To extract the information about news reports on the triumph of a certain coach from the search engine, first, we use Wordnet[18] as our tool to obtain a host of synonyms of the word winning , the result is:
booming; flourishing; palmy; prospering; prosperous; roaring; thriving; in; made; no-hit; productive; self-made; sure-fire; triple-crown; victorious; successful
Using these words as our alternative keywords , we can obtain the numbers of winning search results ui for coach i.
The result turns out to be an indication that the ratio between winning search results and overall search results is negatively correlated with the degree of reputation. That is, the higher reputation one coach gets, the more likely the mass media will concentrate on the other aspects of life of this coach. According to this rule, we establish a function of ICR:
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苑
4.3.3. The individual influence vector
The individual influence vector l can be interpreted as the overall search results modified by ICT and ICR.
li
The individual influence vector gives an accurate estimation of the media attention certain coach got. It is a normalized vector, so that we can conveniently put it into use in the later section.
4.4. The Cross-Reference Matrix
With the help of the Google search engine, the degree of correlation of two coaches can be measured by the number of search results using two names as Citation Keywords [17] simultaneously. And we define the original cross-reference matrix Z. The entries of the matrix is:
Since exchange of the two names does not affect the result, the matrix Z is symmetrical. And we set all of the diagonal elements of this matrix to be 0.
mo.crotha.mww w模数
a
ICRi(influence coefficient of reputation)=1 i i 1,2, ,n
ui
2
ai ICTi ICRi
j
j
a ICT ICR
j 1
i 1,2, ,n (9)
j
Zij=number of search results number of coach i and coach j
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4.4.1. The weight function
The elements of cross-reference matrix are influenced by the distinct period of time and reputation. However, things get a bit more complicated here: if two coaches exist in the same period of time, then there could be more reports on competitions they engaged. The competition reports are the redundant information that we want to avoid. What we are aiming to do is to evaluate a certain coach s impact over the span of the sports history and to rule out the redundant information. To do that, we assign a lower weight to the
matrix element in which the two coaches is in the same period of time, and a higher weight to those in a different period of time.
First, let ti and tj to be the characteristic year of two coaches, we want to construct a weight function related to ti and tj. Because we previously set the diagonal elements to be 0, the weight on the diagonal can be zeros. Assuming that the average term of office is 2σ, according to the 2σ principle[3], there is little likelihood that the two coaches can encounter each other in the sport games. Then the corresponding weight can be approximate to be 1 outside the interval 2σ. By carefully weighing the pros and cons of diverse types of function, we establish the original weight function as
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Additionally, to take into consideration of ICT, we simply transform the one variable function IIT to two variable function multiplied by the original weight function. The final weight function WF is:
WF=
1 ekti ktj b22
(ti tj)22
From (10), the values of the function in intervals (1910, 2010), (1910, 2010) are drawn in
3D graph as showed in Figure 8 and Figure 9.
Figure 8: Contour plot of weight function Figure 9: 3D graphic of weight function As can be seen from the graphs above, as the characteristic year increases, the weight decreases linearly. And with the gap between two characteristic years increase, the weight increases somehow similar to a normal distribution curve.
4.4.2. The final cross-reference matrix
The weighted cross-reference matrix is defined as the original cross-reference matrix multiplied by the function value of weight function, via:
mo.crotha.m
数
e
(ti tj)22 2
)
) i,j 1,2, ,n (10)
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Wij Zij WF(ti,tj)
Normalizing the weighted cross-reference matrix by column sums, we obtain the final
cross-reference matrix N.
Nij
Wij
n
(11)
ij
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W
k 1
4.5. The Evaluation Vector
So far we have obtained the individual influence vector and the cross-reference matrix. Each of them partly reflect the impact that a certain coach has over the course of sports history. Furthermore, if one is related to a very influential coach, then this relationship can be more valuable to him. This law is far better than merely counting the correlated search results. Following this law, we sophistically combine the Article Influence Algorithm[19] with our data.
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