[R] mahalanobis confusion
Prof Brian Ripley
ripley at stats.ox.ac.uk
Thu Jan 3 22:04:52 CET 2002
On Thu, 3 Jan 2002, Clayton Springer wrote:
> Dear r-help,
>
> My understanding of Mahalanobois distance is that when calculating the distance
> between a vector and the origin should be the same as the absolute value of that
> vector and the origin.
Your understanding is wrong. Why do you think so?
> Apparently they are different:
>
> > mahalanobis(as.vector(featureset.all),as.vector(zero20),COVDtotal)
> [1] 2.638582
>
> > mahalanobis(as.vector(abs(featureset.all)),as.vector(zero20),COVDtotal)
> [1] 7.458376
>
>
> Can anyone give me some insight into what is going on?
>
>
>
>
>
>
>
> There were the vectors used:
>
> > featureset.all
> [1] 0.6152346 -0.6220563 0.6159433 -0.6865233 0.5832620 0.5379156
> [7] 0.6188826 -0.5838474 0.5558164 -0.6454835 0.6099608 -0.6083904
> [13] 0.6768469 0.6761911 -0.5519884 0.6242095 -0.5272882 -0.6317221
> [19] 0.5755202 0.6436219
>
> > zero20
> [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>
> > COVDtotal
> X1 X2 X3 X4 X5 X6
> X1 1.05967820 -0.10707972 0.07900894 -0.11026558 0.06998268 0.07632845
> X2 -0.10707972 1.07949619 -0.12731106 0.08694136 -0.04438987 -0.06448543
> X3 0.07900894 -0.12731106 1.10047417 -0.10260288 0.10462419 0.03106977
> X4 -0.11026558 0.08694136 -0.10260288 1.09180220 -0.11520023 -0.05080485
> X5 0.06998268 -0.04438987 0.10462419 -0.11520023 1.08372167 0.07315313
> X6 0.07632845 -0.06448543 0.03106977 -0.05080485 0.07315313 1.09188363
> X7 0.11063123 -0.08141751 0.13237254 -0.08852752 0.07388682 0.09528542
> X8 -0.08381439 0.12026316 -0.08355477 0.06264001 -0.05734851 -0.11195461
> X9 0.06296985 -0.07161381 0.12431183 -0.07784136 0.08356674 0.05189387
> X10 -0.11204672 0.13975040 -0.11037433 0.08570182 -0.06277695 -0.03487686
> X11 0.11903957 -0.10903915 0.08809574 -0.07815082 0.04762978 0.11193407
> X12 -0.09370656 0.12271898 -0.09733936 0.08824304 -0.08304823 -0.09379661
> X13 0.10933205 -0.09057703 0.12125739 -0.15732956 0.09481943 0.08323671
> X14 0.10529610 -0.09744663 0.08032255 -0.10119252 0.06234175 0.06065037
> X15 -0.08266871 0.07953344 -0.06585605 0.05625921 -0.08829623 -0.07704608
> X16 0.07293699 -0.10314218 0.08811019 -0.11278371 0.06360624 0.08096588
> X17 -0.07715753 0.07535229 -0.11229116 0.10637164 -0.03974483 -0.04946984
> X18 -0.10696503 0.11797366 -0.15729346 0.08507554 -0.11331309 -0.09101065
> X19 0.12832256 -0.06828018 0.08285553 -0.17515631 0.13462381 0.06286161
> X20 0.10178729 -0.09395206 0.08629152 -0.12057459 0.08848807 0.02981165
> X7 X8 X9 X10 X11 X12
> X1 0.11063123 -0.08381439 0.06296985 -0.11204672 0.11903957 -0.09370656
> X2 -0.08141751 0.12026316 -0.07161381 0.13975040 -0.10903915 0.12271898
> X3 0.13237254 -0.08355477 0.12431183 -0.11037433 0.08809574 -0.09733936
> X4 -0.08852752 0.06264001 -0.07784136 0.08570182 -0.07815082 0.08824304
> X5 0.07388682 -0.05734851 0.08356674 -0.06277695 0.04762978 -0.08304823
> X6 0.09528542 -0.11195461 0.05189387 -0.03487686 0.11193407 -0.09379661
> X7 1.08577268 -0.09797477 0.06781984 -0.11304299 0.09545183 -0.10580662
> X8 -0.09797477 1.10198194 -0.07366283 0.06636062 -0.08480604 0.09904522
> X9 0.06781984 -0.07366283 1.05239001 -0.11370459 0.08262987 -0.07737044
> X10 -0.11304299 0.06636062 -0.11370459 1.10229003 -0.11033549 0.13175960
> X11 0.09545183 -0.08480604 0.08262987 -0.11033549 1.10971715 -0.10008936
> X12 -0.10580662 0.09904522 -0.07737044 0.13175960 -0.10008936 1.06434180
> X13 0.10689546 -0.10163852 0.09954915 -0.09616881 0.11806829 -0.12041825
> X14 0.11436260 -0.11530532 0.11007362 -0.08119362 0.12552855 -0.07775921
> X15 -0.12945785 0.09931512 -0.07671993 0.14733664 -0.08053384 0.10103581
> X16 0.11283056 -0.06778883 0.05151053 -0.08579178 0.05614164 -0.10019822
> X17 -0.08553127 0.09685377 -0.09564487 0.10696805 -0.05081043 0.06812122
> X18 -0.11385031 0.06771728 -0.13036095 0.11896321 -0.11624387 0.09183934
> X19 0.08297921 -0.10961300 0.05993383 -0.10337781 0.09866079 -0.09255143
> X20 0.04686709 -0.11134721 0.07076651 -0.09653739 0.10925212 -0.07555833
> X13 X14 X15 X16 X17 X18
> X1 0.10933205 0.10529610 -0.08266871 0.07293699 -0.07715753 -0.10696503
> X2 -0.09057703 -0.09744663 0.07953344 -0.10314218 0.07535229 0.11797366
> X3 0.12125739 0.08032255 -0.06585605 0.08811019 -0.11229116 -0.15729346
> X4 -0.15732956 -0.10119252 0.05625921 -0.11278371 0.10637164 0.08507554
> X5 0.09481943 0.06234175 -0.08829623 0.06360624 -0.03974483 -0.11331309
> X6 0.08323671 0.06065037 -0.07704608 0.08096588 -0.04946984 -0.09101065
> X7 0.10689546 0.11436260 -0.12945785 0.11283056 -0.08553127 -0.11385031
> X8 -0.10163852 -0.11530532 0.09931512 -0.06778883 0.09685377 0.06771728
> X9 0.09954915 0.11007362 -0.07671993 0.05151053 -0.09564487 -0.13036095
> X10 -0.09616881 -0.08119362 0.14733664 -0.08579178 0.10696805 0.11896321
> X11 0.11806829 0.12552855 -0.08053384 0.05614164 -0.05081043 -0.11624387
> X12 -0.12041825 -0.07775921 0.10103581 -0.10019822 0.06812122 0.09183934
> X13 1.14484088 0.09993548 -0.08107109 0.11669608 -0.09978561 -0.11341623
> X14 0.09993548 1.07022203 -0.12068641 0.12959327 -0.06042948 -0.09090972
> X15 -0.08107109 -0.12068641 1.09079524 -0.08826068 0.07943239 0.09220653
> X16 0.11669608 0.12959327 -0.08826068 1.11416921 -0.09210416 -0.09377126
> X17 -0.09978561 -0.06042948 0.07943239 -0.09210416 1.03520003 0.12858473
> X18 -0.11341623 -0.09090972 0.09220653 -0.09377126 0.12858473 1.11017146
> X19 0.10733188 0.08778220 -0.06650838 0.05337207 -0.04552405 -0.10608081
> X20 0.09451811 0.07541007 -0.05356769 0.07092049 -0.06626285 -0.10648554
> X19 X20
> X1 0.12832256 0.10178729
> X2 -0.06828018 -0.09395206
> X3 0.08285553 0.08629152
> X4 -0.17515631 -0.12057459
> X5 0.13462381 0.08848807
> X6 0.06286161 0.02981165
> X7 0.08297921 0.04686709
> X8 -0.10961300 -0.11134721
> X9 0.05993383 0.07076651
> X10 -0.10337781 -0.09653739
> X11 0.09866079 0.10925212
> X12 -0.09255143 -0.07555833
> X13 0.10733188 0.09451811
> X14 0.08778220 0.07541007
> X15 -0.06650838 -0.05356769
> X16 0.05337207 0.07092049
> X17 -0.04552405 -0.06626285
> X18 -0.10608081 -0.10648554
> X19 1.08391161 0.09885423
> X20 0.09885423 1.14504480
>
> --
> Clayton Springer, Ph. D.
> Sandia National Laboratories csprin at ca.sandia.gov
> Biosystems Research Department (925) 294-2143
> P.O. Box 969, MS 9951 fax: (925) 294-3020
> Livermore, CA, 94551-0969
>
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--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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