mahalanobis_distance: Mahalanobis Distance
In anomalyDetection: Implementation of Augmented Network Log Anomaly Detection Procedures
Description
Usage
Arguments
Value
References
Examples
View source: R/mahalanobis_distance.R
Description
Calculates the distance between the elements in a data set and the mean
vector of the data for outlier detection. Values are independent of the scale
between variables.
Usage
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mahalanobis_distance(data, output = c("md", "bd", "both"),
normalize = FALSE)
## S3 method for class 'matrix'
mahalanobis_distance(data, output = c("md", "bd", "both"),
normalize = FALSE)
## S3 method for class 'data.frame'
mahalanobis_distance(data, output = c("md", "bd",
"both"), normalize = FALSE)
Arguments
data
A matrix or data frame. Data frames will be converted to matrices
via data.matrix.
output
Character string specifying which distance metric(s) to
compute. Current options include: "md" for Mahalanobis distance
(default); "bd" for absolute breakdown distance (used to see which
columns drive the Mahalanobis distance); and "both" to return both
distance metrics.
normalize
Logical indicating whether or not to normalize the breakdown
distances within each column (so that breakdown distances across columns can
be compared).
Value
If output = "md", then a vector containing the Mahalanobis
distances is returned. Otherwise, a matrix.
References
W. Wang and R. Battiti, "Identifying Intrusions in Computer Networks with
Principal Component Analysis," in First International Conference on
Availability, Reliability and Security, 2006.
Examples
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## Not run:
# Simulate some data
x <- data.frame(C1 = rnorm(100), C2 = rnorm(100), C3 = rnorm(100))
# Add Mahalanobis distances
x %>% dplyr::mutate(MD = mahalanobis_distance(x))
# Add Mahalanobis and breakdown distances
x %>% cbind(mahalanobis_distance(x, output = "both"))
# Add Mahalanobis and normalized breakdown distances
x %>% cbind(mahalanobis_distance(x, output = "both", normalize = TRUE))
## End(Not run)
Example output
C1 C2 C3 MD
1 0.16185767 0.465557280 0.88747732 1.0514126
2 0.84365371 0.737741251 -0.57625718 1.3022942
3 0.37264342 0.199930685 1.42621743 2.2132250
4 -0.41433401 1.549908803 -0.85688115 3.6002895
5 0.74431492 1.602282400 -3.25858026 10.8641344
6 0.40878999 -1.007329448 1.15046588 2.6505490
7 0.99266364 -0.725241990 -1.63804459 3.5612923
8 -0.14328653 1.889305880 -0.78324775 4.3893422
9 1.66960919 -1.011570441 0.58396447 5.3159292
10 0.86706241 -0.031762671 -2.02900621 3.6669311
11 -0.98596177 1.532722563 0.67726750 4.2980205
12 0.85376406 -0.695074847 -0.52352715 1.5536517
13 0.28378339 1.119552837 -0.10382409 1.3610926
14 -2.02917517 1.220003004 0.80232197 7.0176407
15 -0.04912526 0.397432633 -0.57063495 0.4339775
16 -0.99909385 0.077733180 -0.40057636 1.4231368
17 0.23668049 0.571140238 1.17270479 1.7713996
18 0.07914937 -1.019700278 1.06028695 2.0979150
19 -1.68761857 0.372179227 0.98228335 3.8665251
20 0.54926518 -0.816010803 -0.92325718 1.6997111
21 0.18072560 1.407771883 -1.76938109 4.4543639
22 0.55728164 -0.581662237 -0.72395758 1.0791778
23 -0.14317267 0.441434234 0.38238406 0.3951620
24 -0.24158538 0.710890314 0.19616640 0.7035524
25 -1.09414426 -1.165558882 -0.49441728 2.8617873
26 1.10497351 1.410069867 -0.61540545 3.1360529
27 1.34248968 -0.455239903 -0.79550392 2.5616394
28 1.31159432 0.474860161 -1.10046132 2.4810365
29 0.14218357 0.005627344 0.84658476 0.7256851
30 -1.99522562 0.143100932 -0.50597806 5.1780269
31 -0.17989743 -1.059360842 0.43806407 1.2902096
32 1.00184090 0.175649334 0.24338219 1.2865034
33 -1.12084496 -0.037087257 0.43238456 1.4266734
34 -1.22596268 -0.420260955 0.36490227 1.7161329
35 -0.23198034 -0.101186505 1.26782161 1.3956928
36 -1.17210999 -0.798688667 -0.61687477 2.5622810
37 1.11005906 0.953903901 0.04661374 2.1448712
38 1.06293680 0.884622118 0.58794526 2.4782166
39 0.51326344 1.579752556 0.26777780 2.9404404
40 -0.75717151 -0.311790680 2.06882117 3.8663412
41 0.93008783 -0.377632081 0.55568377 1.6853015
42 0.38251904 -0.868498321 -0.60641290 1.2708837
43 0.09391775 -1.672222281 -0.31496066 3.0848914
44 0.60494872 -0.077200275 -0.85777379 0.8395293
45 -0.52513426 -1.074878698 1.50873684 3.0227603
46 -1.04218441 0.443484387 -0.54523909 1.9939522
47 -0.83154600 -0.343820169 2.47272681 5.4166410
48 -1.22769908 -0.234273692 2.11619703 4.6832902
49 -0.77726408 -0.168765504 -1.40702996 2.7130661
50 -0.05489791 -1.081158598 -0.91220022 1.9541719
51 -0.78284695 0.197798357 0.62617953 0.9850828
52 0.43659660 1.271995924 0.35815465 2.0421906
53 -0.81367374 -0.662416259 0.76387281 1.3510889
54 1.25242378 1.258586660 0.80165669 4.1060568
55 -0.34772580 0.774734417 -0.19162645 0.9053089
56 0.66504072 -0.261610627 -0.53058206 0.7123662
57 0.86710181 -0.319446295 -1.43150475 2.2978729
58 -0.85177598 0.898191375 -0.26021560 2.0194083
59 -0.92807615 0.278123026 -0.36108562 1.3445812
60 -0.29799551 -0.184343952 -2.12700373 4.1444723
61 -0.60237342 -0.354070594 2.26658514 4.4707162
62 0.91744323 -0.907065407 0.18953027 2.1239067
63 0.57443241 -0.211533680 1.68127927 3.2872954
64 0.79907845 0.287901004 -0.59551447 0.8555230
65 0.58898539 -0.859643772 -1.21957409 2.3151866
66 -0.30155864 0.287514551 -1.45465358 2.0964187
67 0.74594985 0.291754794 -1.41032062 1.9083833
68 -0.32129976 -0.180873123 2.91048081 7.1865103
69 1.00614809 0.088841025 0.15176850 1.2221988
70 -0.70243892 -2.005221879 0.09313122 4.4119763
71 0.52766909 -3.327095358 -1.04067465 13.3954070
72 0.48253861 0.943507215 -0.46072663 1.1728430
73 2.50530044 0.280012806 0.18972293 7.2580053
74 -1.65176277 0.428301489 0.79990078 3.6313729
75 0.34570892 0.370227059 0.70780826 0.8282996
76 -0.23851817 -0.901230701 -0.33809536 0.9817427
77 1.32896459 0.478536554 0.08876840 2.1548317
78 -1.68331093 -0.096208512 1.64583926 4.5943093
79 -0.37956176 -1.231537068 0.73754305 1.9801680
80 -1.78444631 -0.896193054 -1.16547997 5.9512611
81 1.21441969 0.257613421 0.43998954 2.0599242
82 0.46778063 0.642326234 -1.47139877 2.1072616
83 -0.83448792 -0.565240621 -0.82756468 1.8170364
84 0.35308217 2.668538874 0.31236036 7.7508791
85 2.44494544 0.668246258 -1.49079550 7.3286217
86 0.67000101 -0.213880584 0.83976786 1.4313851
87 0.81081590 -0.989957575 2.13298965 6.4870938
88 -0.29234243 -0.817921397 -1.39908389 2.5529898
89 0.58155073 3.007588109 0.53457199 10.1357875
90 -0.58788094 -0.147886958 -0.49259987 0.6819147
91 -0.90552955 -0.314098301 -0.89350439 1.9024244
92 -1.62580563 -0.601495744 0.08243134 3.0800386
93 0.49950100 0.016982913 0.32643645 0.4500061
94 0.05884231 0.851526580 -0.43898014 0.8979754
95 -1.10339587 -0.385677414 -1.33237468 3.4359655
96 -1.40881767 -0.943221164 -0.79525962 3.7840041
97 0.33374188 -0.655439434 0.14073530 0.6625540
98 -1.98380693 -1.385614955 1.35907680 6.3458473
99 0.98214482 -2.053593700 -0.11959262 6.0543157
100 -0.15308456 -0.040369767 -0.95315502 0.8123856
C1 C2 C3 MD C1_BD C2_BD
1 0.16185767 0.465557280 0.88747732 1.0514126 0.16470914 0.48741929
2 0.84365371 0.737741251 -0.57625718 1.3022942 0.87386592 0.76619691
3 0.37264342 0.199930685 1.42621743 2.2132250 0.38395381 0.21535791
4 -0.41433401 1.549908803 -0.85688115 3.6002895 0.43460533 1.59803917
5 0.74431492 1.602282400 -3.25858026 10.8641344 0.77054063 1.65168152
6 0.40878999 -1.007329448 1.15046588 2.6505490 0.42155095 1.02114804
7 0.99266364 -0.725241990 -1.63804459 3.5612923 1.02885567 0.73222702
8 -0.14328653 1.889305880 -0.78324775 4.3893422 0.15268061 1.94565813
9 1.66960919 -1.011570441 0.58396447 5.3159292 1.73296731 1.02549177
10 0.86706241 -0.031762671 -2.02900621 3.6669311 0.89821402 0.02194821
11 -0.98596177 1.532722563 0.67726750 4.2980205 1.02917273 1.58043660
12 0.85376406 -0.695074847 -0.52352715 1.5536517 0.88438200 0.70132908
13 0.28378339 1.119552837 -0.10382409 1.3610926 0.29152779 1.15725786
14 -2.02917517 1.220003004 0.80232197 7.0176407 2.11425069 1.26014142
15 -0.04912526 0.397432633 -0.57063495 0.4339775 0.05474062 0.41764433
16 -0.99909385 0.077733180 -0.40057636 1.4231368 1.04283181 0.09020017
17 0.23668049 0.571140238 1.17270479 1.7713996 0.24253463 0.59555999
18 0.07914937 -1.019700278 1.06028695 2.0979150 0.07868172 1.03381855
19 -1.68761857 0.372179227 0.98228335 3.8665251 1.75898730 0.39177916
20 0.54926518 -0.816010803 -0.92325718 1.6997111 0.56766346 0.82519471
21 0.18072560 1.407771883 -1.76938109 4.4543639 0.18433425 1.45245899
22 0.55728164 -0.581662237 -0.72395758 1.0791778 0.57600163 0.58516906
23 -0.14317267 0.441434234 0.38238406 0.3951620 0.15256219 0.46271187
24 -0.24158538 0.710890314 0.19616640 0.7035524 0.25492423 0.73869551
25 -1.09414426 -1.165558882 -0.49441728 2.8617873 1.14169663 1.18321057
26 1.10497351 1.410069867 -0.61540545 3.1360529 1.14567258 1.45481265
27 1.34248968 -0.455239903 -0.79550392 2.5616394 1.39272037 0.45568415
28 1.31159432 0.474860161 -1.10046132 2.4810365 1.36058516 0.49694754
29 0.14218357 0.005627344 0.84658476 0.7256851 0.14424551 0.01634758
30 -1.99522562 0.143100932 -0.50597806 5.1780269 2.07893873 0.15715146
31 -0.17989743 -1.059360842 0.43806407 1.2902096 0.19076072 1.07443989
32 1.00184090 0.175649334 0.24338219 1.2865034 1.03840123 0.19048834
33 -1.12084496 -0.037087257 0.43238456 1.4266734 1.16946884 0.02740178
34 -1.22596268 -0.420260955 0.36490227 1.7161329 1.27880497 0.41985784
35 -0.23198034 -0.101186505 1.26782161 1.3956928 0.24493374 0.09305383
36 -1.17210999 -0.798688667 -0.61687477 2.5622810 1.22279115 0.80745294
37 1.11005906 0.953903901 0.04661374 2.1448712 1.15096222 0.98759608
38 1.06293680 0.884622118 0.58794526 2.4782166 1.10194892 0.91663595
39 0.51326344 1.579752556 0.26777780 2.9404404 0.53021696 1.62860589
40 -0.75717151 -0.311790680 2.06882117 3.8663412 0.79120103 0.30875988
41 0.93008783 -0.377632081 0.55568377 1.6853015 0.96376868 0.37619629
42 0.38251904 -0.868498321 -0.60641290 1.2708837 0.39422574 0.87895373
43 0.09391775 -1.672222281 -0.31496066 3.0848914 0.09404277 1.70214786
44 0.60494872 -0.077200275 -0.85777379 0.8395293 0.62558161 0.06848653
45 -0.52513426 -1.074878698 1.50873684 3.0227603 0.54985204 1.09033366
46 -1.04218441 0.443484387 -0.54523909 1.9939522 1.08765161 0.46481169
47 -0.83154600 -0.343820169 2.47272681 5.4166410 0.86856020 0.34156528
48 -1.22769908 -0.234273692 2.11619703 4.6832902 1.28061106 0.22936505
49 -0.77726408 -0.168765504 -1.40702996 2.7130661 0.81209992 0.16226993
50 -0.05489791 -1.081158598 -0.91220022 1.9541719 0.06074492 1.09676569
51 -0.78284695 0.197798357 0.62617953 0.9850828 0.81790684 0.21317392
52 0.43659660 1.271995924 0.35815465 2.0421906 0.45047345 1.31339387
53 -0.81367374 -0.662416259 0.76387281 1.3510889 0.84997072 0.66787934
54 1.25242378 1.258586660 0.80165669 4.1060568 1.29904009 1.29965977
55 -0.34772580 0.774734417 -0.19162645 0.9053089 0.36532411 0.80408623
56 0.66504072 -0.261610627 -0.53058206 0.7123662 0.68808513 0.25736422
57 0.86710181 -0.319446295 -1.43150475 2.2978729 0.89825500 0.31660095
58 -0.85177598 0.898191375 -0.26021560 2.0194083 0.88960201 0.93053393
59 -0.92807615 0.278123026 -0.36108562 1.3445812 0.96896414 0.29544445
60 -0.29799551 -0.184343952 -2.12700373 4.1444723 0.31359813 0.17822576
61 -0.60237342 -0.354070594 2.26658514 4.4707162 0.63019084 0.35206402
62 0.91744323 -0.907065407 0.18953027 2.1239067 0.95061664 0.91845510
63 0.57443241 -0.211533680 1.68127927 3.2872954 0.59384067 0.20607416
64 0.79907845 0.287901004 -0.59551447 0.8555230 0.82750184 0.30545930
65 0.58898539 -0.859643772 -1.21957409 2.3151866 0.60897767 0.86988468
66 -0.30155864 0.287514551 -1.45465358 2.0964187 0.31730424 0.30506349
67 0.74594985 0.291754794 -1.41032062 1.9083833 0.77224116 0.30940645
68 -0.32129976 -0.180873123 2.91048081 7.1865103 0.33783758 0.17467085
69 1.00614809 0.088841025 0.15176850 1.2221988 1.04288126 0.10157711
70 -0.70243892 -2.005221879 0.09313122 4.4119763 0.73427200 2.04321436
71 0.52766909 -3.327095358 -1.04067465 13.3954070 0.54520071 3.39711015
72 0.48253861 0.943507215 -0.46072663 1.1728430 0.49825913 0.97694754
73 2.50530044 0.280012806 0.18972293 7.2580053 2.60219518 0.29738001
74 -1.65176277 0.428301489 0.79990078 3.6313729 1.72169259 0.44926098
75 0.34570892 0.370227059 0.70780826 0.8282996 0.35593842 0.38977970
76 -0.23851817 -0.901230701 -0.33809536 0.9817427 0.25173393 0.91247905
77 1.32896459 0.478536554 0.08876840 2.1548317 1.37865252 0.50071299
78 -1.68331093 -0.096208512 1.64583926 4.5943093 1.75450678 0.08795524
79 -0.37956176 -1.231537068 0.73754305 1.9801680 0.39843766 1.25078707
80 -1.78444631 -0.896193054 -1.16547997 5.9512611 1.85970077 0.90731937
81 1.21441969 0.257613421 0.43998954 2.0599242 1.25951088 0.27443801
82 0.46778063 0.642326234 -1.47139877 2.1072616 0.48290891 0.66847047
83 -0.83448792 -0.565240621 -0.82756468 1.8170364 0.87162018 0.56834963
84 0.35308217 2.668538874 0.31236036 7.7508791 0.36360755 2.74376800
85 2.44494544 0.668246258 -1.49079550 7.3286217 2.53941810 0.69501840
86 0.67000101 -0.213880584 0.83976786 1.4313851 0.69324447 0.20847792
87 0.81081590 -0.989957575 2.13298965 6.4870938 0.83971031 1.00335533
88 -0.29234243 -0.817921397 -1.39908389 2.5529898 0.30771818 0.82715159
89 0.58155073 3.007588109 0.53457199 10.1357875 0.60124465 3.09103068
90 -0.58788094 -0.147886958 -0.49259987 0.6819147 0.61511677 0.14088560
91 -0.90552955 -0.314098301 -0.89350439 1.9024244 0.94551274 0.31112340
92 -1.62580563 -0.601495744 0.08243134 3.0800386 1.69469377 0.60548303
93 0.49950100 0.016982913 0.32643645 0.4500061 0.51590223 0.02797824
94 0.05884231 0.851526580 -0.43898014 0.8979754 0.05755973 0.88273868
95 -1.10339587 -0.385677414 -1.33237468 3.4359655 1.15131952 0.38443652
96 -1.40881767 -0.943221164 -0.79525962 3.7840041 1.46899800 0.95548673
97 0.33374188 -0.655439434 0.14073530 0.6625540 0.34349114 0.66073351
98 -1.98380693 -1.385614955 1.35907680 6.3458473 2.06706180 1.40859749
99 0.98214482 -2.053593700 -0.11959262 6.0543157 1.01791473 2.09275798
100 -0.15308456 -0.040369767 -0.95315502 0.8123856 0.16287184 0.03076381
C3_BD
1 0.83480246
2 0.49687317
3 1.32493717
4 0.75217910
5 2.93719571
6 1.07406406
7 1.46286559
8 0.68518895
9 0.55867270
10 1.81855445
11 0.64355788
12 0.44890047
13 0.06706323
14 0.75732987
15 0.49175818
16 0.33704236
17 1.09429657
18 0.99202112
19 0.92105504
20 0.81256665
21 1.58235284
22 0.63124797
23 0.37527897
24 0.20586196
25 0.42241691
26 0.53248946
27 0.69633936
28 0.97378335
29 0.79759926
30 0.43293467
31 0.42593551
32 0.24881793
33 0.42076841
34 0.35937440
35 1.18083190
36 0.53382622
37 0.06980202
38 0.56229434
39 0.27101255
40 1.90956487
41 0.53294350
42 0.52430823
43 0.25915096
44 0.75299121
45 1.40001164
46 0.46865354
47 2.27702995
48 1.95266646
49 1.25269321
50 0.80250726
51 0.59707910
52 0.35323555
53 0.72234962
54 0.75672461
55 0.14694402
56 0.45531888
57 1.27495987
58 0.20934502
59 0.30111449
60 1.90771058
61 2.08948648
62 0.19982455
63 1.55698720
64 0.51439306
65 1.08214971
66 1.29602021
67 1.25568698
68 2.67528956
69 0.16546967
70 0.11212267
71 0.91939066
72 0.39176585
73 0.19999983
74 0.75512713
75 0.67134324
76 0.28019843
77 0.10815347
78 1.52474461
79 0.69839534
80 1.03293598
81 0.42768726
82 1.31125464
83 0.72550758
84 0.31157284
85 1.32890138
86 0.79139738
87 1.96794404
88 1.24546404
89 0.51373643
90 0.42076346
91 0.78549818
92 0.10238813
93 0.32437899
94 0.37198133
95 1.18477337
96 0.69611710
97 0.15543189
98 1.26385400
99 0.08140912
100 0.83976710
C1 C2 C3 MD C1_BD C2_BD
1 0.16185767 0.465557280 0.88747732 1.0514126 0.4701479 -0.47168471
2 0.84365371 0.737741251 -0.57625718 1.3022942 2.4943739 -0.74146299
3 0.37264342 0.199930685 1.42621743 2.2132250 1.0959626 -0.20840585
4 -0.41433401 1.549908803 -0.85688115 3.6002895 1.2405430 -1.54645222
5 0.74431492 1.602282400 -3.25858026 10.8641344 2.1994409 -1.59836292
6 0.40878999 -1.007329448 1.15046588 2.6505490 1.2032804 -0.98818394
7 0.99266364 -0.725241990 -1.63804459 3.5612923 2.9367787 -0.70858971
8 -0.14328653 1.889305880 -0.78324775 4.3893422 0.4358135 -1.88284955
9 1.66960919 -1.011570441 0.58396447 5.3159292 4.9466038 -0.99238745
10 0.86706241 -0.031762671 -2.02900621 3.6669311 2.5638735 -0.02123969
11 -0.98596177 1.532722563 0.67726750 4.2980205 2.9376837 -1.52941788
12 0.85376406 -0.695074847 -0.52352715 1.5536517 2.5243912 -0.67868920
13 0.28378339 1.119552837 -0.10382409 1.3610926 0.8321406 -1.11989995
14 -2.02917517 1.220003004 0.80232197 7.0176407 6.0349440 -1.21946229
15 -0.04912526 0.397432633 -0.57063495 0.4339775 0.1562523 -0.40416218
16 -0.99909385 0.077733180 -0.40057636 1.4231368 2.9766723 -0.08728839
17 0.23668049 0.571140238 1.17270479 1.7713996 0.6922939 -0.57633448
18 0.07914937 -1.019700278 1.06028695 2.0979150 0.2245901 -1.00044543
19 -1.68761857 0.372179227 0.98228335 3.8665251 5.0208756 -0.37913198
20 0.54926518 -0.816010803 -0.92325718 1.6997111 1.6203458 -0.79855626
21 0.18072560 1.407771883 -1.76938109 4.4543639 0.5261660 -1.40557158
22 0.55728164 -0.581662237 -0.72395758 1.0791778 1.6441463 -0.56627898
23 -0.14317267 0.441434234 0.38238406 0.3951620 0.4354754 -0.44777488
24 -0.24158538 0.710890314 0.19616640 0.7035524 0.7276590 -0.71484938
25 -1.09414426 -1.165558882 -0.49441728 2.8617873 3.2588733 -1.14501487
26 1.10497351 1.410069867 -0.61540545 3.1360529 3.2702223 -1.40784925
27 1.34248968 -0.455239903 -0.79550392 2.5616394 3.9753987 -0.44097403
28 1.31159432 0.474860161 -1.10046132 2.4810365 3.8836715 -0.48090537
29 0.14218357 0.005627344 0.84658476 0.7256851 0.4117362 -0.01581986
30 -1.99522562 0.143100932 -0.50597806 5.1780269 5.9341491 -0.15207839
31 -0.17989743 -1.059360842 0.43806407 1.2902096 0.5445098 -1.03975546
32 1.00184090 0.175649334 0.24338219 1.2865034 2.9640256 -0.18433911
33 -1.12084496 -0.037087257 0.43238456 1.4266734 3.3381467 -0.02651721
34 -1.22596268 -0.420260955 0.36490227 1.7161329 3.6502371 -0.40630424
35 -0.23198034 -0.101186505 1.26782161 1.3956928 0.6991420 -0.09004992
36 -1.17210999 -0.798688667 -0.61687477 2.5622810 3.4903506 -0.78138723
37 1.11005906 0.953903901 0.04661374 2.1448712 3.2853211 -0.95571509
38 1.06293680 0.884622118 0.58794526 2.4782166 3.1454170 -0.88704566
39 0.51326344 1.579752556 0.26777780 2.9404404 1.5134580 -1.57603220
40 -0.75717151 -0.311790680 2.06882117 3.8663412 2.2584142 -0.29879268
41 0.93008783 -0.377632081 0.55568377 1.6853015 2.7509935 -0.36405214
42 0.38251904 -0.868498321 -0.60641290 1.2708837 1.1252829 -0.85057987
43 0.09391775 -1.672222281 -0.31496066 3.0848914 0.2684369 -1.64720014
44 0.60494872 -0.077200275 -0.85777379 0.8395293 1.7856681 -0.06627569
45 -0.52513426 -1.074878698 1.50873684 3.0227603 1.5695046 -1.05513616
46 -1.04218441 0.443484387 -0.54523909 1.9939522 3.1046065 -0.44980691
47 -0.83154600 -0.343820169 2.47272681 5.4166410 2.4792292 -0.33053907
48 -1.22769908 -0.234273692 2.11619703 4.6832902 3.6553924 -0.22196082
49 -0.77726408 -0.168765504 -1.40702996 2.7130661 2.3180683 -0.15703162
50 -0.05489791 -1.081158598 -0.91220022 1.9541719 0.1733911 -1.06136055
51 -0.78284695 0.197798357 0.62617953 0.9850828 2.3346436 -0.20629237
52 0.43659660 1.271995924 0.35815465 2.0421906 1.2858371 -1.27099567
53 -0.81367374 -0.662416259 0.76387281 1.3510889 2.4261672 -0.64631926
54 1.25242378 1.258586660 0.80165669 4.1060568 3.7079965 -1.25770492
55 -0.34772580 0.774734417 -0.19162645 0.9053089 1.0427858 -0.77812920
56 0.66504072 -0.261610627 -0.53058206 0.7123662 1.9640789 -0.24905614
57 0.86710181 -0.319446295 -1.43150475 2.2978729 2.5639905 -0.30638063
58 -0.85177598 0.898191375 -0.26021560 2.0194083 2.5392913 -0.90049498
59 -0.92807615 0.278123026 -0.36108562 1.3445812 2.7658235 -0.28590709
60 -0.29799551 -0.184343952 -2.12700373 4.1444723 0.8951385 -0.17247238
61 -0.60237342 -0.354070594 2.26658514 4.4707162 1.7988247 -0.34069890
62 0.91744323 -0.907065407 0.18953027 2.1239067 2.7134522 -0.88880608
63 0.57443241 -0.211533680 1.68127927 3.2872954 1.6950663 -0.19942179
64 0.79907845 0.287901004 -0.59551447 0.8555230 2.3620317 -0.29559865
65 0.58898539 -0.859643772 -1.21957409 2.3151866 1.7382736 -0.84180358
66 -0.30155864 0.287514551 -1.45465358 2.0964187 0.9057172 -0.29521561
67 0.74594985 0.291754794 -1.41032062 1.9083833 2.2042950 -0.29941838
68 -0.32129976 -0.180873123 2.91048081 7.1865103 0.9643279 -0.16903223
69 1.00614809 0.088841025 0.15176850 1.2221988 2.9768135 -0.09829805
70 -0.70243892 -2.005221879 0.09313122 4.4119763 2.0959153 -1.97725652
71 0.52766909 -3.327095358 -1.04067465 13.3954070 1.5562278 -3.28744666
72 0.48253861 0.943507215 -0.46072663 1.1728430 1.4222372 -0.94541030
73 2.50530044 0.280012806 0.18972293 7.2580053 7.4277389 -0.28778017
74 -1.65176277 0.428301489 0.79990078 3.6313729 4.9144211 -0.43475821
75 0.34570892 0.370227059 0.70780826 0.8282996 1.0159951 -0.37719707
76 -0.23851817 -0.901230701 -0.33809536 0.9817427 0.7185525 -0.88302295
77 1.32896459 0.478536554 0.08876840 2.1548317 3.9352432 -0.48454927
78 -1.68331093 -0.096208512 1.64583926 4.5943093 5.0080864 -0.08511593
79 -0.37956176 -1.231537068 0.73754305 1.9801680 1.1373055 -1.21040991
80 -1.78444631 -0.896193054 -1.16547997 5.9512611 5.3083534 -0.87802982
81 1.21441969 0.257613421 0.43998954 2.0599242 3.5951638 -0.26557876
82 0.46778063 0.642326234 -1.47139877 2.1072616 1.3784213 -0.64689130
83 -0.83448792 -0.565240621 -0.82756468 1.8170364 2.4879637 -0.55000251
84 0.35308217 2.668538874 0.31236036 7.7508791 1.0378860 -2.65519531
85 2.44494544 0.668246258 -1.49079550 7.3286217 7.2485472 -0.67258223
86 0.67000101 -0.213880584 0.83976786 1.4313851 1.9788058 -0.20174796
87 0.81081590 -0.989957575 2.13298965 6.4870938 2.3968798 -0.97096561
88 -0.29234243 -0.817921397 -1.39908389 2.5529898 0.8783547 -0.80044997
89 0.58155073 3.007588109 0.53457199 10.1357875 1.7162004 -2.99124786
90 -0.58788094 -0.147886958 -0.49259987 0.6819147 1.7557971 -0.13633761
91 -0.90552955 -0.314098301 -0.89350439 1.9024244 2.6988835 -0.30107990
92 -1.62580563 -0.601495744 0.08243134 3.0800386 4.8373554 -0.58593719
93 0.49950100 0.016982913 0.32643645 0.4500061 1.4725979 -0.02707506
94 0.05884231 0.851526580 -0.43898014 0.8979754 0.1642992 -0.85424263
95 -1.10339587 -0.385677414 -1.33237468 3.4359655 3.2863410 -0.37202636
96 -1.40881767 -0.943221164 -0.79525962 3.7840041 4.1931265 -0.92464228
97 0.33374188 -0.655439434 0.14073530 0.6625540 0.9804654 -0.63940410
98 -1.98380693 -1.385614955 1.35907680 6.3458473 5.9002474 -1.36312598
99 0.98214482 -2.053593700 -0.11959262 6.0543157 2.9055487 -2.02520081
100 -0.15308456 -0.040369767 -0.95315502 0.8123856 0.4649035 -0.02977071
C3_BD
1 -0.27724751
2 -0.16501730
3 -0.44002689
4 -0.24980734
5 -0.97547651
6 -0.35670904
7 -0.48583450
8 -0.22755914
9 -0.18554164
10 -0.60396287
11 -0.21373298
12 -0.14908501
13 -0.02227247
14 -0.25151797
15 -0.16331855
16 -0.11193565
17 -0.36342849
18 -0.32946163
19 -0.30589298
20 -0.26986274
21 -0.52551760
22 -0.20964472
23 -0.12463447
24 -0.06836913
25 -0.14028952
26 -0.17684588
27 -0.23126232
28 -0.32340466
29 -0.26489190
30 -0.14378259
31 -0.14145809
32 -0.08263530
33 -0.13974203
34 -0.11935238
35 -0.39216787
36 -0.17728983
37 -0.02318206
38 -0.18674442
39 -0.09000639
40 -0.63418848
41 -0.17699667
42 -0.17412880
43 -0.08606702
44 -0.25007705
45 -0.46495998
46 -0.15564524
47 -0.75622786
48 -0.64850301
49 -0.41603384
50 -0.26652190
51 -0.19829684
52 -0.11731359
53 -0.23990062
54 -0.25131696
55 -0.04880180
56 -0.15121664
57 -0.42342885
58 -0.06952589
59 -0.10000359
60 -0.63357265
61 -0.69394252
62 -0.06636403
63 -0.51709338
64 -0.17083586
65 -0.35939438
66 -0.43042323
67 -0.41702810
68 -0.88849446
69 -0.05495438
70 -0.03723723
71 -0.30534022
72 -0.13010995
73 -0.06642224
74 -0.25078641
75 -0.22296082
76 -0.09305713
77 -0.03591901
78 -0.50638524
79 -0.23194513
80 -0.34304993
81 -0.14203986
82 -0.43548276
83 -0.24094942
84 -0.10347693
85 -0.44134345
86 -0.26283218
87 -0.65357687
88 -0.41363295
89 -0.17061778
90 -0.13974039
91 -0.26087299
92 -0.03400428
93 -0.10773000
94 -0.12353928
95 -0.39347688
96 -0.23118850
97 -0.05162072
98 -0.41974046
99 -0.02703691
100 -0.27889632
anomalyDetection documentation built on March 18, 2018, 1:21 p.m.
R Package Documentation
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Description Usage Arguments Value References Examples
View source: R/mahalanobis_distance.R
Description
Calculates the distance between the elements in a data set and the mean vector of the data for outlier detection. Values are independent of the scale between variables.
Usage
1 2 3 4 5 6 7 8 9 10 | mahalanobis_distance(data, output = c("md", "bd", "both"),
normalize = FALSE)
## S3 method for class 'matrix'
mahalanobis_distance(data, output = c("md", "bd", "both"),
normalize = FALSE)
## S3 method for class 'data.frame'
mahalanobis_distance(data, output = c("md", "bd",
"both"), normalize = FALSE)
|
Arguments
data |
A matrix or data frame. Data frames will be converted to matrices
via |
output |
Character string specifying which distance metric(s) to
compute. Current options include: |
normalize |
Logical indicating whether or not to normalize the breakdown distances within each column (so that breakdown distances across columns can be compared). |
Value
If output = "md", then a vector containing the Mahalanobis
distances is returned. Otherwise, a matrix.
References
W. Wang and R. Battiti, "Identifying Intrusions in Computer Networks with Principal Component Analysis," in First International Conference on Availability, Reliability and Security, 2006.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ## Not run:
# Simulate some data
x <- data.frame(C1 = rnorm(100), C2 = rnorm(100), C3 = rnorm(100))
# Add Mahalanobis distances
x %>% dplyr::mutate(MD = mahalanobis_distance(x))
# Add Mahalanobis and breakdown distances
x %>% cbind(mahalanobis_distance(x, output = "both"))
# Add Mahalanobis and normalized breakdown distances
x %>% cbind(mahalanobis_distance(x, output = "both", normalize = TRUE))
## End(Not run)
|
Example output
C1 C2 C3 MD
1 0.16185767 0.465557280 0.88747732 1.0514126
2 0.84365371 0.737741251 -0.57625718 1.3022942
3 0.37264342 0.199930685 1.42621743 2.2132250
4 -0.41433401 1.549908803 -0.85688115 3.6002895
5 0.74431492 1.602282400 -3.25858026 10.8641344
6 0.40878999 -1.007329448 1.15046588 2.6505490
7 0.99266364 -0.725241990 -1.63804459 3.5612923
8 -0.14328653 1.889305880 -0.78324775 4.3893422
9 1.66960919 -1.011570441 0.58396447 5.3159292
10 0.86706241 -0.031762671 -2.02900621 3.6669311
11 -0.98596177 1.532722563 0.67726750 4.2980205
12 0.85376406 -0.695074847 -0.52352715 1.5536517
13 0.28378339 1.119552837 -0.10382409 1.3610926
14 -2.02917517 1.220003004 0.80232197 7.0176407
15 -0.04912526 0.397432633 -0.57063495 0.4339775
16 -0.99909385 0.077733180 -0.40057636 1.4231368
17 0.23668049 0.571140238 1.17270479 1.7713996
18 0.07914937 -1.019700278 1.06028695 2.0979150
19 -1.68761857 0.372179227 0.98228335 3.8665251
20 0.54926518 -0.816010803 -0.92325718 1.6997111
21 0.18072560 1.407771883 -1.76938109 4.4543639
22 0.55728164 -0.581662237 -0.72395758 1.0791778
23 -0.14317267 0.441434234 0.38238406 0.3951620
24 -0.24158538 0.710890314 0.19616640 0.7035524
25 -1.09414426 -1.165558882 -0.49441728 2.8617873
26 1.10497351 1.410069867 -0.61540545 3.1360529
27 1.34248968 -0.455239903 -0.79550392 2.5616394
28 1.31159432 0.474860161 -1.10046132 2.4810365
29 0.14218357 0.005627344 0.84658476 0.7256851
30 -1.99522562 0.143100932 -0.50597806 5.1780269
31 -0.17989743 -1.059360842 0.43806407 1.2902096
32 1.00184090 0.175649334 0.24338219 1.2865034
33 -1.12084496 -0.037087257 0.43238456 1.4266734
34 -1.22596268 -0.420260955 0.36490227 1.7161329
35 -0.23198034 -0.101186505 1.26782161 1.3956928
36 -1.17210999 -0.798688667 -0.61687477 2.5622810
37 1.11005906 0.953903901 0.04661374 2.1448712
38 1.06293680 0.884622118 0.58794526 2.4782166
39 0.51326344 1.579752556 0.26777780 2.9404404
40 -0.75717151 -0.311790680 2.06882117 3.8663412
41 0.93008783 -0.377632081 0.55568377 1.6853015
42 0.38251904 -0.868498321 -0.60641290 1.2708837
43 0.09391775 -1.672222281 -0.31496066 3.0848914
44 0.60494872 -0.077200275 -0.85777379 0.8395293
45 -0.52513426 -1.074878698 1.50873684 3.0227603
46 -1.04218441 0.443484387 -0.54523909 1.9939522
47 -0.83154600 -0.343820169 2.47272681 5.4166410
48 -1.22769908 -0.234273692 2.11619703 4.6832902
49 -0.77726408 -0.168765504 -1.40702996 2.7130661
50 -0.05489791 -1.081158598 -0.91220022 1.9541719
51 -0.78284695 0.197798357 0.62617953 0.9850828
52 0.43659660 1.271995924 0.35815465 2.0421906
53 -0.81367374 -0.662416259 0.76387281 1.3510889
54 1.25242378 1.258586660 0.80165669 4.1060568
55 -0.34772580 0.774734417 -0.19162645 0.9053089
56 0.66504072 -0.261610627 -0.53058206 0.7123662
57 0.86710181 -0.319446295 -1.43150475 2.2978729
58 -0.85177598 0.898191375 -0.26021560 2.0194083
59 -0.92807615 0.278123026 -0.36108562 1.3445812
60 -0.29799551 -0.184343952 -2.12700373 4.1444723
61 -0.60237342 -0.354070594 2.26658514 4.4707162
62 0.91744323 -0.907065407 0.18953027 2.1239067
63 0.57443241 -0.211533680 1.68127927 3.2872954
64 0.79907845 0.287901004 -0.59551447 0.8555230
65 0.58898539 -0.859643772 -1.21957409 2.3151866
66 -0.30155864 0.287514551 -1.45465358 2.0964187
67 0.74594985 0.291754794 -1.41032062 1.9083833
68 -0.32129976 -0.180873123 2.91048081 7.1865103
69 1.00614809 0.088841025 0.15176850 1.2221988
70 -0.70243892 -2.005221879 0.09313122 4.4119763
71 0.52766909 -3.327095358 -1.04067465 13.3954070
72 0.48253861 0.943507215 -0.46072663 1.1728430
73 2.50530044 0.280012806 0.18972293 7.2580053
74 -1.65176277 0.428301489 0.79990078 3.6313729
75 0.34570892 0.370227059 0.70780826 0.8282996
76 -0.23851817 -0.901230701 -0.33809536 0.9817427
77 1.32896459 0.478536554 0.08876840 2.1548317
78 -1.68331093 -0.096208512 1.64583926 4.5943093
79 -0.37956176 -1.231537068 0.73754305 1.9801680
80 -1.78444631 -0.896193054 -1.16547997 5.9512611
81 1.21441969 0.257613421 0.43998954 2.0599242
82 0.46778063 0.642326234 -1.47139877 2.1072616
83 -0.83448792 -0.565240621 -0.82756468 1.8170364
84 0.35308217 2.668538874 0.31236036 7.7508791
85 2.44494544 0.668246258 -1.49079550 7.3286217
86 0.67000101 -0.213880584 0.83976786 1.4313851
87 0.81081590 -0.989957575 2.13298965 6.4870938
88 -0.29234243 -0.817921397 -1.39908389 2.5529898
89 0.58155073 3.007588109 0.53457199 10.1357875
90 -0.58788094 -0.147886958 -0.49259987 0.6819147
91 -0.90552955 -0.314098301 -0.89350439 1.9024244
92 -1.62580563 -0.601495744 0.08243134 3.0800386
93 0.49950100 0.016982913 0.32643645 0.4500061
94 0.05884231 0.851526580 -0.43898014 0.8979754
95 -1.10339587 -0.385677414 -1.33237468 3.4359655
96 -1.40881767 -0.943221164 -0.79525962 3.7840041
97 0.33374188 -0.655439434 0.14073530 0.6625540
98 -1.98380693 -1.385614955 1.35907680 6.3458473
99 0.98214482 -2.053593700 -0.11959262 6.0543157
100 -0.15308456 -0.040369767 -0.95315502 0.8123856
C1 C2 C3 MD C1_BD C2_BD
1 0.16185767 0.465557280 0.88747732 1.0514126 0.16470914 0.48741929
2 0.84365371 0.737741251 -0.57625718 1.3022942 0.87386592 0.76619691
3 0.37264342 0.199930685 1.42621743 2.2132250 0.38395381 0.21535791
4 -0.41433401 1.549908803 -0.85688115 3.6002895 0.43460533 1.59803917
5 0.74431492 1.602282400 -3.25858026 10.8641344 0.77054063 1.65168152
6 0.40878999 -1.007329448 1.15046588 2.6505490 0.42155095 1.02114804
7 0.99266364 -0.725241990 -1.63804459 3.5612923 1.02885567 0.73222702
8 -0.14328653 1.889305880 -0.78324775 4.3893422 0.15268061 1.94565813
9 1.66960919 -1.011570441 0.58396447 5.3159292 1.73296731 1.02549177
10 0.86706241 -0.031762671 -2.02900621 3.6669311 0.89821402 0.02194821
11 -0.98596177 1.532722563 0.67726750 4.2980205 1.02917273 1.58043660
12 0.85376406 -0.695074847 -0.52352715 1.5536517 0.88438200 0.70132908
13 0.28378339 1.119552837 -0.10382409 1.3610926 0.29152779 1.15725786
14 -2.02917517 1.220003004 0.80232197 7.0176407 2.11425069 1.26014142
15 -0.04912526 0.397432633 -0.57063495 0.4339775 0.05474062 0.41764433
16 -0.99909385 0.077733180 -0.40057636 1.4231368 1.04283181 0.09020017
17 0.23668049 0.571140238 1.17270479 1.7713996 0.24253463 0.59555999
18 0.07914937 -1.019700278 1.06028695 2.0979150 0.07868172 1.03381855
19 -1.68761857 0.372179227 0.98228335 3.8665251 1.75898730 0.39177916
20 0.54926518 -0.816010803 -0.92325718 1.6997111 0.56766346 0.82519471
21 0.18072560 1.407771883 -1.76938109 4.4543639 0.18433425 1.45245899
22 0.55728164 -0.581662237 -0.72395758 1.0791778 0.57600163 0.58516906
23 -0.14317267 0.441434234 0.38238406 0.3951620 0.15256219 0.46271187
24 -0.24158538 0.710890314 0.19616640 0.7035524 0.25492423 0.73869551
25 -1.09414426 -1.165558882 -0.49441728 2.8617873 1.14169663 1.18321057
26 1.10497351 1.410069867 -0.61540545 3.1360529 1.14567258 1.45481265
27 1.34248968 -0.455239903 -0.79550392 2.5616394 1.39272037 0.45568415
28 1.31159432 0.474860161 -1.10046132 2.4810365 1.36058516 0.49694754
29 0.14218357 0.005627344 0.84658476 0.7256851 0.14424551 0.01634758
30 -1.99522562 0.143100932 -0.50597806 5.1780269 2.07893873 0.15715146
31 -0.17989743 -1.059360842 0.43806407 1.2902096 0.19076072 1.07443989
32 1.00184090 0.175649334 0.24338219 1.2865034 1.03840123 0.19048834
33 -1.12084496 -0.037087257 0.43238456 1.4266734 1.16946884 0.02740178
34 -1.22596268 -0.420260955 0.36490227 1.7161329 1.27880497 0.41985784
35 -0.23198034 -0.101186505 1.26782161 1.3956928 0.24493374 0.09305383
36 -1.17210999 -0.798688667 -0.61687477 2.5622810 1.22279115 0.80745294
37 1.11005906 0.953903901 0.04661374 2.1448712 1.15096222 0.98759608
38 1.06293680 0.884622118 0.58794526 2.4782166 1.10194892 0.91663595
39 0.51326344 1.579752556 0.26777780 2.9404404 0.53021696 1.62860589
40 -0.75717151 -0.311790680 2.06882117 3.8663412 0.79120103 0.30875988
41 0.93008783 -0.377632081 0.55568377 1.6853015 0.96376868 0.37619629
42 0.38251904 -0.868498321 -0.60641290 1.2708837 0.39422574 0.87895373
43 0.09391775 -1.672222281 -0.31496066 3.0848914 0.09404277 1.70214786
44 0.60494872 -0.077200275 -0.85777379 0.8395293 0.62558161 0.06848653
45 -0.52513426 -1.074878698 1.50873684 3.0227603 0.54985204 1.09033366
46 -1.04218441 0.443484387 -0.54523909 1.9939522 1.08765161 0.46481169
47 -0.83154600 -0.343820169 2.47272681 5.4166410 0.86856020 0.34156528
48 -1.22769908 -0.234273692 2.11619703 4.6832902 1.28061106 0.22936505
49 -0.77726408 -0.168765504 -1.40702996 2.7130661 0.81209992 0.16226993
50 -0.05489791 -1.081158598 -0.91220022 1.9541719 0.06074492 1.09676569
51 -0.78284695 0.197798357 0.62617953 0.9850828 0.81790684 0.21317392
52 0.43659660 1.271995924 0.35815465 2.0421906 0.45047345 1.31339387
53 -0.81367374 -0.662416259 0.76387281 1.3510889 0.84997072 0.66787934
54 1.25242378 1.258586660 0.80165669 4.1060568 1.29904009 1.29965977
55 -0.34772580 0.774734417 -0.19162645 0.9053089 0.36532411 0.80408623
56 0.66504072 -0.261610627 -0.53058206 0.7123662 0.68808513 0.25736422
57 0.86710181 -0.319446295 -1.43150475 2.2978729 0.89825500 0.31660095
58 -0.85177598 0.898191375 -0.26021560 2.0194083 0.88960201 0.93053393
59 -0.92807615 0.278123026 -0.36108562 1.3445812 0.96896414 0.29544445
60 -0.29799551 -0.184343952 -2.12700373 4.1444723 0.31359813 0.17822576
61 -0.60237342 -0.354070594 2.26658514 4.4707162 0.63019084 0.35206402
62 0.91744323 -0.907065407 0.18953027 2.1239067 0.95061664 0.91845510
63 0.57443241 -0.211533680 1.68127927 3.2872954 0.59384067 0.20607416
64 0.79907845 0.287901004 -0.59551447 0.8555230 0.82750184 0.30545930
65 0.58898539 -0.859643772 -1.21957409 2.3151866 0.60897767 0.86988468
66 -0.30155864 0.287514551 -1.45465358 2.0964187 0.31730424 0.30506349
67 0.74594985 0.291754794 -1.41032062 1.9083833 0.77224116 0.30940645
68 -0.32129976 -0.180873123 2.91048081 7.1865103 0.33783758 0.17467085
69 1.00614809 0.088841025 0.15176850 1.2221988 1.04288126 0.10157711
70 -0.70243892 -2.005221879 0.09313122 4.4119763 0.73427200 2.04321436
71 0.52766909 -3.327095358 -1.04067465 13.3954070 0.54520071 3.39711015
72 0.48253861 0.943507215 -0.46072663 1.1728430 0.49825913 0.97694754
73 2.50530044 0.280012806 0.18972293 7.2580053 2.60219518 0.29738001
74 -1.65176277 0.428301489 0.79990078 3.6313729 1.72169259 0.44926098
75 0.34570892 0.370227059 0.70780826 0.8282996 0.35593842 0.38977970
76 -0.23851817 -0.901230701 -0.33809536 0.9817427 0.25173393 0.91247905
77 1.32896459 0.478536554 0.08876840 2.1548317 1.37865252 0.50071299
78 -1.68331093 -0.096208512 1.64583926 4.5943093 1.75450678 0.08795524
79 -0.37956176 -1.231537068 0.73754305 1.9801680 0.39843766 1.25078707
80 -1.78444631 -0.896193054 -1.16547997 5.9512611 1.85970077 0.90731937
81 1.21441969 0.257613421 0.43998954 2.0599242 1.25951088 0.27443801
82 0.46778063 0.642326234 -1.47139877 2.1072616 0.48290891 0.66847047
83 -0.83448792 -0.565240621 -0.82756468 1.8170364 0.87162018 0.56834963
84 0.35308217 2.668538874 0.31236036 7.7508791 0.36360755 2.74376800
85 2.44494544 0.668246258 -1.49079550 7.3286217 2.53941810 0.69501840
86 0.67000101 -0.213880584 0.83976786 1.4313851 0.69324447 0.20847792
87 0.81081590 -0.989957575 2.13298965 6.4870938 0.83971031 1.00335533
88 -0.29234243 -0.817921397 -1.39908389 2.5529898 0.30771818 0.82715159
89 0.58155073 3.007588109 0.53457199 10.1357875 0.60124465 3.09103068
90 -0.58788094 -0.147886958 -0.49259987 0.6819147 0.61511677 0.14088560
91 -0.90552955 -0.314098301 -0.89350439 1.9024244 0.94551274 0.31112340
92 -1.62580563 -0.601495744 0.08243134 3.0800386 1.69469377 0.60548303
93 0.49950100 0.016982913 0.32643645 0.4500061 0.51590223 0.02797824
94 0.05884231 0.851526580 -0.43898014 0.8979754 0.05755973 0.88273868
95 -1.10339587 -0.385677414 -1.33237468 3.4359655 1.15131952 0.38443652
96 -1.40881767 -0.943221164 -0.79525962 3.7840041 1.46899800 0.95548673
97 0.33374188 -0.655439434 0.14073530 0.6625540 0.34349114 0.66073351
98 -1.98380693 -1.385614955 1.35907680 6.3458473 2.06706180 1.40859749
99 0.98214482 -2.053593700 -0.11959262 6.0543157 1.01791473 2.09275798
100 -0.15308456 -0.040369767 -0.95315502 0.8123856 0.16287184 0.03076381
C3_BD
1 0.83480246
2 0.49687317
3 1.32493717
4 0.75217910
5 2.93719571
6 1.07406406
7 1.46286559
8 0.68518895
9 0.55867270
10 1.81855445
11 0.64355788
12 0.44890047
13 0.06706323
14 0.75732987
15 0.49175818
16 0.33704236
17 1.09429657
18 0.99202112
19 0.92105504
20 0.81256665
21 1.58235284
22 0.63124797
23 0.37527897
24 0.20586196
25 0.42241691
26 0.53248946
27 0.69633936
28 0.97378335
29 0.79759926
30 0.43293467
31 0.42593551
32 0.24881793
33 0.42076841
34 0.35937440
35 1.18083190
36 0.53382622
37 0.06980202
38 0.56229434
39 0.27101255
40 1.90956487
41 0.53294350
42 0.52430823
43 0.25915096
44 0.75299121
45 1.40001164
46 0.46865354
47 2.27702995
48 1.95266646
49 1.25269321
50 0.80250726
51 0.59707910
52 0.35323555
53 0.72234962
54 0.75672461
55 0.14694402
56 0.45531888
57 1.27495987
58 0.20934502
59 0.30111449
60 1.90771058
61 2.08948648
62 0.19982455
63 1.55698720
64 0.51439306
65 1.08214971
66 1.29602021
67 1.25568698
68 2.67528956
69 0.16546967
70 0.11212267
71 0.91939066
72 0.39176585
73 0.19999983
74 0.75512713
75 0.67134324
76 0.28019843
77 0.10815347
78 1.52474461
79 0.69839534
80 1.03293598
81 0.42768726
82 1.31125464
83 0.72550758
84 0.31157284
85 1.32890138
86 0.79139738
87 1.96794404
88 1.24546404
89 0.51373643
90 0.42076346
91 0.78549818
92 0.10238813
93 0.32437899
94 0.37198133
95 1.18477337
96 0.69611710
97 0.15543189
98 1.26385400
99 0.08140912
100 0.83976710
C1 C2 C3 MD C1_BD C2_BD
1 0.16185767 0.465557280 0.88747732 1.0514126 0.4701479 -0.47168471
2 0.84365371 0.737741251 -0.57625718 1.3022942 2.4943739 -0.74146299
3 0.37264342 0.199930685 1.42621743 2.2132250 1.0959626 -0.20840585
4 -0.41433401 1.549908803 -0.85688115 3.6002895 1.2405430 -1.54645222
5 0.74431492 1.602282400 -3.25858026 10.8641344 2.1994409 -1.59836292
6 0.40878999 -1.007329448 1.15046588 2.6505490 1.2032804 -0.98818394
7 0.99266364 -0.725241990 -1.63804459 3.5612923 2.9367787 -0.70858971
8 -0.14328653 1.889305880 -0.78324775 4.3893422 0.4358135 -1.88284955
9 1.66960919 -1.011570441 0.58396447 5.3159292 4.9466038 -0.99238745
10 0.86706241 -0.031762671 -2.02900621 3.6669311 2.5638735 -0.02123969
11 -0.98596177 1.532722563 0.67726750 4.2980205 2.9376837 -1.52941788
12 0.85376406 -0.695074847 -0.52352715 1.5536517 2.5243912 -0.67868920
13 0.28378339 1.119552837 -0.10382409 1.3610926 0.8321406 -1.11989995
14 -2.02917517 1.220003004 0.80232197 7.0176407 6.0349440 -1.21946229
15 -0.04912526 0.397432633 -0.57063495 0.4339775 0.1562523 -0.40416218
16 -0.99909385 0.077733180 -0.40057636 1.4231368 2.9766723 -0.08728839
17 0.23668049 0.571140238 1.17270479 1.7713996 0.6922939 -0.57633448
18 0.07914937 -1.019700278 1.06028695 2.0979150 0.2245901 -1.00044543
19 -1.68761857 0.372179227 0.98228335 3.8665251 5.0208756 -0.37913198
20 0.54926518 -0.816010803 -0.92325718 1.6997111 1.6203458 -0.79855626
21 0.18072560 1.407771883 -1.76938109 4.4543639 0.5261660 -1.40557158
22 0.55728164 -0.581662237 -0.72395758 1.0791778 1.6441463 -0.56627898
23 -0.14317267 0.441434234 0.38238406 0.3951620 0.4354754 -0.44777488
24 -0.24158538 0.710890314 0.19616640 0.7035524 0.7276590 -0.71484938
25 -1.09414426 -1.165558882 -0.49441728 2.8617873 3.2588733 -1.14501487
26 1.10497351 1.410069867 -0.61540545 3.1360529 3.2702223 -1.40784925
27 1.34248968 -0.455239903 -0.79550392 2.5616394 3.9753987 -0.44097403
28 1.31159432 0.474860161 -1.10046132 2.4810365 3.8836715 -0.48090537
29 0.14218357 0.005627344 0.84658476 0.7256851 0.4117362 -0.01581986
30 -1.99522562 0.143100932 -0.50597806 5.1780269 5.9341491 -0.15207839
31 -0.17989743 -1.059360842 0.43806407 1.2902096 0.5445098 -1.03975546
32 1.00184090 0.175649334 0.24338219 1.2865034 2.9640256 -0.18433911
33 -1.12084496 -0.037087257 0.43238456 1.4266734 3.3381467 -0.02651721
34 -1.22596268 -0.420260955 0.36490227 1.7161329 3.6502371 -0.40630424
35 -0.23198034 -0.101186505 1.26782161 1.3956928 0.6991420 -0.09004992
36 -1.17210999 -0.798688667 -0.61687477 2.5622810 3.4903506 -0.78138723
37 1.11005906 0.953903901 0.04661374 2.1448712 3.2853211 -0.95571509
38 1.06293680 0.884622118 0.58794526 2.4782166 3.1454170 -0.88704566
39 0.51326344 1.579752556 0.26777780 2.9404404 1.5134580 -1.57603220
40 -0.75717151 -0.311790680 2.06882117 3.8663412 2.2584142 -0.29879268
41 0.93008783 -0.377632081 0.55568377 1.6853015 2.7509935 -0.36405214
42 0.38251904 -0.868498321 -0.60641290 1.2708837 1.1252829 -0.85057987
43 0.09391775 -1.672222281 -0.31496066 3.0848914 0.2684369 -1.64720014
44 0.60494872 -0.077200275 -0.85777379 0.8395293 1.7856681 -0.06627569
45 -0.52513426 -1.074878698 1.50873684 3.0227603 1.5695046 -1.05513616
46 -1.04218441 0.443484387 -0.54523909 1.9939522 3.1046065 -0.44980691
47 -0.83154600 -0.343820169 2.47272681 5.4166410 2.4792292 -0.33053907
48 -1.22769908 -0.234273692 2.11619703 4.6832902 3.6553924 -0.22196082
49 -0.77726408 -0.168765504 -1.40702996 2.7130661 2.3180683 -0.15703162
50 -0.05489791 -1.081158598 -0.91220022 1.9541719 0.1733911 -1.06136055
51 -0.78284695 0.197798357 0.62617953 0.9850828 2.3346436 -0.20629237
52 0.43659660 1.271995924 0.35815465 2.0421906 1.2858371 -1.27099567
53 -0.81367374 -0.662416259 0.76387281 1.3510889 2.4261672 -0.64631926
54 1.25242378 1.258586660 0.80165669 4.1060568 3.7079965 -1.25770492
55 -0.34772580 0.774734417 -0.19162645 0.9053089 1.0427858 -0.77812920
56 0.66504072 -0.261610627 -0.53058206 0.7123662 1.9640789 -0.24905614
57 0.86710181 -0.319446295 -1.43150475 2.2978729 2.5639905 -0.30638063
58 -0.85177598 0.898191375 -0.26021560 2.0194083 2.5392913 -0.90049498
59 -0.92807615 0.278123026 -0.36108562 1.3445812 2.7658235 -0.28590709
60 -0.29799551 -0.184343952 -2.12700373 4.1444723 0.8951385 -0.17247238
61 -0.60237342 -0.354070594 2.26658514 4.4707162 1.7988247 -0.34069890
62 0.91744323 -0.907065407 0.18953027 2.1239067 2.7134522 -0.88880608
63 0.57443241 -0.211533680 1.68127927 3.2872954 1.6950663 -0.19942179
64 0.79907845 0.287901004 -0.59551447 0.8555230 2.3620317 -0.29559865
65 0.58898539 -0.859643772 -1.21957409 2.3151866 1.7382736 -0.84180358
66 -0.30155864 0.287514551 -1.45465358 2.0964187 0.9057172 -0.29521561
67 0.74594985 0.291754794 -1.41032062 1.9083833 2.2042950 -0.29941838
68 -0.32129976 -0.180873123 2.91048081 7.1865103 0.9643279 -0.16903223
69 1.00614809 0.088841025 0.15176850 1.2221988 2.9768135 -0.09829805
70 -0.70243892 -2.005221879 0.09313122 4.4119763 2.0959153 -1.97725652
71 0.52766909 -3.327095358 -1.04067465 13.3954070 1.5562278 -3.28744666
72 0.48253861 0.943507215 -0.46072663 1.1728430 1.4222372 -0.94541030
73 2.50530044 0.280012806 0.18972293 7.2580053 7.4277389 -0.28778017
74 -1.65176277 0.428301489 0.79990078 3.6313729 4.9144211 -0.43475821
75 0.34570892 0.370227059 0.70780826 0.8282996 1.0159951 -0.37719707
76 -0.23851817 -0.901230701 -0.33809536 0.9817427 0.7185525 -0.88302295
77 1.32896459 0.478536554 0.08876840 2.1548317 3.9352432 -0.48454927
78 -1.68331093 -0.096208512 1.64583926 4.5943093 5.0080864 -0.08511593
79 -0.37956176 -1.231537068 0.73754305 1.9801680 1.1373055 -1.21040991
80 -1.78444631 -0.896193054 -1.16547997 5.9512611 5.3083534 -0.87802982
81 1.21441969 0.257613421 0.43998954 2.0599242 3.5951638 -0.26557876
82 0.46778063 0.642326234 -1.47139877 2.1072616 1.3784213 -0.64689130
83 -0.83448792 -0.565240621 -0.82756468 1.8170364 2.4879637 -0.55000251
84 0.35308217 2.668538874 0.31236036 7.7508791 1.0378860 -2.65519531
85 2.44494544 0.668246258 -1.49079550 7.3286217 7.2485472 -0.67258223
86 0.67000101 -0.213880584 0.83976786 1.4313851 1.9788058 -0.20174796
87 0.81081590 -0.989957575 2.13298965 6.4870938 2.3968798 -0.97096561
88 -0.29234243 -0.817921397 -1.39908389 2.5529898 0.8783547 -0.80044997
89 0.58155073 3.007588109 0.53457199 10.1357875 1.7162004 -2.99124786
90 -0.58788094 -0.147886958 -0.49259987 0.6819147 1.7557971 -0.13633761
91 -0.90552955 -0.314098301 -0.89350439 1.9024244 2.6988835 -0.30107990
92 -1.62580563 -0.601495744 0.08243134 3.0800386 4.8373554 -0.58593719
93 0.49950100 0.016982913 0.32643645 0.4500061 1.4725979 -0.02707506
94 0.05884231 0.851526580 -0.43898014 0.8979754 0.1642992 -0.85424263
95 -1.10339587 -0.385677414 -1.33237468 3.4359655 3.2863410 -0.37202636
96 -1.40881767 -0.943221164 -0.79525962 3.7840041 4.1931265 -0.92464228
97 0.33374188 -0.655439434 0.14073530 0.6625540 0.9804654 -0.63940410
98 -1.98380693 -1.385614955 1.35907680 6.3458473 5.9002474 -1.36312598
99 0.98214482 -2.053593700 -0.11959262 6.0543157 2.9055487 -2.02520081
100 -0.15308456 -0.040369767 -0.95315502 0.8123856 0.4649035 -0.02977071
C3_BD
1 -0.27724751
2 -0.16501730
3 -0.44002689
4 -0.24980734
5 -0.97547651
6 -0.35670904
7 -0.48583450
8 -0.22755914
9 -0.18554164
10 -0.60396287
11 -0.21373298
12 -0.14908501
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