Adaptive Preferential Attached kNN Graph with Distribution-Awareness

Graph-based kNN algorithms have garnered widespread popularity for machine learning tasks due to their simplicity and effectiveness. However, as factual data often inherit complex distributions, the conventional kNN graph's reliance on a unified k-value can hinder its performance. A crucial factor behind this challenge is the presence of ambiguous samples along decision boundaries that are inevitably more prone to incorrect classifications. To address the situation, we propose the Preferential Attached k-Nearest Neighbors Graph (paNNG), which adopts distribution-aware adaptive-k into graph construction. By incorporating distribution information as a cohesive entity, paNNG can significantly improve performance on ambiguous samples by "pulling" them towards their original classes and hence enhance overall generalization capability. Through rigorous evaluations on diverse datasets, paNNG outperforms state-of-the-art algorithms, showcasing its adaptability and efficacy across various real-world scenarios.

Modeling Multi-Dimensional Datasets via a Fast Scale-Free Network Model

Compared with network datasets, multi-dimensional data are much more common nowadays. If we can model multi-dimensional datasets into networks with accurate network properties, while, in the meantime, preserving the original dataset features, we can not only explore the dataset dynamic but also acquire abundant synthetic network data. This paper proposed a fast scale-free network model for large-scale multi-dimensional data not limited to the network domain. The proposed network model is dynamic and able to generate scale-free graphs within linear time regardless of the scale or field of the modeled dataset. We further argued that in a dynamic network where edge-generation probability represents influence, as the network evolves, that influence also decays. We demonstrated how this influence decay phenomenon is reflected in our model and provided a case study using the Global Terrorism Database.