## 4 Results and Discussions
### Key Findings
#### 4.2.2 Improvement for Each Setup  
The first configuration, Figure 10, shows the earliest signs of improvement compared to the others. It can be said that the algorithm performs well when shopping lists are smaller. In particular, the agglomerative clustering variant performs better than its affinity propagation counterpart, averaging 1-2 s faster when it comes to the average time per item. It can be deduced that DProSA-AG performs better than DProSA-AP because fewer linkages are required for smaller lists. It was also observed that there were times that DProSA-AP performed better than DProSA-AG; in such instances, the shopping lists' items had not yet obtained a sufficiently robust linkage. As the same shopping lists were run again, the agglomerative model had already obtained proximity data from previous runs. Figure 8: Performance of the setups. _The three setups have similar performances when no sorting is applied, indicating no bias in any of the three._The medium-sized list, as shown in Figure 11, has the least definitive result of the three list configurations. Aside from the drop in average time per item for the fourth group of 50 shoppers, the performances of the algorithms do not seem to portray any relevant improvement. The reason for this could be the range of the item count for the medium-sized lists, which was set to 8-14. This wider spread results in a mix of smaller and larger lists, which results in the overall performance being normalized. The previous statement is further substantiated in the performance data of large lists. As shown in Figure 12, agglomerative clustering loses its advantage over affinity propagation due to larger lists not being able to form robust linkages when the number of lists is smaller. Even though there are more items in each individual list, the pairwise connections formed are not substantially greater since there are only 100 lists. The ratio between shopping list item count and pairwise connections formed is much more efficient for smaller lists than larger lists. In fact, for the shopping list used in configuration 1c, only 1303 pairs were formed; in contrast, the shopping list used in configuration 1a generated 838 pairs. As such, it is expected that DProSA-AP would be able to perform much better since it does not require robust linkages as much as DProSA-AG. After analyzing the algorithmic trends and patterns for varied list sizes, 100 shoppers with a mixed assortment of small, medium, and large lists were looped five times. The first scenario used a pool of 60 items, and the clusters were precomputed before run-time via the 60 item pool training set. The first 200 shoppers do not exhibit any significant changes; however, by the third group of 100 shoppers, the average dwell time for these shoppers dropped by 13 s and 20 s for DProSA-AG and DProSA-AP, respectively. This number is already significant considering the number of shoppers that it took to achieve this; by the end of the fifth loop, the average dwell time for the last 100 shoppers reached 28 s for DProSA-AG and DProSA-AP. Figure 9: Scaled performance of the setups. _Applying the scaling equation defined previously yields similar performances, showing that the scaling process is unbiased._  
Figure 11: Configuration 1b. _This scenario depicts the performance of the three setups for medium-sized lists. The average time gap for every 50 shoppers is also shown._  
Figure 10: Configuration 1a. _This scenario depicts the performance of the three setups for small-sized lists. The average time gap for every 50 shoppers is also shown._  
In configuration 2, as shown in Figure 13, since there are only 60 items, the linkage between pairs achieves robustness sooner. This is the reason why the agglomerative clustering variant performs similarly to the affinity propagation variant. Configuration 3, as shown in Figure 14, challenges DProSA-AG as it introduces a full 555 pool of items to generate lists from.