1、Team#12386 Page 1 of 11 Non-conspirator？ Conspirator ！ Content 1 Introduction 2 1.1 Background and Analysis of the Problems 2 1.2 Method of the Analysis . 2 1.3 Assumptions . 2 2 Model Approach 3 2.1 The Confirmation of the Indexes Judging Ones Suspicion 3 2.2 Molding Using AHP . 3 2.2.1The Establis
2、hment of the Model 3 2.2.2The Construction of the Judging Matrix . 3 2.2.3The Total Hierarchical Order . 7 2.3Conclusions . 7 2.3.1 The Final Suspicion Order of the Eighty-Three Nodes 7 2.3.2 A Discriminate Line Separating Conspirators From Non-conspirators 8 2.3.3Who Is The Leader 8 2.4Model Testin
3、g 8 2.4.1Sensitivity Testing . 8 2.4.2Accuracy Testing . 8 3 Model Enhancement 8 3.1 Semantic Network Analysis . 8 3.2 Application of the Model 9 4 Conclusions 9 4.1 Strengths 9 4.2 Weakness 10 References 11 Team#12386 Page 2 of 11 1 Introduction 1.1 Background and Analysis of the Problems With the
4、development of crimes, organized crimes appeared. Those people who are involved in these kinds of crimes always connected with each other because of the same goal and some restrictive factors. These crimes bring more harm to the society than individual crimes. Our organization, ICM, is investigating
5、 a conspiracy. The 83 people who are investigated are members of a software company, which mainly markets with banks and credit card companies. At present, ICM has already known some information. Those investigators think that the information will help them to find out the most-possible people selec
6、ted of the ambiguous conspirators and unknown leaders. The goal of molding is to find out who are the most-possible conspirators in the complicated office. According to those known conspirators, 15 topics (three of which have been deemed to be suspicious), and 400 message links, our goal is to assur
7、e who are conspirators, who are leaders, prioritize the 83 nodes by likelihood of being part of the conspiracy, and determine a discriminate line separating conspirators from non-conspirators. We should also think about what to do if some of those known conditions changed (According to the text, Chr
8、is becomes the conspirator, Topic one becomes suspicious.) We should get what changes the result finally has. When dealing with the problem, we get more information (the original massage text), it is needed to be known how our model will finally be enhanced. When the model is used more widely, it mu
9、st be made sure that it can be applied into any condition. 1.2 Methods of the Analysis As investigators, we now know well about the 83nodes, 400 links over 21,000 words of message traffic, 15 topics (three have been deemed to be suspicious), 7 known conspirators, and 8known non-conspirators. We now
10、call the known information about the company INTELLIGENCE. From the practice, the method which is always used in the intelligence work is a combination of qualitative reasoning and quantified reasoning, that is called Analytic Hierarchy Process (called AHP in the later part). At the same time, we al
11、so use Structural Model Analysis (SMA). 1.3 Assumptions There is only linguistic communication between people. Body language never exists. People can talk to each other freely, without the limit of distance. The information of known conspiractors and non-conspiractors is correct. The talk happens on
12、ly between two people. Talks between 3 or over 3 members never exists. Team#12386 Page 3 of 11 Suspected topics are only those claimed in the text. Other topics never become suspected. There is no false information. The suspicion is never influenced by gender, age and any other personal information.
13、 2. Model Approach 2.1 The confirmation of the indexes judging ones suspicion As a group of conspirators, they connect each other through communication, so there must be interaction of information between them. The three suspicious topics are also included in the information. Considering suspicious
14、topics and conspirators, we consider that the indexes judging the suspicion are the three points below: The frequency individuals send and receive suspicious topics. The frequency individuals interact with conspirators. The accessible level to suspicious messages. 2.2 Molding Using AHP 2.2.1 The Est
15、ablishment of the Model Suspicion Suspicious Topics Known Conspirators Alternative P Standard C Objective A The Judgment of Suspicion The Accessibility of suspicious messages The Frequency of Touching Suspicious Messages The Suspicion of Each Individual The Frequency of Connecting with conpirators T
16、eam#12386 Page 4 of 11 2.2.2 The Construction of the Judging Matrix 2.2.2.1 Judging Matrix A-C (Compare the Significance of Each Standard In Order to Judge the Suspicion) Except for the special circumstances, people in the same company communicate with each other unavoidably. Therefore, the signific
17、ance of the connecting with conspirators is the least important standard, while the accessibility is the most important. We consider the order of the significance of the three standards is: C1C2C3. Thus the judging matrix A-C is: A C1 C2 C3 C1 1 2 4 C2 1/2 1 3 C3 1/4 1/3 1 In the judging matrix, the
18、 meanings of the values of Aij are as follows: Aij=1: Ai is as important as Aj; Aij =2: Ai is a little more important than Aj (suspicion) Aij =3: Ai is more important than Aj; Aij j=4: Ai is extremely important than Aj. Either factor in the matrix (Aij)stands for how more important Ai is than Aj. Ac
19、cording to the document, it can be calculated by the formula below: Normalization of each line of the judging matrix:. 31, , 1, 2 , 3ijijkjkAA i jA Sum up each judging matrix that has already been normalized in each row: 31 , 1, 2, 3i ijjW A j . Normalize the vector:. 31, 1, 2 , 3ijjWWiW , Thus the
20、characteristic vector can be got: 1 2 3( , , ) = ( 0 . 5 5 8 4 0 . 3 1 9 6 0 . 1 2 2 0 )TTW W W W . Then the characteristic root can also be calculated: im a x1 i= 3 .0 1 8 3nni W （ AW ） , maxBW W ., i(AW) stands for the i-th component of vector AW. The last step is consistency check. The formula is
21、 max 1nCI n , in which RI stands for the index of average random consistency. It is in the chart below: Order 1 2 3 4 5 6 7 8 9 RI 0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45 the average random consistency index of the first order to ninth order matrix CR CI/RI=0.01760.10, thus the matrix gets the
22、satisfied consistency. Team#12386 Page 5 of 11 At last, the weight of each standard, which is the value of characteristic vector. C1 is 0.5584. C2 is 0.3196. C3 is 0.1224. 2.2.2.2 Judging Matrix C1-P (Compare the relative level of suspicion only considering the accessible level of suspicious message
23、s from each node.) The accessible level of suspicious messages is the ones frequency of receiving suspicious messages. Apparently, the more suspicious access one receives, the more people pass suspicious topics to him or her. So this node gets more suspected degree. Therefore, the suspected level ca
24、n be characterized by each of the factors and Yj in the accessible matrix. Those Yjs are got by structurally analyzing the accessible matrix. It can be seen in the picture. The adjacency matrix can be worked out through how those messages are converted. “Lij=0” means suspected messages cannot be con
25、verted to j. “Lij=1” means suspected messages can be converted to j. The matrix I is an 83*83 unit matrix. 2 . ( )nnR I L L L I L , I is unit matrix. Make out the sum of each line: 831Yj i RijYj and the factors in the accessible matrix characterizes the amount of people who can convert suspected mes
26、sages. By using the result the suspected degree can be characterized. There are 83 objectives in this model. These 83 objectives can be sorted into five sets by considering factors in line and Yj. It is considered that every person in the same set have the same suspected level. For those people who
27、are in the different sets, the more the Y-value of the set they are in, the more their suspected degrees are. Team#12386 Page 6 of 11 And the more the Y-values different, the more their suspected degrees differ form each other. It is defined that b4 is the relative importance between the i-th (i=1,2
28、,83) objective and the ht j-th (j=1,2,83) objective. I t is recorded as C1-P=(bij)83*83. bij=1, bji=1/bij. bij in the judging matrix is valued as follow: bij =1: means Bi is of the same suspected degree as Bj; bij =3: means the suspected degree of Bi is lightly more important than that of Bj; bij =5
29、: means the suspected degree of Bi is more important than that of Bj; bij =7: means the suspected degree of Bi is largely more important than that of Bj; bij =9: means the suspected degree of Bi is extremely more important than that of Bj. The judging matrix C1-P is as follow: C 1-P B1 B2 B83 B1 B2
30、B83 b11 b21 b83,1 b12 b22 b83,2 b1,83 b2,83 b83,83 Then make the hierarchical order separately. According to 2.2.1.1, the characteristic vector can be worked out. Wn, the value of this vector, cam indicate the suspected degree of n, using which can make the order. 2.2.2.3 Judging Matrix C2-P( Compar
31、e the relative suspicion of each people thinking about only the connect of suspected messages.) The frequency individuals send and receive suspicious topics Define: Xi=X1+X2 ， i=1,2， n， X1 indicates how many links （ involving any known suspicious message topics） starts at this node， X2 indicates how
32、 many links（ involving any known suspicious message topics） ends at this node We consider that suspicious topics are only No.7, No.11, and No.13. In the next step, we should screen out all the messages that talks about either one of those suspicious topics, and then calculate X, indicating the inten
33、sity of contact between every node and either suspicious messages. We assume that suspected topics are only No.7, No.11, and No.13. Firstly, using the 400 messages between these people(links), we can screen out messages including Team#12386 Page 7 of 11 either suspected topic. We can then make out h
34、ow many times each node sends and receives messages, standing for the level each node connects with suspected messages. The sum is recorded as X. The next step is to divide the 83 objectives into five sets according to the sum of sending and receiving of each node, just like what has been done in 2.
35、2.2.2. Then we should list the judging matrix C2-P, and then do what we have done in 2.2.2.1 to make out the characteristic vector W. cengcidanpaixu! 2.2.2.4 The Judging Matrix C3-P (Compare the relative suspicion of each node thinking about only the connect of suspected messages) So far, it is know
36、n that Jean, Alex, Elsie, Paul, Ulf, Yao and Harvey are conspirators. Therefore, we can make out the amount of interactions between every node and every known conspirator, using the 400 messages between these people. The amount is called Z, which means the interactive level between individuals and c
37、onspirators. Therefore, we consider that the more frequently nodes connected with conspirators, the more suspicious they are. The next step is to divide the 83 objectives into five sets according to the sum of sending and receiving of each node, just like what has been done in 2.2.2.2. Then we shoul
38、d list the judging matrix C3-P, and then do what we have done in 2.2.2.1 to make out the characteristic vector W. Then make the hierarchical order separately. 2.2.3 The Total Hierarchical Order From 2.2.2.1, we know that the value of those weights. C1 is 0.5584. C2 is 0.3196. C3 is 0.1220. Supposed
39、that the weight of ones suspicion of C1 is WC1, C2 is WC2, and C3 is WC3. We can make out the weight of the total order by the formula below. 1 2 3* 0 . 5 5 8 4 * 0 . 3 1 9 6 * 0 . 1 2 2 0C C CU W W W We can make out the final suspicion order according to U. 2.3 Conclusions 2.3.1 The Final Suspicion
40、 Order of the Eighty-three Nodes: According to the value of U, we can make the list of the suspicion of 83 nodes, as the chart following. Rank Node 110 21* 67* 7* 54* 10 43* 17 13 18* 49* 1120 81 3 38 50 6 32 16 30 44 4 2130 11 42 34 28 20 37 15 2# 47 22 3140 48# 36 41 19 29 46 33 35 31 14 4150 5 80
41、 27 82 65# 12 57 75 45 8 5160 9 40 60 69 24 79 23 39 51 56 6170 72 78# 1 77 26 52 53 55 68# 58 7180 59 70 74# 25 66 73 0# 61 62 63 8183 64# 71 76 (* indicates prior known conspirators, # indicate prior known non-conspirators) Team#12386 Page 8 of 11 2.3.2 Discriminate Line Separating Conspirators fr
42、om Non-conspirators. Do cluster analysis of the U of 83 nodes,the result of which indicates that the 63 nodes of lower suspicion, so that the dividing line should be set up between No.4 Gretchen and No.11 Francis. 2.3.3Who Is the Leader According to the speculation, Dolores is the leader. Firstly, h
43、is suspicion is very big. Secondly, he is a manager. He communicates with others is more frequently than others. 2.4 Model Testing 2.4.1 Sensitivity Testing In the new condition that Chris becomes the conspirator and Topic 1 becomes suspicious, we can use the model above to get the suspicion rank of
44、 these 83 people, as the chart following, Rank Node 110 48# 34 21* 67* 7* 54* 5 43* 17 18* 1120 2# 10 32 13 15 22 49* 20 81 47 2130 3 28 31 41 50 4 14 27 44 0* 3140 6 19 37 38 16 9 11 29 30 33 4150 45 46 25 36 69 1 12 24 42 35 5160 82 56 80 66 57 63 75 40 65# 8 6170 60 68# 23 26 39 51 55 62 64# 71 7
45、180 72 78# 79 61 73 52 53 58 59 70 8183 74# 76 77 (* indicates prior known conspirators, # indicate prior known non-conspirators) Analysis: According to the list, we can get that the ranks of some people has little changes. Some people get big changes in their ranks, who are close connected with Chr
46、is and Topic 1. It substantiates that the model has high sensitivity. 2.4.2 Accuracy Testing Using the model to deal with EZ case, we can get the suspicion rank as following. George* Dave* Ellen Harry Bob Carol Fred Inez Anne# Jaye# (* indicates prior known conspirators, # indicate prior known non-c
47、onspirators) Analysis: Bob ranks fifth, while Carol ranks sixth. It mostly coincides with the eventual crime condition, which substantiates that the model is accurate. 3. Model Enhancement 3.1 Semantic Network Analysis Team#12386 Page 9 of 11 For the third requirement, it is mentioned in the former
48、part of the essay that the team get a more powerful method (semantic network analysis). In this condition, we can do a lot to enhance our model. Semantic network analysis is a kind of idea in artificial intelligence. According to the description in the published documents, we get that the most important factor related to SNA is word frequency of the text of those messages. Therefore, we conclude the enhanced model and some significant points as following. We should first of all manage the statistics of the word frequency and make a list of it from the highest to the lowest.
