2014年美赛数模B题-Finalist(4)

Team # 24270 Page 15 of 26

4.3.1. Original data

Here we define ti as the characteristic year, the average of the year that the coach i start coaching and the year of his or her retirement. (If the coach i is still active, then t is the average of the year that the coach i start coaching and this year, that is, 2014)

The search results vector a is the original data we use to estimate the individual influence, where ai is the number of search results of coach i. Particularly, the coaches here are sorted by

characteristic year in a descend order. This can be a great convenience to our later discussion about time factor.

4.3.2. The influence coefficient of time

According to the growth law of web information[16], the information aiming at a certain field is similar to an exponent increase. To test this hypothesis and better apply it to sports, we entered the Google website. Using “1910 basketball”, “1920 basketball” ， and “1930 basketball” as the “exact keywords”[17] respectively. The numbers of search results are shown

in Table 10:

Table 10: The Numbers of Search Results

Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Results 2750 5160 7440 11700 16200 26400 40200 25800 27000 67700 326000

Assuming that this is an exponential function: y1?? c?? edt . We use the least squared method

to obtain the unknown numbers in the function. See Figure 6.

Figure 6: Trend of exponential function y1 Figure 7: Trend of linear function y2

The result gives a satisfying simulation to the numbers of search results. However, the distinction between 2000s and 1900s is too large. In our observation, the search results of coaches at different period of time is almost of the same magnitude of as each other. So, here we use the natural logarithm of the search results. Again we obtain a linear function y2 as showed in Figure 7.

The difference between maximum and minimum is about half of the minimum value. This is a modest value that we can safely put into use to estimate ICT. Common sense told us that the greater number of total reports is, the more “valuable” the search result is, the greater weight the search result will get. So, we define ICT as

(influence coefficient of time)=iICT 1

1, 2, ,i n??????????????kti?? b

感谢作者分享

Team # 24270 Page 16 of 26 where k and b are the unknown variables related to searching data.

4.3.3. The influence coefficient of reputation

As mentioned in the overview, by searching data with different methods and using diverse keywords, we observe that on the track of fame, the media will turn at first to the

achievements of sports one has then to the other aspects in his or her life. Therefore, the media attention can be interpreted and quantified by using the overall search results of one coach and his or her triumph and achievement.

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:

2

ia????

ICRi (influence coefficient of reputation)=1????????i?? 1,2,?, n??? ui???

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.

i

l???

i i in j??1

a ICT ICR??????j j j a ICT CRI????????????????1, 2, ,i n?????(9)

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:

Zij =number of search results number of coach i and coach j

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.

感谢作者分享

Team # 24270 Page 17 of 26

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. …… 此处隐藏：9554字，全部文档内容请下载后查看。喜欢就下载吧 ……