论文标题
谨慎的主动聚类
Cautious Active Clustering
论文作者
论文摘要
我们考虑从欧几里得空间上未知概率度量采样的点的分类问题。我们研究了以很少数量的明智选择的点查询类标签的问题，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的概率度量视为每个类别概率的凸组合。我们的技术涉及使用由Hermite多项式构建的高度局部核，以创建对组成概率措施的支持的层次结构估计。我们不需要对任何概率措施的性质做出任何假设，也不需要事先知道所涉及的类数量。我们给出了由$ f $ - 分类计划衡量的理论保证。示例包括超光谱图像和MNIST分类中的分类。
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.
