Active learning is a major area of interest within the field of machine learning, especially when the labeled instances are very difficult, time-consuming or expensive to obtain. In this paper, we review various active learning methods for manifold data, where the intrinsic manifold structure of data is also incorporated into the active learning query strategies. In addition, we present a new manifold-based active learning algorithm for Gaussian process classification. This new method uses a data-dependent kernel derived from a semi-supervised model that considers both labeled and unlabeled data. The method performs a regularization on the smoothness of the fitted function with respect to both the ambient space and the manifold where the data lie. The regularization parameter is treated as an additional kernel (covariance) parameter and estimated from the data, permitting adaptation of the kernel to the given dataset manifold geometry. Comparisons with other AL methods for manifold data show faster learning performance in our empirical experiments. MATLAB code that reproduces all examples is provided as supplementary materials.

中文翻译：

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关于流形数据的主动学习方法

主动学习是机器学习领域中的一个主要兴趣领域，尤其是在获得标记的实例非常困难，耗时或昂贵的情况下。在本文中，我们回顾了流形数据的各种主动学习方法，其中数据的固有流形结构也被纳入了主动学习查询策略。此外，我们为高斯过程分类提出了一种新的基于流形的主动学习算法。这种新方法使用从半监督模型派生的数据相关内核，该模型同时考虑标记数据和未标记数据。该方法对拟合函数相对于周围空间和数据所在的歧管的平滑度进行正则化。正则化参数被视为附加的内核（协方差）参数，并根据数据进行估算，从而可以使内核适应给定的数据集流形几何形状。与其他用于流形数据的AL方法的比较表明，在我们的经验实验中，学习性能更快。复制所有示例的MATLAB代码作为补充材料提供。