Clustering based on Stochastic Dominance with application for risk averters and risk seekers

Stochastic Dominance (SD) theory provides a rigorous framework for selecting superior assets tailored to the asset allocation needs of investors with varying risk preferences (i.e., risk-averse, risk-seeking, and risk-neutral). However, traditional stock clustering methods typically rely on geometric metrics such as Euclidean distance, which often fail to effectively capture the intrinsic risk dominance relationships among assets. To address this limitation, this paper proposes an innovative clustering analysis framework based on SD test statistics. Methodologically, this study deeply integrates SD theory with machine learning algorithms. Transcending the limitations of traditional reliance on geometric distance, we innovatively utilize test statistics from first-, second-, and third-order SD to construct a "Stochastic Dominance Coefficient Matrix." Building upon this matrix, we modify the classic K-means and Hierarchical Clustering algorithms. Specifically, we derive 12 distinct algorithm variants tailored to different orders of SD relationships. Simultaneously, we construct the SD-SC coefficient and the SD-DBI index as specialized validity indices to evaluate the clustering performance. Empirically, we analyze constituent stock data from a representative developed market (the US NASDAQ Index) and an emerging market (China's CSI 100 Index). The results verify the effectiveness and robustness of the proposed method. Furthermore, we apply the clustering results to the modification of the Single Index Model and the construction of Global Minimum Variance Portfolios (GMVP). The findings demonstrate that the proposed method effectively facilitates customized asset allocation for investors, holding significant theoretical value and practical implications.

Materials Map Integrating Experimental and Computational Data through Graph-Based Machine Learning for Enhanced Materials Discovery

Materials informatics (MI), which emerges from the integration of materials science and data science, is expected to greatly streamline the material discovery and development. The data used for MI are obtained from both computational and experimental studies, while their integration remains challenging. In our previous study, we reported the integration of these datasets by applying a machine learning model that captures trends hidden in the experimental datasets to compositional data stored in the computational database. In this study, we use the obtained data to construct materials maps, which visualize the relation in the structural features of materials, aiming to support study by the experimental researchers. The map is constructed using the MatDeepLearn (MDL) framework, which implements the graph-based representation of material structures, deep learning, and dimensional reduction for the map construction. We evaluate the obtained materials maps through statistical analysis and found that the MDL using message passing neural network (MPNN) enables efficient extraction of features that reflect the structural complexity of materials. Moreover, we found that this advantage does not necessarily translate into improved accuracy in predicting material properties. We attribute this unexpected outcome to the high learning performance inherent in MPNN, which can contribute to the structuring of data points within the materials map.