عنوان مقاله [English]
Identification and modification of multivariate outlier data is the first step to analyze exploration data through multivariate statistics. A key to this problem is reducing the data dimension to one by the distance between the sample and central point of the data set and then by comparing it with a threshold. To calculate this distance, the location and scatter matrixes are used instead of the mean and variance-covariance matrixes in the robust estimators. Therefore, to maintain the robustness of distance, these estimators apply the optimal subset rather than the entire data matrix. This paper introduces four robust estimators namely the MVE, MCD, S and SD. Then these estimators are used to determine outlier data of 146 regional stream sediment samples of Shah Soliman Ali at South Khorasan province and also to analyze 18 elements. The results show that the Mahalanobis distance classical methods display 7 samples and robust estimators MVE, MCD, S and SD introduce 23, 35, 20 and 34 samples as outliers, respectively. The principal component analysis in Q mode also show that the outlier samples with negative loads and the other samples with approximately positive loads show themselves in the second and the third components, respectively. It is also possible to separate outlier data from the rest in the scatter plot of the loads of PC 2 vs the loads of PC 3. The use of the location and scatter matrixes done by robust estimators is another important application of these estimators in multivariate statistics methods of exploration data analysis.
Human errors and changing nature of exploration data distribution are two main reasons in the creation of Outliers. The first step in the processing of the exploration data will be Identification and then modification of them. Existence of outliers is also caused the bias in the mean matrix and inflation in the variance-covariance matrix. So in this paper, we propose the use of robust estimators as one of the solutions and their performance is also evaluated.
Methodology and Approaches
Results of the analysis of 18 elements to 146 stream sediments samples is used at the exploration region of Shad Soliman Ali as a data set. Four robust estimators such as MVE, MCD, S and SD have been also used to identify outlier data. And finally the results of the four estimator has been evaluated and compared with each other by PCA in Q mode.
Results and Conclusions
From 146 samples, the MVE, MCD, S and SD robust estimators detected 23, 35, 20 and 34 as outlier data, respectively. Outlier samples also show up themselves with the negative loads on the PC2 and other samples with positive loads on the PC1. The population of the Outlier samples and the population of another samples are separated in the scatter plot of the PC2 loads vs the PC3 loads. So depending on the number of samples, one of these estimators can be used to identify outlier data.