Baoyi Shi

Hanchao Zhang, Xiaomeng Ju, Baoyi Shi et al.

This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors. The method identifies structured subsets of the SPSD cone characterized by common principal component (CPC) representations, where each subset corresponds to matrices sharing a common eigenstructure. Unlike conventional clustering approaches that rely on vectorization or transformations of SPSD matrices, thereby losing critical geometric and spectral information, K-Tensors introduces a divergence that respects the intrinsic geometry of SPSD matrices. This divergence preserves the shape and eigenstructure information and yields principal SPSD tensors, defined as a set of representative matrices that summarize the distribution of SPSD matrices. By exploring its theoretical properties, we show that the proposed clustering algorithm is self-consistent under mild distribution assumptions and converges to a local optimum. We demonstrate the use of the algorithm through an application to resting-state functional magnetic resonance imaging (rs-fMRI) data from the Human Connectome Project, where we cluster brain connectivity matrices to discover groups of subjects with shared connectivity structures.

Jikai Jin, Kenneth Hung, Sanath Kumar Krishnamurthy et al.

The multi-armed bandit problem is a core framework for sequential decision-making under uncertainty, but classical algorithms often fail in environments with hidden, time-varying states that confound reward estimation and optimal action selection. We address key challenges arising from unobserved confounders, such as biased reward estimates and limited state information, by introducing a family of state-model-free bandit algorithms that leverage lagged contextual features and coordinated probing strategies. These implicitly track latent states and disambiguate state-dependent reward patterns. Our methods and their adaptive variants can learn optimal policies without explicit state modeling, combining computational efficiency with robust adaptation to non-stationary rewards. Empirical results across diverse settings demonstrate superior performance over classical approaches, and we provide practical recommendations for algorithm selection in real-world applications.