主基底分析方法及在水质监测指标筛选中的研究

Principal Basis Analysis and Application in Feature Selection of Water Quality Data

摘要: 随着人们对环境的日益重视和监测技术的提高，水质监测中出现了越来越多变量相关的多变量数据。其中，太子河水质数据属于数据相关的多变量数据。由于传统方法的局限性，本文利用基于Gram-Schmidt变换的主基底分析方法进行太子河水质数据的监测指标筛选工作。这种方法能够在原数据信息损失尽可能小的前提下，排除所有的冗余变量以及变量集合中的重叠信息，有效地对大规模变量集中的信息进行筛选，从而得到一个标准正交的主基底。并且，通过对所选基底的“净信息含量比”的测度，可以有效地选择具有代表性的水质监测变量。有利于对水质监测工作进行科学合理的改进。数值实验表明，使用Gram-Schmidt变换的主基底分析方法对太子河水质数据进行分析是有效的。

Abstract: With the increasing emphasis on the environment and the improvement of monitoring technology, there appear more and more multivariate data in which the variable sets have multi-collinearity problem. The water quality data of Taizi River belong to this kind of data. In order to avoid the li-mitation of the traditional method, the principal basis analysis method based on the Gram- Schmidt transform is used to the feature selection of the water quality data of the Taizi River. This method selects information effectively from the large-scale variable set with the minimal loss of original information. Meanwhile, this method can exclude all redundant variables and reduplicate information. Furthermore, it can obtain a mini-dimensional orthogonal basis. Using the measure-ment of the net information content ratio of the selected features, it is effective to select the rep-resentative water quality monitoring variables. It is conducive to the improvement of water quality monitoring work and the experimental results indicate the effectiveness of this method.