## 2 Materials and Methods
### Represent the Distribution of Age Groups among Commenters on a News Article Using word2 vec  
This study used the _news2 vec_ model to represent a news article \(n\), i.e., the age group distribution of the news article. The news2 vec vectors for the collected news articles were generated by following five steps, which can be summarized as: (i) extracting unigrams from news comments; (ii) removing extremely long unigrams; (iii) generating 300-dimensional word2 vec embeddings for the unigrams, i.e., _unigram2 vec_; (iv) generating feature vectors for news comments, i.e., _comment2 vec_; and (v) generating feature vectors for news articles, i.e., _news2 vec_. Here, to generate unigram2 vec vectors, a news comment \(c\) was considered as a sentence and represented by its unigrams, considered as words in the sentence. Thereafter, it was used as an input to train the word2 vec model, using GENSIM's word2 vec module with default settings. Moreover, to generate comment2 vec vectors, unigram2 vec vectors were aggregated for related news metrics. The _comment2 vec_ and _news2 vec_ are defined as follows:  
\[\textit{comment2 vec}(c)=\frac{1}{n(\text{UNIGRAM}(c))}\sum_{u\in\text{UNIGRAM} (c)}\textit{unigram2 vec}(u), \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Section \(S\)**} & \multirow{2}{*}{**Subsection \(s\)**} & \multirow{2}{*}{ \begin{tabular}{c} **Labeled** \\ **News** \\ **Articles (\%)** \\ \end{tabular}  } & \multicolumn{6}{c}{\(\textit{agerate}_{\textit{eras}}(n\),g)} \\ \cline{3-13}  & & & **10s** & & **20s** & & **30s** & & **40s** & \(\geq\)**50s** \\ \cline{3-13}  & & & **Mean** & **S.D. ** & **Mean** & **S.D. ** & **Mean** & **S.D. ** & **Mean** & **S.D. ** \\ \hline \multirow{11}{*}{\ \begin{tabular}{c} Lifestyle/ \\ Culture \\ \end{tabular}  } & Travel/Leisure & 0.2134\% & 0.0221 & 0.0195 & 0.1670 & 0.0606 & 0.3852 & 0.0630 & 0.2785 & 0.0703 & 0.1464 & 0.0586 \\ \cline{2-13}  & Food/Restaurant & 0.0517\% & 0.0100 & 0.0076 & 0.2062 & 0.0457 & 0.3712 & 0.0671 & 0.2775 & 0.0231 & 0.1350 & 0.0746 \\ \cline{2-13}  & Car/Test Drive & 0.2651\% & 0.0100 & 0.0095 & 0.1254 & 0.0466 & 0.3685 & 0.0708 & 0.3220 & 0.0533 & 0.1754 & 0.0797 \\ \cline{2-13}  & Road/Traffic & 0.1099\% & 0.0118 & 0.0101 & 0.1053 & 0.0511 & 0.2865 & 0.0775 & 0.3241 & 0.0537 & 0.2735 & 0.0962 \\ \cline{2-13}  & Health Information & 0.3362\% & 0.0187 & 0.0114 & 0.1904 & 0.0761 & 0.3590 & 0.0581 & 0.2831 & 0.0646 & 0.1494 & 0.0675 \\ \cline{2-13}  & \begin{tabular}{c} Performance/ \\ Exhibition \\ \end{tabular}  } & 0.2198\% & 0.0221 & 0.0271 & 0.1712 & 0.1363 & 0.2874 & 0.0717 & 0.3174 & 0.0956 & 0.2012 & 0.1005 \\ \cline{2-13}  & Book & 0.1616\% & 0.0432 & 0.0409 & 0.2100 & 0.1112 & 0.2660 & 0.0870 & 0.2724 & 0.0842 & 0.2072 & 0.1195 \\ \cline{2-13}  & Religion & 0.4655\% & 0.0225 & 0.0198 & 0.1582 & 0.0848 & 0.3033 & 0.0944 & 0.3040 where UNIGRAM\((c)\) is a set of unigrams appearing in a news comment \(c\). \[\mathbf{news2 vec}(n)\frac{1}{n(\text{COMMENT}(n))}\sum_{c\in\text{COMMENT}(n)}\mathbf{ comment2 vec}(c)\text{,} \tag{3}\]  
where COMMENT\((n)\) is a set of news comments on a news article \(n\). In addition, for the 15,080 labeled news articles, each age group rate of a news article \(n\), i.e., \(\mathbf{agesrate}_{\mathbf{news}}(n,\ g)\), was transformed into log odds to avoid having a negative value in the prediction, and the log odds was given by  
\[\mathbf{agescore}_{\mathbf{news}}(n,\ g)=\log\biggl{(}\frac{\mathbf{agerate}_{\mathbf{news}} (n,g)}{1-\mathbf{agerate}_{\mathbf{news}}(n,g)}\biggr{)}\text{.} \tag{4}\]  
Additionally, for the labeled news article \(n\), \(\mathbf{agescore}_{\mathbf{news}}(n,g)\), values of all five age groups were obtained and used as a multi-label target, which was defined as  
\[\mathbf{agescore}_{\mathbf{news}}(n)= \begin{bmatrix}\mathbf{agescore}_{\mathbf{news}}(n,10 \text{s})\\ \vdots\\ \mathbf{agescore}_{\mathbf{news}}(n,\geq 50\text{s})\end{bmatrix} \text{.}