# A Model for Deriving Trust and Reputation on Blockchain-Based e-Payment System +
## 5 Evaluation via Real Bitcoin Transaction Dataset
### Analysis of Model-Applied TX Set:  
To analyze the result of applying our model to the transactions, we plot the reputation, \(\mathit{NE}\), and \(\mathit{ARNE}\) of four representative clusters among 155,040 clusters as shown in Figure 12(a)-d.  
Figure 12(a) presents the reputation of cluster #111936122. This cluster was selected as type \"Seller D\" in Table 2 which receives good ratings at the beginning for 3 months and changes to receive bad ratings for the rest of the period. The cluster has dealt with other 108 clusters 297 times for 6 months from 13 May to 6 December on the same year of 2017. Her reputation begins from 0.5 (neutral), and slightly increases for 3 months while making 65 transactions with the others. During the month of September, she loses her reputation relatively faster than the other months, from 0.5036 to 0.1848, as we intended for this seller. For this month, she receives comparatively lower \(\mathit{NE}\)s than during the other months, which are on average 0.47 and 0.31, respectively. This means that the ratings made by the numerous buyers are well reflected on her reputation, via appropriately normalized \(\mathit{NE}\), regardless of _who_ rated them (regardless of various \(\mathit{PEC}\) of the buyers). Figure 12: Distribution of transactions between addresses. Figure 13b plots a more interesting case with cluster #138537707, which was set to treat other clusters badly for the first 4 months and to behave well afterwards. While having 273 transactions during roughly 1 year, her reputation does not go down as we expected. Investigation revealed that this unusual behavior comes from the single-hit clusters. When it comes to a user who creates an address and does a transaction with another for the first time, that rating value cannot be normalized due to lack of _PEC_. For the first 4 months during which the cluster should have received _NE_s below 0.5, it's transactions were 189 single-hit clusters reaching up to roughly 80% of 236 transactions. As defined in Section 3, the _NE_ is derived from the evaluation based on the user's _PEC_. However, first time evaluator does not have a _PEC_ defined, and if the _PEC_ is not initialized, _NE_ is set to the evaluation divided by 10. For instance, if [PERSON] rates [PERSON] as 8 for the first time on an e-commerce store, her _NE_ is set to be 0.8, which affects [PERSON]'s reputation positively despite the fact that [PERSON] always grades between 8 and 10 and 8 is a bad rating for her. This is the sparsity problem, which could be exploited by malicious users who would like to manipulate data. However, recall that the data we use for this evaluation are extracted from Bitcoin, and single-hit addresses are a peculiarity of Bitcoin. In our real-life, there are very few users who create a new account to buy a product for every transaction. And as long as the user makes a second transaction, the model could derive desired _NE_ successfully from her _PEC_. Cluster #137987649 presented in Figure 13c has 248 transactions with 192 clusters from 27 August 27 of 2017 to 18 July of 2018. As she was had the \"bad\" type seller, she loses reputation gradually and continuously. On the other hand, Figure 13d presents the reputation of cluster #67863927 which the seller type is set to be good. From 19 October of 2016 to 2 February of 2017, she had transactions with 564 clusters of which the number of single-hit clusters are only 51 (9.04%). As there are few of single-hit clusters, evaluation values are properly normalized based on the concerned clusters' _PEC_ unlike the case of Figure 13b. As expected, her reputation improves as time goes by, and she maintains her reputation regardless of what type of buyers rate her. To summarize, we exploited the experiments with the dataset generated by two distinct methods. First, we experimented with the dataset consisting of randomly generated timestamps, transactions and users including their way to grade others.