Missing data methods in PCA and PLS: Score calculations with incomplete observations
Missing data methods in PCA and PLS: Score calculations with incomplete observations
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DOI：
10.1016/s0169-7439(96)00007-x
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发表时间：
1996-11-01
影响因子：
3.9
通讯作者：
MacGregor, JF
中科院分区：
文献类型：
--
作者：
Nelson, PRC;Taylor, PA;MacGregor, JF
在PCA和PLS模型的工业应用中，例如过程建模或监控，一个非常重要的问题是当观测向量有缺失测量时的分数估计。暂停应用程序直到所有测量都可用的替代方案通常是不可接受的。在这项工作中处理的问题是，估计得分从现有的PCA或PLS模型时，新的观察向量是不完整的。建立模型与不完整的观察，这里不处理，虽然在本文中给出的分析提供了相当深入的了解这个问题。几种方法估计分数缺失测量数据，并分析：一种方法，称为单组分投影，来自NIPALS算法的模型建设与缺失数据;投影到模型平面的方法;和数据替换的条件平均值。表达式中开发的每种方法计算的分数的误差。错误分析说明使用模拟数据集，旨在突出问题的情况。一个更大的工业数据集也被用来比较的方法。一般来说，所有的方法都表现得相当好，具有中等数量的缺失数据（高达20%的测量值）。然而，在极端情况下，关键的组合的测量丢失，条件平均值替换方法通常是优于其他方法上级。
A very important problem in industrial applications of PCA and PLS models, such as process modelling or monitoring, is the estimation of scores when the observation vector has missing measurements. The alternative of suspending the application until all measurements are available is usually unacceptable. The problem treated in this work is that of estimating scores from an existing PCA or PLS model when new observation vectors are incomplete. Building the model with incomplete observations is not treated here, although the analysis given in this paper provides considerable insight into this problem. Several methods for estimating scores from data with missing measurements are presented, and analysed: a method, termed single component projection, derived from the NIPALS algorithm for model building with missing data; a method of projection to the model plane; and data replacement by the conditional mean. Expressions are developed for the error in the scores calculated by each method. The error analysis is illustrated using simulated data sets designed to highlight problem situations. A larger industrial data set is also used to compare the approaches. In general, all the methods perform reasonable well with moderate amounts of missing data (up to 20% of the measurements). However, in extreme cases where critical combinations of measurements are missing, the conditional mean replacement method is generally superior to the other approaches.