{"title":"A structured covariance ensemble for sufficient dimension reduction","authors":"Qin Wang, Yuan Xue","doi":"10.1007/s11634-022-00524-4","DOIUrl":null,"url":null,"abstract":"<div><p>Sufficient dimension reduction (SDR) is a useful tool for high-dimensional data analysis. SDR aims at reducing the data dimensionality without loss of regression information between the response and its high-dimensional predictors. Many existing SDR methods are designed for the data with continuous responses. Motivated by a recent work on aggregate dimension reduction (Wang in Stat Si 30:1027–1048, 2020), we propose a unified SDR framework for both continuous and binary responses through a structured covariance ensemble. The connection with existing approaches is discussed in details and an efficient algorithm is proposed. Numerical examples and a real data application demonstrate its satisfactory performance.\n</p></div>","PeriodicalId":49270,"journal":{"name":"Advances in Data Analysis and Classification","volume":"17 3","pages":"777 - 800"},"PeriodicalIF":1.4000,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Data Analysis and Classification","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s11634-022-00524-4","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
Sufficient dimension reduction (SDR) is a useful tool for high-dimensional data analysis. SDR aims at reducing the data dimensionality without loss of regression information between the response and its high-dimensional predictors. Many existing SDR methods are designed for the data with continuous responses. Motivated by a recent work on aggregate dimension reduction (Wang in Stat Si 30:1027–1048, 2020), we propose a unified SDR framework for both continuous and binary responses through a structured covariance ensemble. The connection with existing approaches is discussed in details and an efficient algorithm is proposed. Numerical examples and a real data application demonstrate its satisfactory performance.
充分降维（SDR）是高维数据分析的一种有用工具。SDR旨在降低数据维度，而不会丢失响应与其高维预测因子之间的回归信息。许多现有的SDR方法都是针对具有连续响应的数据而设计的。受最近一项关于聚合降维的工作的启发（Wang在Stat Si 30:1027-10482020中），我们通过结构化协方差集合为连续和二进制响应提出了一个统一的SDR框架。详细讨论了与现有方法的联系，并提出了一种有效的算法。数值算例和实际数据应用表明，该方法具有令人满意的性能。
期刊介绍：
The international journal Advances in Data Analysis and Classification (ADAC) is designed as a forum for high standard publications on research and applications concerning the extraction of knowable aspects from many types of data. It publishes articles on such topics as structural, quantitative, or statistical approaches for the analysis of data; advances in classification, clustering, and pattern recognition methods; strategies for modeling complex data and mining large data sets; methods for the extraction of knowledge from data, and applications of advanced methods in specific domains of practice. Articles illustrate how new domain-specific knowledge can be made available from data by skillful use of data analysis methods. The journal also publishes survey papers that outline, and illuminate the basic ideas and techniques of special approaches.
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