社交网络建模: Wolfram 语言 11 的新功能

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社交网络建模

偏移 Gompertz 分布是按独立指数和极值分布的随机变量的最大值的分布. 该分布可用于模拟社交网络关注的增长和下降. 以下为偏移 Gompertz 分布的 CDF 形式.

In[1]:=

CDF[ShiftedGompertzDistribution[\[Lambda], \[Xi]], x]

Out[1]=

谷歌趋势（Google trends）的 Facebook 中的每周关注计数.

In[2]:=

ts = TemporalData[TimeSeries, {CompressedData["
1:eJyFz2tPwjAUBmDA+7wRNCpeQBTRiAGvXLoNYYytPW03QHSybiYav/tX/Ume
GRO/mPg0p+l72pykpbeP8VsmlUqlsT5xS/8n82smM/Nt9sdcYv4vC2gxoWlL
mqYto5WVVbS2tp7N5nK5jY3N7Z2tnXx+d3dvbx/XQbFwUCgUi4eHpdLRcbl8
UjmtnJ1XqxeoVqvV65dX9cvrZvP2pnHXaLUbjWaLIJMYuk4MwzTNTue+1+1a
qO9a9qA/cPq2PRg4ILnLgHPGgLkuABfSdRyHUs5AAghvyD3peb4U+IhLJoCB
NxLUk0JwgXcCRNIT2AYpPS4YByo5cGBsFL+oOFaRCqP4/VWpOFQqCKbhVEXh
9BmFKopjTFEQBs9PweRxNHkYj/yh7/ueEHI8xDGAg7AAqMsodRw3OTP2HWxK
XfyFbVl2z+p2kGn1jATRSZsQXW+RNkpSmxjkC/7xXxc=
"], {
TemporalData`DateSpecification[{2006, 8, 26, 0, 0, 0.}, {
      2015, 7, 11, 0, 0, 0.}, {1, "Week"}]}, 1, {"Continuous", 1}, {
    "Discrete", 1}, 1, {
    ValueDimensions -> 1, DateFunction -> Automatic, 
     ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}},
    True, 314.1];

显示完整的 Wolfram 语言输入

In[3]:=

DateListPlot[ts, ImageSize -> Medium, PlotTheme -> "Detailed", 
 Filling -> Axis]

Out[3]=

用截断偏移 Gompertz 分布拟合数据.

In[4]:=

rawcounts = ts["Values"];
length = Length[rawcounts];
x = Range[length] - 0.5;
wdata = WeightedData[x, rawcounts];

In[5]:=

edist = EstimatedDistribution[wdata, 
  TruncatedDistribution[{0, length}, 
   ShiftedGompertzDistribution[\[Lambda], \[Xi]]], {{\[Lambda], 
    1}, {\[Xi], 6}}]

Out[5]=

比较模型预测和数据.

显示完整的 Wolfram 语言输入

In[6]:=

counts = Total[rawcounts] PDF[edist , x];
DateListPlot[{rawcounts, counts}, {ts["FirstDate"], Automatic, 
  "Week"}, Filling -> Axis, PlotLegends -> {"data", "model"}, 
 ImageSize -> Medium, PlotTheme -> "Detailed"]

Out[6]=

Wolfram 语言™

社交网络建模

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