Geometric classifiers for high-dimensional noisy data
Geometric classifiers for high-dimensional noisy data
复制标题
高维噪声数据的几何分类器
DOI：
10.1016/j.jmva.2021.104850
复制
发表时间：
2022
影响因子：
1.6
通讯作者：
Aoshima Makoto
中科院分区：
文献类型：
--
作者：
Ishii Aki;Yata Kazuyoshi;Aoshima Makoto
研究了强尖峰特征值（SSE）模型下高维数据的二次分类问题。高维数据包含了大量的信息，但同时也包含了大量的噪声。我们检测高维噪声作为高维协方差矩阵的尖峰特征结构。为了找到两个群体之间的差异，我们利用高维数据的几何特征。基于高维数据几何特征的分类分析称为几何二次判别分析（GQDA）。我们创建新的GQDA的基础上的高维尖峰特征结构。我们精确地研究了尖峰特征结构对GQDA的影响，使用几个例子。为了去除尖峰噪声，我们使用了数据变换技术。我们表明，我们提出的分类有一个一致性属性的错误率误分类的个人。通过计算机模拟，我们讨论了所提出的分类器的性能。最后，我们给出了几个使用微阵列数据集进行数据分析的演示。
We consider the quadratic classification for high-dimensional data under the strongly spiked eigenvalue (SSE) model. High-dimensional data contain much information, however, it also contains huge amount of noise. We detect the high-dimensional noise as a spiked eigenstructure of high-dimensional covariance matrices. In order to find the difference between two populations, we utilize a geometric feature of high-dimensional data. The classification analysis based on the geometric feature of high-dimensional data is called geometrical quadratic discriminant analysis (GQDA). We create new GQDA on the basis of the high-dimensional spiked eigenstructures. We precisely study the influence of the spiked eigenstructure on GQDA using several examples. In order to remove the spiked noise, we use a data transformation technique. We show that our proposed classifier has a consistency property with respect to the error rate of misclassifying an individual. By using computer simulation, we discuss the performance of the proposed classifier. Finally, we give several demonstrations of data analysis using a microarray data set.