## 3 Material and Methods
### Thematic Analysis
#### 3.3.3 Sentence Similarity Measurement  
To uncover the conceptual and thematic patterns of the sustainability reports, it was necessary to calculate the similarity between each sentence in a report and the representative sentences of the SDG. For document-similarity measurement, cosine similarity is widely used, because this metric is proven to be powerful in handling the rearrangement of words, spelling errors, and other differences in strings [42]. The cosine similarity considers vector \begin{table}
\begin{tabular}{l l l l} \hline \hline
**No** & **Category** & **Goal** & **Sentence** \\ \hline
0 & Life & Goal 1 & End poverty in all its forms everywhere \\
1 & Life & Goal 1 & Despite progress under the MDGs, approximately... \\
2 & Life & Goal 1 & Over the past decade, markets in developing countries... \\
3 & Life & Goal 1 & Certain groups are disproportionately represented... \\
4 & Life & Goal 1 & These include women, persons with disabilities,... \\... &... &... &... \\
636 & Social development & Goal 17 & 17.16 Enhance the global partnership for sustainable... \\
637 & Social development & Goal 17 & 17.17 Encourage and promote effective public,... \\
638 & Social development & Goal 17 & Data, monitoring and accountability \\
639 & Social development & Goal 17 & 17.18 By 2020, enhance capacity-building support to... \\
640 & Social development & Goal 17 & 17.19 By 2030, build on existing initiatives to develop... \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Sentences obtained from the 17 SDGs. orientation independent of vector magnitude. Since converting a sentence into a vector tends to produce a high-dimensional sparse matrix, using similarity metrics based on the size of the vector for such sparse matrices results in poor accuracy. Therefore, the cosine similarity is advantageous when measuring the degree of similarity, irrespective of the document size. This study also used the cosine similarity, because with the SBERT model, there are no significant differences with the results of Manhattan and Euclidean distances in comparing the similarity between two sentence embeddings [41]. We used the cosine similarity module from the Scikit-Learn library [43], and Equation (1) is the formula for calculating cosine similarity:  
\[\text{Similarity score}=\frac{A\cdot B}{\parallel A\parallel\parallel B \parallel}=\frac{\sum_{i}^{n}A_{i}\times B_{i}}{\sqrt{\sum_{i}^{n}\left(A_{i} \right)^{2}}\times\sqrt{\sum_{i}^{n}\left(B_{i}\right)^{2}}} \tag{1}\]  
where \(A\) is a sentence vector from similarity reports, \(B\) is a representative sentence vector from the SDG, and n is the dimension of vectors. Moreover, we converted score numbers to 0-100 values by using min-max scaler. This is to guarantee that all scores have the exact same scale. Equation (2) is the formula for scaling the scores:  
\[z_{i}=\frac{x_{i}-\min(x)}{\max(x)-\min(x)}\times 100 \tag{2}\]  
where \(x\) is the similarity score of a sentence and \(z\) is the scaled similarity score. Similarity calculation was performed sequentially for each report. The procedure used is as follows: Let \(n_{1}\) denote the number of sentences in Report 1 and \(n_{k}\) the number of representative sentences in \(k\)th SDG. Then, \(S_{ij}^{k}\) can be defined as follows:  
\(S_{ij}^{k}=\) similarity scores between \(i\)th sentence in Report 1 and \(j\)th representative sentence on \(k\)th SDG, where \(k\) = 1, 2,..., 17; \(i\) = 1, 2,..., \(n_{1}\) (\(n_{1}\) is the number of sentences in Report 1); \(j\) = 1, 2,..., \(n_{k}\) (\(n_{k}\) is the number of representative sentences in \(k\)th SDG). Each sentence therefore has 641 similarity measures because there are 641 representative sentences across SDGs. The total number of similarity scores is 69,979,893 (109,173 \(\times\) 641), with an average of 42.9 and standard deviation of 11.4. Therefore, about 95% of the similarity scores are between 20.1 and 65.7.