Some notes on the consequences of pretreatment of multivariate data

IF 8.1 1区 计算机科学 0 COMPUTER SCIENCE, INFORMATION SYSTEMS Information Sciences Pub Date : 2024-10-24 DOI:10.1016/j.ins.2024.121580
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Abstract

With the advent of data technologies, we have various types of data, such as structured, unstructured and semi-structured. Performing certain statistical or machine learning techniques may require careful preprocessing or pretreatment of the data to make them suitable for analysis. For example, given a data matrix X, which represents n multivariate observations or cases on p variables or features, the columns/rows of X may be pretreated before applying statistical or machine learning techniques to the data. While centering and/or scaling the variables do not alter the correlation structure nor the graphical representation of the data, centering/scaling the observations do. We investigate various row pretreatment methods more closely and show with theoretical proofs and numerical examples that centering/scaling the rows of X changes both the graphical structure of the observations in the multi-dimensional space and the correlation structure among the variables. There may be good reasons for performing row centering/scaling on the data and we are not against it, but analysts who use such row operations should be aware of the geometrical and correlation structures one has performed on the data and should also demonstrate that the process results in a new, more appropriate structure for their questions.
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关于多元数据预处理后果的一些说明
随着数据技术的发展,我们拥有了各种类型的数据,如结构化、非结构化和半结构化数据。在执行某些统计或机器学习技术时,可能需要对数据进行仔细的预处理或预处理后才能使其适合分析。例如,给定的数据矩阵 X 表示 p 个变量或特征的 n 个多元观测值或案例,在对数据应用统计或机器学习技术之前,可以对 X 的列/行进行预处理。虽然变量的居中和/或缩放不会改变数据的相关结构或图形表示,但观测数据的居中和/或缩放却会改变数据的相关结构或图形表示。我们对各种行预处理方法进行了更深入的研究,并通过理论证明和数值示例表明,对 X 行进行居中/缩放会改变多维空间中观测数据的图形结构和变量间的相关结构。对数据进行行居中/缩放处理可能有很好的理由,我们并不反对这样做,但使用这种行操作的分析师应该意识到对数据进行的几何结构和相关结构,并且还应该证明这一过程会为他们的问题带来新的、更合适的结构。
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来源期刊
Information Sciences
Information Sciences 工程技术-计算机:信息系统
CiteScore
14.00
自引率
17.30%
发文量
1322
审稿时长
10.4 months
期刊介绍: Informatics and Computer Science Intelligent Systems Applications is an esteemed international journal that focuses on publishing original and creative research findings in the field of information sciences. We also feature a limited number of timely tutorial and surveying contributions. Our journal aims to cater to a diverse audience, including researchers, developers, managers, strategic planners, graduate students, and anyone interested in staying up-to-date with cutting-edge research in information science, knowledge engineering, and intelligent systems. While readers are expected to share a common interest in information science, they come from varying backgrounds such as engineering, mathematics, statistics, physics, computer science, cell biology, molecular biology, management science, cognitive science, neurobiology, behavioral sciences, and biochemistry.
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