用信号分离思路做分类，能自动发现类别数并精准区分重叠类
A signal separation view of classification
- 基于局部三角多项式核，将分类视为概率分布支持集的分离
- 理论保证在最小标签查询下实现完美分类，可处理边界重叠情况
- 适合高维数据、类别边界模糊或未知类数的场景
机器学习中的分类问题通常被当作函数逼近问题处理。本文提出一种在任意紧致度量空间中进行分类的替代方法，理论上可同时确定类别数量，并仅通过最少的标签查询实现完美分类。该方法利用最初为信号处理中点源分离设计的局部三角多项式核。我们不再将类别视为点源，而是认为不同类别来自不同的概率测度。用于分离点源的局部核技术被证明可有效分离这些分布的支持集。我们的MASC算法以分层方式实现此过程，以适应类别边界接触或重叠的情况。我们在多个模拟和真实数据集上验证了该理论，包括萨利纳斯和印第安溪高光谱数据集以及一个文档数据集。
原文摘要 · Abstract (English)
The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields both the number of classes, and a perfect classification using a minimal number of queried labels. Our approach uses localized trigonometric polynomial kernels initially developed for the point source signal separation problem in signal processing. Rather than point sources, we argue that the various classes come from different probability measures. The localized kernel technique developed for separating point sources is then shown to separate the supports of these distributions. This is done in a hierarchical manner in our MASC algorithm to accommodate touching/overlapping class boundaries. We illustrate our theory on several simulated and real life datasets, including the Salinas and Indian Pines hyperspectral datasets and a document dataset.
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