Multiscale laplacian learning
Multiscale laplacian learning
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DOI：
10.1007/s10489-022-04333-2
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发表时间：
2021-09
影响因子：
5.3
通讯作者：
E. Merkurjev;D. Nguyen;Guo-Wei Wei-Guo-Wei-Wei-2113827098
中科院分区：
文献类型：
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作者：
E. Merkurjev;D. Nguyen;Guo-Wei Wei-Guo-Wei-Wei-2113827098
机器学习极大地影响了包括科学在内的各个领域。然而，尽管机器学习取得了巨大的成就，但大多数现有机器学习方法的关键局限性之一是它们依赖于大型标记集，因此，有限标记样本的数据仍然是一个重要的挑战。此外，在不同数据的情况下，机器学习方法的性能往往受到严重阻碍，这些数据通常与较小的数据集有关，或者与数据集的大小受到高实验成本和/或伦理限制的研究领域相关的数据。这些挑战需要创新的战略来处理这些类型的数据。在这项工作中，通过集成基于图的框架、半监督技术、多尺度结构以及修改和适应的优化程序来解决上述挑战。这导致了两种创新的多尺度拉普拉斯学习（MLL）方法，用于机器学习任务，如数据分类，以及处理有限样本、不同数据和小数据集的数据。第一种方法是多核流形学习（MML），它将流形学习与多核信息相结合，并使用多尺度图拉普拉斯算子结合一个扭曲核正则化器。第二种方法是多尺度MBO （MMBO）方法，该方法将多尺度拉普拉斯算子引入到著名的经典Merriman-Bence-Osher （MBO）格式的修正中，并利用了快速求解器。我们在各种基准数据集上实验展示了我们的算法的性能，并将它们与最先进的方法进行了比较。
Machine learning has greatly influenced a variety of fields, including science. However, despite tremendous accomplishments of machine learning, one of the key limitations of most existing machine learning approaches is their reliance on large labeled sets, and thus, data with limited labeled samples remains an important challenge. Moreover, the performance of machine learning methods is often severely hindered in case of diverse data, which is usually associated with smaller data sets or data associated with areas of study where the size of the data sets is constrained by high experimental cost and/or ethics. These challenges call for innovative strategies for dealing with these types of data.In this work, the aforementioned challenges are addressed by integrating graph-based frameworks, semi-supervised techniques, multiscale structures, and modified and adapted optimization procedures. This results in two innovative multiscale Laplacian learning (MLL) approaches for machine learning tasks, such as data classification, and for tackling data with limited samples, diverse data, and small data sets. The first approach, multikernel manifold learning (MML), integrates manifold learning with multikernel information and incorporates a warped kernel regularizer using multiscale graph Laplacians. The second approach, the multiscale MBO (MMBO) method, introduces multiscale Laplacians to the modification of the famous classical Merriman-Bence-Osher (MBO) scheme, and makes use of fast solvers. We demonstrate the performance of our algorithms experimentally on a variety of benchmark data sets, and compare them favorably to the state-of-art approaches.