We consider the problem of classification of points sampled from an unknown probability measure on a Euclidean space. We study the question of querying the class label at a very small number of judiciously chosen points so as to be able to attach the appropriate class label to every point in the set. Our approach is to consider the unknown probability measure as a convex combination of the conditional probabilities for each class. Our technique involves the use of a highly localized kernel constructed from Hermite polynomials, in order to create a hierarchical estimate of the supports of the constituent probability measures. We do not need to make any assumptions on the nature of any of the probability measures nor know in advance the number of classes involved. We give theoretical guarantees measured by the F-score for our classification scheme. Examples include classification in hyper-spectral images and MNIST classification.

我们考虑从欧几里得空间上的未知概率测度中采样的点的分类问题。我们研究了在极少数明智选择的点上查询类标签的问题，以便能够将适当的类标签附加到集合中的每个点上。我们的方法是将未知概率度量视为每个类的条件概率的凸组合。我们的技术涉及使用从Hermite多项式构造的高度局部化的内核，以创建对构成概率测度的支持的层次估计。我们不需要对任何概率测度的性质做任何假设，也不需要事先知道所涉及的类别数。我们给出由F度量的理论保证-score为我们的分类方案。示例包括高光谱图像中的分类和MNIST分类。