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Volume 16 How To Detect And Handle Outliers Pdf 22


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Volume 16 How To Detect And Handle Outliers Pdf 22


The HD is generally sensitive to outliers. Because noise and outliers are common in medical segmentations, it is not recommended to use the HD directly [8, 40]. However, the quantile method proposed by Huttenlocher et al. [41] is one way to handle outliers. According to the Hausdorff quantile method, the HD is defined to be the qth quantile of distances instead of the maximum, so that possible outliers are excluded, where q is selected depending on the application and the nature of the measured point sets.


Now, we provide guidelines for choosing a suitable metric based on the results so far. These guidelines are additionally summarized in Table 5 in form of matching between data properties, requirements, and metric properties: (i) When the objective is to evaluate the general alignment of the segments, especially when the segments are small (the overlap is likely small or zero), it is recommended to use distance based metrics rather than overlap based metrics. The volumetric similarity (VS) is not suitable in this case. (ii) Distance based metrics are recommended when the contour of the segmentation, i.e. the accuracy at the boundary, is of importance [6]. This follows from being the only category of metrics that takes into consideration the spatial position of false negatives and false positives. (iii) The Hausdorff distance is sensitive to outliers and thus not recommended to be used when outliers are likely. However, methods for handling the outliers, such as the quantile method [41], could solve the problem, otherwise the average distance (AVG) and the overlap based metrics as well as probabilistic based metrics are known to be stable against outliers. (iv) Probabilistic distance (PBD) and overlap based metrics are recommended when the alignment of the segments is of interest rather than the overall segmentation accuracy [2]. (v) Metrics considering the true negatives in their definitions have sensitivity to segment size. They reward segmentations with small segments and penalize those with large segments [10]. Therefore, they tend to generally penalize algorithms that aim to maximize recall and reward algorithms that aim to maximize precision. Such metrics should be avoided in general, especially when the objective is to reward recall (vi) When the segmentations have a high class imbalance, e.g. segmentations with small segments, it is recommended to use metrics with chance adjustment, e.g. the Kappa measure (KAP) and the adjusted rand index (ARI) [29, 55]. (vii) When the segments are not solid, but rather have low densities, then all metrics that are based on volume or on the four cardinalities (TP, TN, FP, FN), are not recommended. In such cases distance-based metrics, especially MHD and HD, are recommended. (viii) Volumetric similarity is not recommended when the quality of the segmentations being evaluated is low in general, because the segments are likely to have low overlap with their corresponding segments in the ground truth. In this case, overlap-based and distance-based metrics are recommended. (ix) When the segmented volume is of importance, volumetric similarity and overlap based metrics are recommended rather than distance based-metrics. (x) When more than one objective is to be considered, which are in conflict, then it is recommended to to combine more than one metric, so that each of the objective is considered by one of the metrics. Thereby, it is recommended to possibly avoid selecting metrics that are strongly correlated (Fig. 3).


In practice, in any analysis of dates some are usually rejected as obvious outliers. However, there are Bayesian statistical methods which can be used to perform this rejection in a more objective way (Christen 1994b), but these are not often used. This paper discusses the underlying statistics and application of these methods, and extensions of them, as they are implemented in OxCal v 4.1. New methods are presented fo




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