Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to obtain accurate classification performance when the feature distributions in the different classes are complex, with nonlinear, overlapping and intersecting supports. This is particularly true when training data are limited. To address this problem, this article proposes a new type of classifier based on obtaining a local approximation to the support of the data within each class in a neighborhood of the feature to be classified, and assigning the feature to the class having the closest support. This general algorithm is referred to as LOcal Manifold Approximation (LOMA) classification. As a simple and theoretically supported special case having excellent performance in a broad variety of examples, we use spheres for local approximation, obtaining a SPherical Approximation (SPA) classifier. We illustrate substantial gains for SPA over competitors on a variety of challenging simulated and real data examples.

中文翻译：

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通过局部流形近似分类

分类器根据输入特征将数据标记为属于一组组中的一个。当不同类别中的特征分布复杂，具有非线性、重叠和交叉支持时，获得准确的分类性能具有挑战性。当训练数据有限时尤其如此。为了解决这个问题，本文提出了一种新的分类器，它基于获取待分类特征邻域内每个类内数据的支持度的局部近似，并将该特征分配给支持度最接近的类。这种通用算法称为局部流形近似 (LOMA) 分类。作为在各种示例中具有出色性能的简单且有理论支持的特殊情况，我们使用球体进行局部逼近，获得球面逼近 (SPA) 分类器。我们在各种具有挑战性的模拟和真实数据示例中说明了 SPA 相对于竞争对手的实质性收益。