Multiple kernel $k$-means integrates complementary nonlinear similarities by learning a combination of base kernels. Its pointwise optimization, however, is sensitive to noisy and boundary samples and repeatedly operates on sample-scale kernel matrices. Granular-ball representations organize local sample groups into mesoscopic units, but granular balls generated once in the input space may be inconsistent with the fused-kernel geometry that evolves during multiple kernel learning. We propose dynamic kernel-space granular-ball multiple kernel $k$-means (DK-GBMKKM). The method generates granular balls in the current fused kernel space and alternates kernel-weight learning with granular-ball membership updates, allowing the representation to adapt to changes in the fused-kernel geometry. A sample-size-weighted granular-ball kernel is further constructed to preserve the contributions of balls of different sizes, and its positive semidefiniteness and related equivalence properties are established. Experiments on 12 public datasets demonstrate the strong overall clustering performance of DK-GBMKKM. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/DK-GBMKKM.
Mariano Caruso, Daniel Ruiz, Alejandro Giraldo +1quant-ph cs.LG
Quantitative Structure-Activity Relationship ($\mathtt{QSAR}$) modeling is a foundational computational methodology in early-stage drug discovery, heavily relied upon for predicting compound toxicity, bioavailability, and therapeutic potential. However, classical methods often struggle to effectively map the highly complex, non-linear, and high-dimensional interactions inherent in molecular data, leading to reduced predictive accuracy and costly late-stage clinical failures. In this paper, we present a Quantum Multiple Kernel Learning ($\mathtt{QMKL}$) framework, dubbed Next-Gen $\mathtt{Q^2SAR}$, that leverages Quantum Support Vector Machines ($\mathtt{QSVMs}$) to overcome these classical limitations. By encoding molecular descriptors into exponentially large quantum Hilbert spaces, our approach substantially enhances the expressiveness of non-linear modeling. Benchmarking our quantum-enhanced framework on a dataset targeting the $\mathtt{DYRK1A}$ kinase (a critical target for Alzheimer's disease), the $\mathtt{QMKL}$-$\mathtt{SVM}$ achieves an impressive Area Under the Curve ($\mathtt{AUC}$) score of $0.8750$, significantly outperforming classical state-of-the-art Gradient Boosting models ($\mathtt{AUC} = 0.8037$). Furthermore, we establish a theoretical and empirical pathway toward resolving classical data bottlenecks through projected quantum kernels ($\mathtt{PQK}$) and measurement accelerators. As quantum computing architecture matures, this framework paves the way for autonomous cognitive architectures and self-improving drug discovery pipelines, promising to unlock deeper insights across vast chemical spaces and to accelerate the development of life-saving therapeutics.