose to not invest.

Notice in Figure 9.1 that the utility of the investment is only 11.3 when nothing is known about the firm. This indicates that, in the absence of any information about a firm, the firm would not be considered a good investment. Figure 9.2 shows the influence diagram with the root nodes instantiated to their most favorable values. We see then that the utility of the investment is over 93. Figure 9.3 shows the influence diagram with the root nodes instantiated to their least favorable values. We see then that the utility of the investment is about 1.47.

Figure 9.2. When the root nodes are instantiated to their most favorable values, the utility of the investment is over 93.

Figure 9.3. When the root nodes are instantiated to their least favorable values, the utility of the investment is about 1.47.

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DECISION AND CONTROL

Judea Pearl , in Probabilistic Reasoning in Intelligent Systems, 1988

STRUCTURING AN INFLUENCE DIAGRAM

Influence diagrams are directed acyclic graphs with three types of nodes— decision nodes, chance nodes, and a value node. Decision nodes, shown as squares, represent choices available to the decision-maker. Chance nodes, shown as circles, represent random variables (or uncertain quantities). Finally, the value node, shown as a diamond, represents the objective (or utility) to be maximized.

The arcs in the graph have different meanings, based on their destinations. Arcs pointing to utility and chance nodes represent probabilistic or functional dependence, like the arcs in Bayesian networks. They do not necessarily imply causality or time precedence although in practice they often do. Arcs into decision nodes imply time precedence and are informational, i.e., they show which variables will be known to the decision-maker before the decision is made.

Formally speaking, an influence diagram can be viewed as a special type of Bayesian network, where the value of each decision variable is not determined probabilistically by its predecessors, but rather is imposed from the outside to meet some optimization objective. However, the decision task cannot be viewed as one of merely assigning values to a subset of variables, the way we found a best explanation in Chapter 5. Whereas the domains of the variables in a Bayesian network are fixed, the domain of each decision variable in an influence diagram varies according to previous decisions. For example, if a decision variable A has no predecessors, its domain is simply the set of actions available at that fork. If the decision variable has one chance node X as a parent, its domain is a set of pairs (a, x), each representing an action a in response to an observation x. If one of A's parents represents a decision T on whether or not to test variable X prior to taking action, then the domain of A will be either the set of (a, x) pairs or the set of unconditional actions {a}, depending on whether the decision to observe X was licensed by T. ^†

Figure 6.8 shows the influence diagram representing the car-buyer example. T denotes the choice of test to be performed, T ∈ {t ₀, t ₁, t ₂}, D stands for the decision of which car to buy, D ∈ {Buy 1, Buy 2}, C_i represents the quality of car i, C_i ∈ {q ₁, q ₂}, and t_i represents the outcome of the test on car i, t_i ∈ {pass, fail}.

Figure 6.8. An influence diagram representation of Example 1.

As in Bayesian networks, the arcs specify dependencies of various types: those entering chance nodes are quantified by conditional probabilities, those entering D indicate which quantities and previous decisions can be consulted before we make the decision D, and those entering V indicate which quantities enter into the computation of the utility. The missing arcs signify conditional independencies; for example, the absence of a direct arc between C ₁ and D asserts that given the result of test t ₁, the buying decision must remain the same, regardless of the actual quality of car 1.

Situation-specific knowledge is represented numerically as a set of functions relating each variable to its parent. Chance variables store the same conditional probabilities that quantify the links in Bayesian networks. For example, t ₁ will store the conditional probability matrix P(t ₁ | C ₁) for all values of C ₁ and t ₁, and C ₁ will store the prior probability P(C ₁ = q ₁) (hence the arc entering C ₁ in Figure 6.8). Knowledge of feasibility of actions is stored as a set of functions relating decision variables to their parents. For example, the knowledge defining the options available at D is expressed in Table 1, showing how the test decision T permits the bifurcation of the buying decision into conditional strategies predicated upon the test results. These strategies are not stored explicitly, as in Table 1, but are encoded procedurally by prohibiting the bifurcation in case t ₀ is chosen.

Table 1.

$\begin{array}{ll}T\hfill & \text{Options available at}D\hfill \\ t_0\hfill & \left\{Buy1,Buy2\right\}\hfill \\ t_1\hfill & \left\{\begin{array}{lll}\left[\begin{array}{lll}Buy1\hfill & \text{if}\hfill & t_1=pass\hfill \\ Buy2\hfill & \text{if}\hfill & t_1=fail\hfill \end{array}\right],\hfill & \left[\begin{array}{lll}Buy2\hfill & \text{if}\hfill & t_1=pass\hfill \\ Buy1\hfill & \text{if}\hfill & t_1=fail\hfill \end{array}\right],\hfill & Buy1,Buy2\hfill \end{array}\right\}\hfill \\ t_1\hfill & \left\{\begin{array}{lll}\left[\begin{array}{lll}Buy1\hfill & \text{if}\hfill & t_1=pass\hfill \\ Buy2\hfill & \text{if}\hfill & t_2=fail\hfill \end{array}\right],\hfill & \left[\begin{array}{lll}Buy2\hfill & \text{if}\hfill & t_2=pass\hfill \\ Buy1\hfill & \text{if}\hfill & t_2=fail\hfill \end{array}\right],\hfill & Buy1,Buy2\hfill \end{array}\right\}\hfill \end{array}$

Normative knowledge likewise can be expressed as a set of functional relationships between the value node and its parents. For example, given the decision D, the quality of the car purchased, and the cost of test T (if any was performed), the value of V is specified unambiguously. Formally, being functionally determined by its parents, the value node is identical to a query node (Section 4.5.1). Once this functional relationship is available, the expected value of V can be calculated as well, given the distribution over its chance parents and the values of its decision parents.

Influence diagrams and decision trees contain the same amount of information, but the former are clearly more parsimonious and more conceptually appealing.

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Decision Analysis Fundamentals

Richard E. Neapolitan , Xia Jiang , in Probabilistic Methods for Financial and Marketing Informatics, 2007

5.2.4 Solving Influence Diagrams Using Netica

In Chapter 3, Section 3.4.3 , we showed how to do inference in a Bayesian network using the software package Netica. Next we show how to solve an influence diagram using it.

Example 5.21

Recall that Figure 5.16 showed an influence diagram representing the problem instance in Example 5.11 . Figure 5.21 shows that influence diagram developed using Netica. Recall from Chapter 3, Section 3.4.3, that Netica computes and shows the prior probabilities of the variables rather than showing the conditional probability distributions, and probabilities are shown as percentages. A peculiarity of Netica is that node values must start with a letter. So we placed an "n" before numeric values. Another unfortunate feature is that both chance and decision nodes are depicted as rectangles.

Figure 5.21. The influence diagram in Figure 5.16 developed using Netica.

The values shown at the decision node D are the expected values of the decision alternatives. We see that

$\begin{array}{l}E(d1)=1.520\times {10}^5=\mathrm{152,000}\\ E(d2)=1.450\times {10}^5=\mathrm{145,000.}\end{array}$

So the decision alternative that maximizes expected value is d1.

Example 5.22

Recall that Figure 5.18 showed an influence diagram representing the problem instance in Example 5.13 . Figure 5.22 shows that influence diagram developed using Netica. We see that the decision alternative of "Run Test" that maximizes expected utility is to buy the Spiffycar without running the test.

Figure 5.22. The influence diagram in Figure 5.18 developed using Netica.

Example 5.23

Recall that Figure 5.19 showed an influence diagram representing the problem instance in Example 5.14 . Figure 5.23 (a) shows that influence diagram developed using Netica. We see that the decision alternative of "Run Test" that maximizes expected utility is to run the test. After running the test, the test will come back either positive or negative, and we must then decide whether or not to buy the car. The influence diagram updated to running the test and the test coming back positive appears in Figure 5.23 (b) . We see that in this case the decision alternative that maximizes expected utility is to not buy the car. The influence diagram updated to running the test and the test coming back negative appears in Figure 5.23 (c) . We see that in this case the decision alternative that maximizes expected utility is to buy the car.

Figure 5.23. The influence diagram in Figure 5.19 developed using Netica appears in (a). The influence diagram updated to running the test and the test coming back positive appears in (b). The influence diagram updated to running the test and the test coming back negative appears in (c).

Example 5.24

Recall that Figure 5.20 showed an influence diagram representing the problem instance in Example 5.15 . Figure 5.24 (a) shows that influence diagram developed using Netica. We see that the decision alternative of "CT Scan" that maximizes expected utility is c1, which is to do the scan. After doing the scan, the scan will come back either positive or negative, and we must then decide whether or not to do the mediastinoscopy. The influence diagram updated to doing the CT scan and the scan coming back positive appears in Figure 5.24 (b) . We see that in this case the decision alternative that maximizes expected utility is to do the mediastinoscopy. The influence diagram updated to then doing the mediastinoscopy and the test coming back negative appears in Figure 5.24 (c) . We see that in this case the decision alternative that maximizes expected utility is to do the thoracotomy.

Figure 5.24. The influence diagram in Figure 5.20 developed using Netica appears in (a). The influence diagram updated to doing the CT scan and the scan coming back positive appears in (b). The influence diagram updated to then doing the mediastinoscopy and the test coming back negative appears in (c).

In the previous example, it is not surprising that the decision alternative that maximizes expected utility is to do the CT scan since that scan has no cost. Suppose instead that there is a financial cost of $1000 involved in doing the scan. Since the utility function is in terms of years of life, to perform a decision analysis we must convert the $1000 to units of years of life (or vice versa). Let's say the decision maker decides $1000 is equivalent to .01 years of life. It is left as an exercise to determine whether in this case the decision alternative that maximizes expected utility is still to do the CT scan.

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Modeling Real Options

Richard E. Neapolitan , Xia Jiang , in Probabilistic Methods for Financial and Marketing Informatics, 2007

8.2 Making a Plan

The influence diagram not only informs the manager of the decision alternative to choose at the top level, but it also yields a plan. That is, it informs the manager of the decision alternative to choose in the future after new information is obtained. This is illustrated in the following examples.

Example 8.5

Suppose we have the situation discussed in Example 8.4 , we make the decision to produce at time t = 0, and M0 ends up taking the value d. What decision should we make at time t = 1? Figure 8.6 shows the influence diagram after D ₀ is instantiated to "Produce" and M0 is instantiated to d. The decision alternative that maximizes D ₁ is now "Liquidate" with value −0.1710. So we are informed that we should cut our losses and get out. Note that this is the opposite of what some decision makers tend to do. Some individuals feel they need to stay in the investment so that they have a chance to get their losses back.

Figure 8.6. The solved influence diagram for the decision in Example 8.5.

Example 8.6

Suppose we have the situation discussed in Example 8.4 , we make the decision to produce at times t = 0, and M0 ends up taking the value u. Then the recommended alternative at time t = 1 would be to produce again. Suppose we choose this alternative, and M1 ends up taking the value d. What decision should we make at time t = 2? Figure 8.7 shows the influence diagram after D0 and D1 are both instantiated to "Produce," M0 is instantiated to u, and M1 is instantiated to d. The decision alternative that maximizes D3 is now "Liquidate" with value .47923. So we are informed that we should get out with our current profit.

Figure 8.7. The solved influence diagram for the decision in Example 8.6.

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Further Techniques in Decision Analysis

Richard E. Neapolitan , Xia Jiang , in Probabilistic Methods for Financial and Marketing Informatics, 2007

Section 6.5

Exercise 6.18

Suppose we have the decision tree in Figure 6.24, except the growth fund will be at $1800, $1100, and $200 if the market is, respectively, up, flat, or down, while the allocation fund will be at $1400, $1000, or $400.

1.

Compute the expected value of perfect information by hand.

2.

Model the problem instance as an influence diagram using Netica, and determine the expected value of perfect information using that influence diagram.

Exercise 6.19

Suppose we have the same decision as in the previous example, except we can consult an expert who is not perfect. Specifically, the expert's accuracy is as follows:

$\begin{array}{c}P\left(\text{Expert}=\text{says}\text{up}|\text{Market}=\text{up}\right)=.7\\ P\left(\text{Expert}=\text{says}\text{flat}|\text{Market}=\text{up}\right)=.2\\ P\left(\text{Expert}=\text{says}\text{down}|\text{Market}=\text{up}\right)=.1\\ P\left(\text{Expert}=\text{says}\text{up}|\text{Market}=\text{flat}\right)=.1\\ P\left(\text{Expert}=\text{says}\text{flat}|\text{Market}=\text{flat}\right)=.8\\ P\left(\text{Expert}=\text{says}\text{down}|\text{Market}=\text{flat}\right)=\mathrm{.1.}\end{array}$

Model the problem instance as an influence diagram using Netica, and determine the expected value of consulting the expert using that influence diagram.

Exercise 6.20

Consider the decision problem discussed in Chapter 5, Exercise 5.10. Represent the problem with an influence diagram using Netica, and, using that influence diagram, determine the EVPI concerning Texaco's reaction to a $5 billion counteroffer.

Exercise 6.21

Recall Chapter 2, Exercise 2.18, in which Professor Neapolitan has the opportunity to drill for oil on his farm in Texas. It costs $25,000 to drill. Suppose that if he drills and oil is present, he will receive $100,000 from the sale of the oil. If only natural gas is present, he will receive $30,000 from the sale of the natural gas. If neither are present, he will receive nothing. The alternative to drilling is to do nothing, which would definitely result in no profit, but he will not have spent the $25,000.

1.

Represent the decision problem with an influence diagram, and solve the influence diagram.

2.

Now include a node for the test discussed in Exercise 6.28, and determine the expected value of running the test.

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Quality management and software process engineering

Nikhil R. Zope , ... Padmalata V. Nistala , in Software Quality Assurance, 2016

4.6.1.1 Requirements engineering and management

The very first phase of any process is to understand the needs to be met by its outcome. There is a need for this aspect to be sound (in relation to the domain of discourse), to be complete, and consistent so that a source of inefficiency in Process Management can be avoided by eschewing possibility of feedback in the process.

Soundness and completeness can be systemically tracked and foreclosed by methodological means like: (i) Zachman's Enterprise Architecture (Zachman, 1987) and Viable Systems Model (Beer, 1966) that support system understanding, and (ii) Policy Objective Matrix (Fukuda, 1997), and SEDAC (Fukuda, 1997) that address managerial concerns. Consistency has to be demonstrated for every instance of application of the methodology and this is the crux of overall Quality Management: tests, inspections and audit to assert that the known cases are handled effectively, contributing to overall Quality Control, and analysis and proof of structures of solutions devised to assert Quality Assurance.

The first step in seeing into the system, is in its first segmentation, which starts here in Requirements Engineering and Management. Such segmentation can be achieved by various methods of systems approach. ¹ The nature of the segmentation is dictated by the approach taken. This segmentation gives rise to a configuration structure, the configuration items being annotated by attributes that signify qualities. The composition of these components lead to an understanding of how the resultant qualities of the system are aggregated and derived. Such composition is a means of asserting the properties of outcome of the process.

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Probabilistic Informatics

Richard E. Neapolitan , Xia Jiang , in Probabilistic Methods for Financial and Marketing Informatics, 2007

1.3 Outline of This Book

In Part I we cover the basics of Bayesian networks and decision analysis. Chapter 2 reviews the probability and statistics necessary to understanding the remainder of the book. In Chapter 3 we present Bayesian networks, which are graphical structures that represent the probabilistic relationships among many related variables. Bayesian networks have become one of the most prominent architectures for representing multivariate probability distributions and enabling probabilistic inference using such distributions. Chapter 4 shows how we can learn Bayesian networks from data. A Bayesian network augmented with a value node and decision nodes is called an influence diagram. We can use an influence diagram to recommend a decision based on the uncertain relationships among the variables and the preferences of the user. The field that investigates such decisions is called decision analysis. Chapter 5 introduces decision analysis, while Chapter 6 covers further topics in decision analysis. Once you have completed Part I, you should have a basic understanding of how Bayesian networks and decision analysis can be used to represent and solve real-world problems. Parts II and III then cover applications to specific problems. Part II covers financial applications. Specifically, Chapter 7 presents the basics of investment science and develops a Bayesian network for portfolio risk analysis. In Chapter 8 we discuss the modeling of real options, which concerns decisions a company must make as to what projects it should pursue. Chapter 9 covers venture capital decision making, which is the process of deciding whether to invest money in a start-up company. In Chapter 10 we show an application to bankruptcy prediction. Finally, Part III contains chapters on two of the most important areas of marketing. First, Chapter 11 shows an application to collaborative filtering/market basket analysis. These disciplines concern determining what products an individual might prefer based on how the user feels about other products. Second, Chapter 12 presents an application to targeted advertising, which is the process of identifying those customers to whom advertisements should be sent.

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Complex Service Computing

Zhaohui Wu , ... Jian Wu , in Service Computing, 2015

9.4.4 Case Study

This section discusses the example of MAP in detail. To analyze the value creation of each role in MAP, we format the process, which is presented in Figure 9.18.

Figure 9.18. The swim lane diagrams of mobile application platform service example.

9.4.4.1 Information flow analysis

With the help of the extraction rule defined in Section 9.4.2, we can extract the n-th order attributes from the origin process in Figure 9.18. Figure 9.19 is the second-order attributes analysis result on feedback. Figure 9.19(a) is the information flow for the second-order attributes of feedback, and Figure 9.19(b) is the attributes influence diagram. We can see that feedback is directly influenced by the quality and price, and the feedback has an impact on the sales of APP by the influence of its ranking.

Figure 9.19. The second-order attributes information flow of feedback.

9.4.4.2 Value flow analysis

With the defined resources and roles, the value flow can be extracted from the origin diagram by the extraction rule defined in Section 9.4.2.8. Figure 9.20 presents the value flow of the MAP.

Figure 9.20. The value flow of four roles in mobile application platform.

To quantitatively analyze the value flow of each role, we study the value flow of the advertiser. The value creation process can be divided into three parts.

•

The investment phase is the first step. The advertiser uses 10 to buy fixed resources, 500 to employ programmers, and 30 to pay the advertising fee to the developer. The relative value of financial resource is (−10)   +   (−500)   +   (−30)   =   −540 now.

•

The creation phase is the second step. The advertiser designs the advertisement and implants it into APP. In this step, 5 of 10 fixed resources and all 500 labor resources are used. The value promotion from the APP is 50. So the relative intangible resource is now 500   +   5   +   50   =   555.

•

The reward phase is the last step. The advertiser converts the value of the advertisement (555) to income. The financial resource is now −540   +   555   =   15.

After performing the three steps, we can see that the labor and intangible resources are not changed, but the financial and fixed resources increased. The last result is depicted in Figure 9.21. With the help of the value flow, we can now understand that the advertiser earns by such a process, and the return on investment is (15   +   5)/(10   +   500   +   30)   =   3.7%. The discussion on how to calculate each resource changing with the influence of activities and how to re-allocate the resources to get a higher return are beyond the scope of this section. It will be presented in a future study.

Figure 9.21. Advertiser value flow.

We have studied 62 enterprises from 355 public companies in the Growth Enterprise Market (GEM) in China and analyzed their service pattern [30]. The GEM is the second-board market, which is very similar to the NASDAQ Stock Market. We have extracted six types of service patterns: long tail service pattern, multiplatforms service pattern, free service pattern, secondary innovation service pattern, unbundling service pattern, and systematic service pattern.

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