Applying Quadri-Partition Neutrosophic Soft Locally Compact Spaces to Enhance Machine Learning and Uncertainty Management

Abstract

Within the broader framework of quadri-partition neutrosophic soft bi-topological spaces (QPNSBTS), the concept of quadri-partition neutrosophic soft locally compact space (QPNSLCS) is introduced in this research. It strengthens the theoretical foundation for handling uncertainty in complex topological structures by demonstrating that local compactness, particularly when combined with the Hausdorff requirement, entails the existence of compact neighbors and compactness in subspaces. The key concepts and theorems illustrate how compactness can be effectively used in the context of neutrosophic soft sets, which are a more powerful way to handle unclear and ambiguous data in advanced mathematical and practical applications. Furthermore, a number of machine learning algorithms are used to explore the concept of a tangent similarity between two quadri-partition neutrosophic soft sets. Additionally, the current study includes a number of studies and visualizations to evaluate the effectiveness of different clustering algorithms and dimensionality reduction techniques. Each of the graphics in the findings illustrates a distinct method for viewing and comprehending complex data. The K-means++ initialization (Fig. 6.1) serves as an illustration of how the algorithm's initialization step improves clustering accuracy by choosing centroid (data points) that are widely distributed, reducing the likelihood of subpar clustering performance. More training is required since hidden units are only activated with low activations, according to restricted Boltzmann Machine (RBM) activation patterns (Fig. 6.2). Additionally, the Linear Discriminant Analysis (LDA) plots (Fig. 6.4) and Heatmaps (Fig. 6.3) might provide helpful details regarding the organization and segregation of the datasets. The discussion of the results, which can be devoted to their applicability in terms of clustering, dimensionality reduction, and feature learning, is based on these methods and the associated visual models.