面向稀缺标注数据分类的持久拉普拉斯增强算法
Persistent Laplacian-enhanced Algorithm for Scarcely Labeled Data Classification
AI总结：
本文提出持久拉普拉斯增强图 MBO（PL-MBO）方法，将持久谱图理论与经典 MBO 格式结合，以极少的标注数据实现优于现有半监督算法的数据分类性能。
摘要：
许多机器学习（ML）方法的成功关键依赖于拥有大量标注数据。然而，对于许多应用而言，获取足够的标注数据可能成本高昂、耗时，并受到伦理约束。应对这一挑战的一种已展现出巨大价值的方法是半监督学习（SSL）；该技术在训练过程中同时利用标注数据和未标注数据，通常标注数据远少于未标注数据，而未标注数据往往相对容易且廉价地获得。事实上，SSL 方法在数据标注成本特别高的应用中尤为有用，例如医学分析、自然语言处理（NLP）或语音识别。在 SSL 方法中，有一类在各个领域取得巨大成功的子集涉及融合基于图的技术的算法。这些方法之所以流行，是因为图框架提供了大量信息，并且其应用具有广泛的通用性。在本工作中，我们通过将持久谱图理论与经典的 Merriman-Bence-Osher（MBO）格式相结合，提出了一种基于代数拓扑的半监督方法，称为持久拉普拉斯增强图 MBO（PL-MBO）。具体来说，我们使用一个过滤过程来生成一列链复形及其相关联的单纯复形族，并由此构造一族持久拉普拉斯算子。总体而言，这是一种非常高效的方法，与许多 ML 技术相比，它只需要少得多的标注数据即可表现良好，并且可以适配小型和大型数据集。我们评估了所提方法在数据分类上的性能，结果表明所提技术优于其他现有的半监督算法。
英文摘要：
The success of many machine learning (ML) methods depends crucially on having large amounts of labeled data. However, obtaining enough labeled data can be expensive, time-consuming, and subject to ethical constraints for many applications. One approach that has shown tremendous value in addressing this challenge is semi-supervised learning (SSL); this technique utilizes both labeled and unlabeled data during training, often with much less labeled data than unlabeled data, which is often relatively easy and inexpensive to obtain. In fact, SSL methods are particularly useful in applications where the cost of labeling data is especially expensive, such as medical analysis, natural language processing (NLP), or speech recognition. A subset of SSL methods that have achieved great success in various domains involves algorithms that integrate graph-based techniques. These procedures are popular due to the vast amount of information provided by the graphical framework and the versatility of their applications. In this work, we propose an algebraic topology-based semi-supervised method called persistent Laplacian-enhanced graph MBO (PL-MBO) by integrating persistent spectral graph theory with the classical Merriman-Bence- Osher (MBO) scheme. Specifically, we use a filtration procedure to generate a sequence of chain complexes and associated families of simplicial complexes, from which we construct a family of persistent Laplacians. Overall, it is a very efficient procedure that requires much less labeled data to perform well compared to many ML techniques, and it can be adapted for both small and large datasets. We evaluate the performance of the proposed method on data classification, and the results indicate that the proposed technique outperforms other existing semi-supervised algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
