## 3 Results and Discussion  
This study presents a comparative analysis of the G-NMS clustering method against six established algorithms, utilizing a total of eleven experimental trials--three from Dataset 1 and eight from Dataset 2. All experiments were performed on a university supercomputer equipped with 20 cores and 20 GB of RAM per core to ensure consistency and reliability in the experimental setup. To evaluate the efficacy of the clustering algorithms, two distinct metrics were employed: adjusted mutual information (AMI) and accuracy (ACC). These metrics were calculated by comparing the clustering results with the ground truth labels. The AMI metric assesses the correlation between the ground truth and the predicted clusters by measuring mutual information, reflecting the knowledge gained about one variable by observing another. An AMI score of 1 indicates perfect alignment with the ground truth, while a score of 0 implies no correlation. The ACC ranges between 0 to 100 percent. Figure 5 presents the AMI scores for each experiment across various clustering algorithms. In the first dataset, for the experiment labeled \"SNR0.5_Spk-1,2\", K-meansand G-NMS achieved the highest AMI, scoring an impressive highest AMI of 0.991. In comparison, agglomerative clustering reached an AMI of 0.906. In scenarios with moderate noise in spike, such as \"SNR1.25_Spk-2,3\", G-NMS excelled with a score of 0.992, outperforming other methods. Notably, agglomerative, HDBSCAN, DBSCAN, and FCM methods faced challenges, reflected by significantly lower AMI scores, indicating difficulties in specific clustering tasks. In experiments with higher noise levels, \"SNR2.0_Spk-3,1\", G-NMS showed robust performance with an AMI score of 0.993, which is slightly lesser than K-means. Other methods, including HDBSCAN and DBSCAN, achieved relative improvements with AMI scores of 0.653 and 0.763, respectively, outpacing agglomerative and FCM in performance. For Dataset 2, in the Easy--1 category, G-NMS recorded AMI scores of 0.979 and 0.962 for \"E1_SNR0.2_Spk-1,2\" and \"E1_SNR0.05_Spk-1,2\", respectively. Interestingly, in the \"E1_SNR0.05_Spk-1,2\" trial, G-NMS led the performance, whereas ISO-SPLIT edged ahead in \"E1_SNR0.2_Spk-1,2\" with a slightly higher AMI of 0.994. Similar patterns emerged in the Easy--2 categories; K-means demonstrated robust performance with an AMI of 0.977 in \"E2_SNR0.05_Spk-2,3\", slightly surpassing G-NMS, which scored 0.958. The other algorithms varied in efficacy, with agglomerative clustering at 0.804, HDBSCAN at 0.797, DBSCAN at 0.785, FCM at 0.844, and ISO-SPLIT at 0.889, with ISO-SPLIT showing a commonable improvement compared to certain traditional methods. In the Difficult 1 category of Dataset 2, all algorithms faced challenges in clustering, particularly in \"D1_SNR0.2_Spk-3,1\". However, in \"D1_SNR0.05_Spk-3,1\", FCM led with an AMI of 0.888, followed by K-means at 0.810, while G-NMS scored 0.274. Agglomerative clustering, HDBSCAN, and DBSCAN registered AMI scores of 0.713, 0.734, and 0.745, respectively. The Difficult 2 categories presented another difficult challenge for clustering spikes, with \"D2_SNR0.05_Spk-1,2\" showing K-means with the highest AMI of 0.959, affirming its clustering capabilities. Agglomerative clustering, FCM, and ISO-SPLIT also displayed strong performances with AMI scores of 0.914, 0.959, and 0.852, respectively. In contrast, G-NMS had a lower AMI of 0.756. In the \"D2_SNR0.2_Spk-1,2\" experiment, K-means maintained high performance with an AMI of 0.850, and ISO-SPLIT surpassed with the  
Figure 5: Evaluation of clustering algorithms using adjusted mutual information. The bar graph compares the adjusted mutual information scores of seven clustering methods—K-means, G-NMS*, agglomerative, HDBSCAN, DBSCAN, FCM, and ISO-SPLIT—across various experimental scenarios characterized by different SNR levels and neural spike class (Spk) pairings. highest AMI of 0.978. Meanwhile, G-NMS performance just had an AMI of 0.753. Agglomerative closely paralleled K-means with an AMI of 0.849.