### Table 1. Comparison of conventional and robust regression methods using hypothetical data and data with one outlier. Detected outliers are italicised

"... In PAGE 1: ...90 + 1.69~ and the calibration results are given in Table1 . The residuals listed show that the LS line is attracted strongly by this single outlier and therefere fits the Table 1.... In PAGE 2: ... 2. Illustration of SM for the data in Table1 . The value of a1 versus the ranks of the slopes of all pairs of points; 4-5 indicates the slope of the line between the fourth and the fifth data point, etc.... In PAGE 3: ... The breakdown point is therefore 50%. To illustrate the method the data in Table1 are again used. Firstly, the slopes of each of the cn2 combinations of pairs of points are calculated, then the squared residuals towards the line for each measuring point are calculated, the resulting squared residuals are sorted and their medians obtained.... In PAGE 3: ... 3. Illustration of RM for the data in Table1 . (a) Ranked slope al for each point i, joined by a line to each of the other points; and (b) ranked median slopes selected from (a).... In PAGE 3: ... 4. Illustration of LMS for the data in Table1 . The ranked log of the median of squared residuals for the lines through the different ... In PAGE 6: ... Such an example is shown in Fig. 9, where the objective function (or rather its inverse for graphical purposes) is given for the data of Table1 as a function of a. and al.... ..."

### Table 5. Results for the data from atomic absorption spectrometry

"... In PAGE 4: ... With the latter of these we can measure outside the linear range. The calibration results are listed in Table5 . The calibration lines obtained with the various methods on each group of data are shown in Figs.... In PAGE 4: ... 5(a). In Table5 , results are also given for another robust approach, which we have described elsewhere,6 namely fuzzy regression. One of the two algorithms, FUZL, seems to perform as well as LMS.... In PAGE 4: ... In univariate regression, it happens that the majority of the data points follow a linear relationship so exactly that most of the calibration points lie on a straight line. For data set 5 in Table5 (used without zero point), no outliers should be found, but the LMS estimators are derived from the line on which 3 points fit well and cause the residuals of 3 points to tend towards zero so that 2 outliers are wrongly rejected. To avoid these problems one must avoid the application of robust methods to good calibration lines.... In PAGE 6: ... . 3 * See Table 4 for complete calibration data. i See Table5 for the outlier(s) rejected by the modified LMS method. CIample With .... In PAGE 6: ... When one compares the results obtained with this adapted version with the original PROGRESS, one observes that the results do not differ very much. The slopes, of course, are the same while the intercepts differ slightly (see Table5 ). For data sets 1-6, the same outliers are rejected.... ..."

### Table 4. Comparison of the outliers detected by explicit and rule-based detection approaches for differently defined patient record classes.

in 5th International Workshop on Intelligent Data Analysis in Medicine and Pharmacology (IDAMAP-2000)

"... In PAGE 19: ... The rule de- tected positive patient records 214 and 230 as outliers within the test set. The results are presented in the first row of Table4 . Comparing results obtained by explicit and rule-based outlier detection it can be noted that the later approach selected the same records as the former approach but that it also detected two more records: 165 and 185.... In PAGE 20: ... The limit values between positive and negative classes are based on induced rules in previous experiments. Table4 in its second and third row includes results obtained for positive classes defined by con- ditions a75a23a76 a75a23a77a23a78a23a79 a80a48a81a83a82 a84 a85 a86 a87a15a87 and a88a48a89a23a90a50a79 a80a48a81a83a82 a84 a91 a86 a87a15a87 respec- tively. In the left column are records detected as outliers in the test set by explicit approach while in the right one are detected by the rule-based method.... In PAGE 27: ...9 95.1 Table4 shows the prediction accuracies of the two methods. Re- duced data set A2, from which the multivariate outliers and the examples with the most univariate outlier values were removed, was the worst nearest neighbour classifier.... In PAGE 53: ... From these subsets Decision Master induced decision trees and calculated the error rate based on cross validation. We observed that a better error rate can be reached if the decision tree is only induced from a subset of features, see Table4 and Figure 4. The method used in this paper does not tell us what is the right number of features.... In PAGE 53: ... Another side effect is that the resulting decision tree is more compact, see Figure 3. Feature Number Unprunend Decision Tree Error Rate pruned Decision Tree Error Rate 19 6,8571 7,428 10 10,85 14,85 13 7,4286 4,5714 15 7,429 4,5714 17 10,28 7,42 Table4... ..."

### Table 4. Integrated errors for the five outlier detection methods on the original power spectrum data and versions with only the first few principal components.

"... In PAGE 19: ... To make a more quantitative comparison, an error measure is derived from the ROC- curves. The fraction of the outliers which is accepted (EII), is averaged over varying EI (Bradley, 1997): EM = integraldisplay B A EII(EI) dEI (38) In Table4 the results on the power spectrum data are shown. The methods are applied to both the original 64 dimensional data set and to the first principal components of that data, ranging from 3 up to 30 features.... ..."

### Table 2. Comparison of the outlier detection methods

"... In PAGE 10: ...Observe that the M estimator based robust regression approach does not identify outliers. Table2 provides values of the three measures used to assess the methods as well as the regression equation parameter values computed in the way explained above. The obtained results show that the multilayer per- cpetron is the best technique for categorizing the data, followed by the PCA based approach.... ..."

### Table 2 Outlier detection performances on the UCI datasetsa

1999

"... In PAGE 6: ... To estimate the errors (of the first and the second kind) n-fold cross-validation with n 5 is used. In Table2 , the performances of the outlier de- tection methods on all UCI datasets are shown. For each method, the performance on a target validation set (left) and an outlier test set (right) is shown.... ..."

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### Table 1. Outlier detection in the Microtox toxicity data set. PModXPS+ 0.5 % PModXPS 0.5 % PModXPS+ 0.1 % PModXPS 0.1 % Modela

"... In PAGE 26: ...5 % and 0.1 % risk levels are shown in Table1 for 9 different PLS models based on different sets of descriptors. The RMSEE and RMSEP values in the second and third column are the root mean squared error of estimation for the training data and the root mean squared error of prediction for the full test set.... In PAGE 46: ... RMSEP values can be compared for models based on different training data, which is not the case for R2 and Q2. Table1 1shows a summary of the models developed for the toxic properties considered in this work based on all descriptors. For the two properties with a large test set (Microtox pEC50 and Daphnia pEC50) the RMSEPs for systematic and random selection was practically equal (although the number of outliers was different as discussed... ..."

### Table 6. Method Detection Llimits (MDL)

"... In PAGE 18: ... The MDLs were determined from analysis of samples from a solution matrix containing the analytes of interest. Detection limits for all compounds studied, as given in Table6 , were determining using the EPA procedure for Method Detection Limits (USEPA, 1982). Standards for TCE and PCE were run at the beginning of each day and an additional set of standards was run later in the day or dispersed throughout the analysis run.... In PAGE 18: ... Because of the low sample volumes available for analysis, the detection limit for alkalinity measurements varied from 2 mg/L CaCO3 for the batch experiments to between 5 and 8 mg/L CaCO3 for the column experiments. Detection limits for the inorganic parameters are included in Table6 . The method detection limit for Cr(VI) measured in the lab is between 0.... ..."

### Table 4. Smart card space requirements

"... In PAGE 11: ... The only systematic accumulation of RAM and ROM information made available to NIST is in Ref. [37]; Table4 in the Appendix summarizes this information. Roughly, the situation is as follows: a.... In PAGE 22: ... Table 3 provides the key setup time, in clock cycles, to encrypt a 128 bit block with a 128 bit key. Table4 provides information taken mainly from [37]. RAM1 is the RAM requirement in bytes for candidates not supporting on-the-fly subkey generation.... ..."

### Table 4. Smart card space requirements

"... In PAGE 20: ... The only systematic accumulation of RAM and ROM information made available to NIST is in Ref. [37]; Table4 in the Appendix summarizes this information. Roughly, the situation is as follows: a.... In PAGE 31: ... Table 3 provides the key setup time, in clock cycles, to encrypt a 128 bit block with a 128 bit key. Table4 provides information taken mainly from [37]. RAM1 is the RAM requirement in bytes for candidates not supporting on-the-fly subkey generation.... In PAGE 64: ...ances of x = 1.27 cm, x = 2.91 cm, and x = 4.70 cm from the radiating aperture. Table4 a summarizes the results of SB-2 calibration in the SPBB. The response of the gage was linear at all three locations over the calibra- tion heat flux range of 0 to 10 kW/m2.... In PAGE 65: ...Journal of Research of the National Institute of Standards and Technology Table4 a. Comparison of heat flux sensor calibration in SPBB with VTBB: Calibration of Schmidt-Boelter sensor SB-2 Test Distance x Schmidt-Boelter Responsivity Difference from date (cm) reference gage mV/(kW/m2) VTBB (%) 07/31/98 1.... In PAGE 65: ...0708 1.08 Table4 b. Comparison of heat flux sensor calibration in SPBB with VTBB: Calibration of Gardon gage GG-1 Test Distance x Schmidt-Boelter Responsivity Difference from date (cm) reference gage mV/(kW/m2) VTBB (%) 02/15/98 1.... ..."