## 4 Experimental Results
### External Comparison
#### 4.2.1 Test Datasets  
The test datasets were developed through a process called harmonization, where notes are modified by addition or deletion. This dataset was developed by a team of music experts for experimental purposes. We further classify test datasets into two subcategories: (a) random restoration and (b) copying-oriented restoration. For _random restoration_, we selected five songs from _Kernscores_ and modified each to create five different versions of the original songs with the help of our experts. We requested that the music experts replace a certain percentage of the original notes with random notes. In this dataset, we did not intend to keep the song melodic for the listeners, so we principally followed the mathematical ratio when modifying the song. In our dataset, the song in subset 1 has all the original notes, followed by versions with 80%, 70%, 60%, and 40% of the original notes in subsets 2, 3, 4, and 5, respectively. Moreover, as stated earlier, the original notes were replaced by random notes according to that version's subset's mathematical ratio. For example, subsets with 80% and 60% original notes contain songs that have 20% and 40%, respectively, of their notes replaced with randomly selected notes. The ground truth is established based on the mathematical percentage of the original notes. We compared the results of each subset against the ground truth. To evaluate TruMuzic, we were only able to compare the performance of DTW on the musical notes feature since we were not able to change the rest of our data types with manually produced test datasets in the same way. As shown in Table 12, we evaluated the performance of DTW against MESMF [9], [PERSON] et al. [7], SiMPle [12], [PERSON] et al. [51], and a traditional edit distance-based similarity  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Features** & **Estimate** & **SE** & \(t\)**-Stat** & \(p\)**-Value** \\ \hline (Intercept) & 2.1717 & 0.36628 & 5.929 & 4.8201 \(\times\) 10\({}^{-9}\) \\ Notes & 1.1048 & 0.020196 & 54.704 & 6.2884 \(\times\) 10\({}^{-253}\) \\ Pitch & 1.0033 & 0.030476 & 32.92 & 1.5882 \(\times\) 10\({}^{-143}\) \\ Census & 0.37196 & 0.037046 & 10.04 & 3.1316 \(\times\) 10\({}^{-22}\) \\ Provenance & 1.1563 & 0.069131 & 16.726 & 5.8422 \(\times\) 10\({}^{-53}\) \\ \hline \hline \end{tabular}
\end{table}
Table 11: Estimated coefficients by the linear regression model.  
comparison method. MESMF introduces a music plagiarism detection model called BMM-Det, which uses a graph-based approach to compare potential plagiarized and original songs, by calculating the edit distance using the BMM-Det algorithm. [PERSON] et al. [7] extracted musical fingerprints and compared them with the database of existing songs through segment matching. SiMPle [12] and methods proposed by [PERSON] et al. [51], also worked on audio fingerprinting; however, they use 'SiMPle'. They calculated music similarity based on the SiMPle (similarity matrix profile) method. The table shows that the DTW, MEMSF, [PERSON] et al. [7], and SiMPle models closely follow the ground truth; however, the edit-distance model and [PERSON] et al. [51] are a little further from the ground truth, but remain somewhat close.  
It should be noted that, in Table 12, we are only comparing the musical notes feature, and all the other features of TruMuzic are not being considered in the comparison. In this way, it was found that DTW improves the similarity measurement of temporal sequences by taking acceleration and declaration into account. However, the evaluation of this test dataset does not contribute to the goal of achieving accurate real-time plagiarism detection after the pattern of a piece of music has been copied. In general, a composer intending to copy a musical piece will make slight changes to some of the chords and tempo, but primarily, the musical structure will remain the same. Therefore, we will apply a more realistic copy-oriented approach in our next experimental setup.