With the development of information technology, a large number of datasets with complex structures, such as multidimensional datasets, need to be processed and analyzed. In this paper we propose a kernel-based statistical learning algorithm, Bayesian Kernel Adaptive Grouping Learning (BKAGL), to provide an innovative solution for the classification problem of multi-dimensional datasets. BKAGL can integrate information from different dimensions adaptively. Meanwhile, we adopt the Bayesian framework which can infer the approximate posterior distributions of parameters. The utilization of grouping features can help find which groups of features have more contributions to the response. Simulation results illustrate that BKAGL outperforms some classical classification methods and the corresponding ungrouped method. The analysis of the electrocardiogram (ECG) and electroencephalography (EEG) datasets shows that BKAGL has the highest classification accuracy and provides explanatory information.

中文翻译：

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多维数据集的贝叶斯核自适应分组学习

随着信息技术的发展，需要处理和分析大量结构复杂的数据集，如多维数据集。在本文中，我们提出了一种基于核的统计学习算法，贝叶斯核自适应分组学习（BKAGL），为多维数据集的分类问题提供了一种创新的解决方案。BKAGL 可以自适应地整合不同维度的信息。同时，我们采用贝叶斯框架，可以推断参数的近似后验分布。分组特征的利用可以帮助找出哪些特征组对响应的贡献更大。仿真结果表明，BKAGL 优于一些经典的分类方法和相应的未分组方法。