One of the most difficult problems, in cluster analysis is the determination of the number of clusters in a data set. Solving this problem consists in detecting and finding the best number of clusters, which is an input parameter for the clustering problems. In this paper, we propose a new approach using the Maximum Stable Set Problem (MSSP) combined by Continuous Hopfield Network (CHN) to determine the number of clusters, which is a basic input parameter for K-Means method. By testing the theoretical results, the proposed approach was validated on a real application for the text mining. Some numerical examples and computational experiments assess the effectiveness of this approach as demonstrated in this paper.

Road traffic accidents (RTAs) are a significant public health and safety concern, resulting in numerous injuries and fatalities. The growing number of cases referred to traffic accident rooms in courts has underscored the necessity for an automated solution to determine victim indemnifications, particularly given the limited number of specialized judges and the complexity of cases involving multiple victims. This paper introduces RTACompensator, an artificial intelligence (AI)-driven decision support system designed to automate indemnification calculations for road accident victims. The system comprises two main components: a calculation module that determines initial compensation based on factors such as age, salary, and medical assessments, and a machine learning (ML) model that assigns liability based on police accident reports. The model uses Arabic bidirectional encoder representations from transformer (AraBERT) embeddings to generate contextual vectors from the report, which are then processed by extreme gradient boosting (XGBoost) to determine responsibility. The model was trained on a purpose-built Arabic corpus derived from real-world legal judgments. To expand the dataset, two data augmentation techniques were employed: multilingual bidirectional encoder representations from transformers (BERT) and Gemini, developed by Google DeepMind. Experimental results demonstrate the model’s effectiveness, achieving accuracy scores of 97% for the BERT-augmented corpus and 97.3% for the Gemini-augmented corpus. These results underscore the system’s potential to improve decision-making in road accident indemnifications. Additionally, the constructed corpus provides a valuable resource for further research in this domain, laying the groundwork for future advancements in automating and refining the indemnification process.

In this paper, we propose a new approach to solve the document-clustering using the K-Means algorithm. The latter is sensitive to the random selection of the k cluster centroids in the initialization phase. To evaluate the quality of K-Means clustering we propose to model the text document clustering problem as the max stable set problem (MSSP) and use continuous Hopfield network to solve the MSSP problem to have initial centroids. The idea is inspired by the fact that MSSP and clustering share the same principle, MSSP consists to find the largest set of nodes completely disconnected in a graph, and in clustering, all objects are divided into disjoint clusters. Simulation results demonstrate that the proposed K-Means improved by MSSP (KM_MSSP) is efficient of large data sets, is much optimized in terms of time, and provides better quality of clustering than other methods.