Robust Mahalanobis-distance based spatial outlier detection on discrete GNSS velocity fields

Abstract

<p>The GNSS velocity field filtering topic can be identified as a multi-dimensional unsupervised spatial outlier detection problem. In the discussed case, we jointly interpreted the horizontal and vertical velocity fields and its uncertainties as a six dimensional space. To detect and classify the spatial outliers, we performed an orthogonal linear transformation technique called Principal Component Analysis (PCA) to dynamically project the data to a lower dimensional subspace, while redacting the most (~99%) of the explained variance of the input data.</p><p>Therefore, the resulting component space can be seen as an attribute function, which describes the investigated deformation patterns. Then we constructed two subspace mapping functions, respectively the k-nearest neighbor (k-NN) and median based neighbor function with Haversine metric, and the samplewise comparison function which compares the samples with the properties of its k-NN environment. Consequently, the resulting comparison function scores highlights the significantly different observations as outliers. Assuming that the data comes from Multivariate Gaussian Distribution (MVD), we evaluated the corresponding Mahalanobis-distance with the estimation of the robust covariance matrix of the investigated area. Then, as the main result of the Robust Mahalanobis-distance (RMD) based approach, we implemented the binary classification via the p-value and critical Mahalanobis-distance thresholding.</p><p>Compared to the formerly investigated and applied One-Class Support Vector machine (OCSVM) approach, the RMD based solution gives <em>~ 17%</em> more accurate results of the European scaled velocity field filtering (like EPN D1933), as well as it corrects the ambiguities and non-desired features (like overfitting) of the former OCSVM approach.</p><p>The results will be also presented as an interactive web page of the velocity fields of the latest version of EPN D2050 filtered with the introduced RMD approach.</p>