## 3 HELIOS Concept in the Real Estate Market--Methodology and Implementation
### Verification of Models Outputs
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Transactions** & **Node X** & **Node Y** & **Real Estate Fingerprint Characteristic** \\ \hline \multirow{6}{*}{99 (the average group)} & \multirow{6}{*}{\(1\)} & \multirow{6}{*}{0} & price per square meter: five thousand, three hundred and twenty-six, \\  & & & transaction date: ten of April, two thousand nineteen year. \\  & & & address: ul. [PERSON] twenty-six, \\  & & & share: one hundred and twenty-eight out of ten thousand, \\  & & & premises area in square meter: forty-five, \\  & & & elevator: no elevator, \\  & & & storey: fourth, \\  & & & year of construction: two thousand and eighteen \\ \hline \multirow{6}{*}{37 (the smallest group)} & \multirow{6}{*}{4} & \multirow{6}{*}{1} & price per square meter: six thousand and forty-six, \\  & & & transaction date: seventeen of July, two thousand twenty year, \\  & & & premises area in square meter: two hundred fifteen \\ \cline{1-1}  & & & storey: fifth, \\ \cline{1-1}  & & & year of construction: two thousand and nineteen, \\ \cline{1-1}  & & & address: ul. Eugeniusza Wegrzyna, \\ \cline{1-1}  & & & function: three-unit building, \\ \cline{1-1}  & & & building construction: brick \\ \hline \hline \end{tabular} Source: own elaboration.  
\end{table} 
Table 3: _Cont._about 21% due to the nature of features like area or price, which are continuous variables. However, it is essential to underscore that TF-IDF serves more as an interpretation tool than as a classification mechanism. For simplification and better understanding, it is worth mentioning that TF-IDF (t, d, D) calculates the importance of individual words in texts, allowing us to determine the significance of a word t in the context of all documents (transaction records) D, and specifically in a particular document d from group D. Thus, we analyze word t in each description of our real estate within a group and calculate TF-IDF for each such word, noting that in our group (2, 0), the descriptions of transactions in which the exact words have similar TF-IDF values. For example, the phrase \"transaction date: fourteen of November, two thousand twenty year\" has a TF-IDF value of 0.037 in one real estate description in our group and a similar value of 0.031 in another. To specify the potential range of values in our text corpus, normalizing TF-IDF is necessary. The range of TF-IDF values can be broad, depending on the specifics of the text corpus. For a word in a document, the TF-IDF value can be low if the word is common across all documents or very high if it appears only in a few documents from the entire corpus. This approach confirmed the authors' fundamental assumption regarding similarity identification and provided a robust framework for analyzing real estate properties based on these metrics. Although the discussed system is introduced as a highly complex source of information in the real estate market, its flexibility and versatility allow for application in a variety of other domains where similar issues are important. To fully assess the utility and quality of the applied methodology, the results were compared with the most common classification method for real estate objects, namely cluster analysis ([PERSON]'s method). An agglomerative hierarchical approach was used to identify groups of homogeneous properties based on minimizing the differences between feature vectors that make up the cluster in relation to the variance to estimate the distance between clusters. A cut-off point determined the number of clusters, where multiple clusters were identified at roughly the same distance. A cut-off value of 0.25 was set based on the agglomeration schedule graph, allowing the creation of 319 homogeneous groups (Figure 8). Figure 8: Dendrogram from the [PERSON] methods clustering. Source: own elaboration. The characteristics of the defined homogeneous groups in terms of their number, the similarity measure, and mean distance are presented in Table 4.