T. Tony Cai

Zheng Fang, Fucai Ke, Jae Young Han et al.

This study addresses the challenge of forming effective groups in collaborative problem-solving environments. Recognizing the complexity of human interactions and the necessity for efficient collaboration, we propose a novel approach leveraging graph theory and reinforcement learning. Our methodology involves constructing a graph from a dataset where nodes represent participants, and edges signify the interactions between them. We conceptualize each participant as an agent within a reinforcement learning framework, aiming to learn an optimal graph structure that reflects effective group dynamics. Clustering techniques are employed to delineate clear group structures based on the learned graph. Our approach provides theoretical solutions based on evaluation metrics and graph measurements, offering insights into potential improvements in group effectiveness and reductions in conflict incidences. This research contributes to the fields of collaborative work and educational psychology by presenting a data-driven, analytical approach to group formation. It has practical implications for organizational team building, classroom settings, and any collaborative scenario where group dynamics are crucial. The study opens new avenues for exploring the application of graph theory and reinforcement learning in social and behavioral sciences, highlighting the potential for empirical validation in future work.

T. Tony Cai, Rong Ma

This paper investigates the theoretical foundations of the t-distributed stochastic neighbor embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data visualization method. A novel theoretical framework for the analysis of t-SNE based on the gradient descent approach is presented. For the early exaggeration stage of t-SNE, we show its asymptotic equivalence to power iterations based on the underlying graph Laplacian, characterize its limiting behavior, and uncover its deep connection to Laplacian spectral clustering, and fundamental principles including early stopping as implicit regularization. The results explain the intrinsic mechanism and the empirical benefits of such a computational strategy. For the embedding stage of t-SNE, we characterize the kinematics of the low-dimensional map throughout the iterations, and identify an amplification phase, featuring the intercluster repulsion and the expansive behavior of the low-dimensional map, and a stabilization phase. The general theory explains the fast convergence rate and the exceptional empirical performance of t-SNE for visualizing clustered data, brings forth interpretations of the t-SNE visualizations, and provides theoretical guidance for applying t-SNE and selecting its tuning parameters in various applications.