First, get two classes of the sample data, come and five for example.
x1 <- AR.data$come
x2 <- AR.data$fiveCreate an S4 object of class ‘dbcsp’
mydbcsp <- new('dbcsp', X1=x1, X2=x2)
summary(mydbcsp)
print(mydbcsp)By default, euclidean distance is used. To change it, just select another distance type. A mixture with euclidean distance and another one can be performed too, changing the mixture parameter value.
mydbcsp <- new('dbcsp', X1=x1, X2=x2, type='dtw')
mydbcsp <- new('dbcsp', X1=x1, X2=x2, mixture=TRUE, type='COR') #EUCL + CORIt is also possible to select the number of vectors q to use in the projection. The default value is q=15.
mydbcsp <- new('dbcsp', X1=x1, X2=x2, q=10)By default, the training is not performed, but this can be changed and the number of folds to use in the cross-validation can be selected. Linear Discriminant Analysis (LDA) classifier is used to perform the classification, with the logarithm of the variances obtained after the CSP projection.
mydbcsp <- new('dbcsp', X1=x1, X2=x2, training=TRUE, fold=10)A summary of the object can be generated with the summary function.
> summary(mydbcsp)
There are 46 instances of class x1 with [50x92] dimension.
There are 45 instances of class x2 with [50x92] dimension.
The DB-CSP method has used 15 vectors for the projection.
EUCL distance has been used.
An accuracy of 0.8463889 has been obtained with 10 fold cross validation.The summary tells us the number of instances for each class, the number of vectors q and the distance type used. If the classification is performed, it also tells us the obtained accuracy value with the used number of folds fold.
The classification can be also performed after creating the object, calling to train function.
> mydbcsp <- new('dbcsp',X1=x1, X2=x2)
> summary(mydbcsp)
There are 46 instances of class x1 with [50x92] dimension.
There are 45 instances of class x2 with [50x92] dimension.
The DB-CSP method has used 15 vectors for the projection.
EUCL distance has been used.
Classification has not been performed yet.
> mydbcsp <- train(mydbcsp)
46 instances for x1 class and 45 instances for x2 class.
Applying DB-CSP with EUCL distance and 15 projections.
Fold 1 - 82 training instances, 9 test instances - Acc: 0.7777778
Fold 2 - 82 training instances, 9 test instances - Acc: 1
Fold 3 - 82 training instances, 9 test instances - Acc: 0.8888889
Fold 4 - 83 training instances, 8 test instances - Acc: 0.875
Fold 5 - 82 training instances, 9 test instances - Acc: 0.6666667
Fold 6 - 83 training instances, 8 test instances - Acc: 0.75
Fold 7 - 81 training instances, 10 test instances - Acc: 0.9
Fold 8 - 81 training instances, 10 test instances - Acc: 0.7
Fold 9 - 81 training instances, 10 test instances - Acc: 0.7
Fold 10 - 82 training instances, 9 test instances - Acc: 1
Final accuracy: 0.825833333333333
> summary(mydbcsp)
There are 46 instances of class x1 with [50x92] dimension.
There are 45 instances of class x2 with [50x92] dimension.
The DB-CSP method has used 15 vectors for the projection.
EUCL distance has been used.
An accuracy of 0.8258333 has been obtained with 10 fold cross validation. The out slot of the object includes the csp output, including proy object@out$proy,vectors object@out$vectors and eigen values object@out$eig, and the training output if it is performed (accuracy object@out$acc, folds accuracy object@out$folds_acc, used folds object@out$used_folds, trained model object@out$model and the selected q value when training object@out$selected_q).
> mydbcsp@out$acc
[1] 0.8258333
> mydbcsp@out$folds_acc
[1] 0.7777778 1.0000000 0.8888889 0.8750000 0.6666667 0.7500000 0.9000000 0.7000000 0.7000000 1.0000000
> mydbcsp@out$used_folds
$Fold01
[1] 1 26 38 44 70 72 75 76 84
$Fold02
[1] 9 18 22 36 41 48 59 62 63
$Fold03
[1] 3 14 23 39 49 50 69 71 78
$Fold04
[1] 15 16 37 42 53 55 87 91
$Fold05
[1] 10 13 21 31 46 52 65 74 81
$Fold06
[1] 5 7 8 20 57 80 88 89
$Fold07
[1] 4 11 24 25 32 56 60 61 67 83
$Fold08
[1] 27 33 34 43 45 54 64 66 79 90
$Fold09
[1] 2 6 28 29 30 47 68 77 85 86
$Fold10
[1] 12 17 19 35 40 51 58 73 82
> mydbcsp@out$vectors
B1 B2 B3 B4 B5 B6 B7 B8 B9
[1,] -0.061726369 -0.0497482230 -0.2567184012 0.026947829 -0.193035790 -0.2997850686 0.0546807637 0.081120134 0.455003958
[2,] 0.123168014 0.0414484153 0.1897973883 -0.249680210 0.241335514 0.1207770505 -0.1179665116 0.142823323 -0.199108587
[3,] -0.108132121 0.0580154072 0.0807479441 -0.016920545 0.071932589 -0.2932081080 -0.0300956101 -0.160936652 0.033146994
[4,] 0.004880829 -0.0012337889 0.0067966727 0.065862165 -0.007127742 0.0748281845 -0.0160163500 0.040758704 0.048765853
[5,] -0.033526344 -0.0069832348 -0.0912992662 0.022501525 0.068833632 -0.0177871463 0.0276684526 -0.019378728 -0.031086117
[6,] 0.200736232 0.0123133534 -0.1501021399 -0.075135517 0.135508451 -0.0523488564 -0.1294107145 0.050233056 0.307292214
[7,] -0.114136463 0.0034324772 0.0834015705 0.129669377 -0.020281359 0.0237939468 0.0428043529 0.145737305 -0.122826810
[8,] 0.010047441 0.0030796146 -0.0211625784 -0.018690330 -0.078920602 -0.0211216526 -0.0014345898 0.005515821 0.003017529
[9,] 0.180565332 0.0009236857 0.0093865978 0.077310006 0.076451416 0.0930539776 -0.0261688193 -0.051381833 0.139690855
[10,] -0.333049809 0.0059724971 0.1228829172 0.158939001 -0.153348560 0.0006191220 -0.0010729397 0.007448235 -0.082994267
[11,] -0.034756871 0.0026009373 0.0099104832 -0.029598672 0.060953422 -0.0810398463 -0.0214330988 0.046274291 -0.036458498
[12,] -0.104015516 -0.0123819827 -0.0959998366 0.095767564 0.037853212 0.0656310618 0.0236132221 -0.039409267 -0.004919892
[13,] 0.244013199 0.0104724248 -0.1620324489 -0.257521244 -0.005960928 -0.0585614396 0.1067262794 -0.259056660 0.037039014
[14,] -0.025058500 -0.0425077264 -0.0124559812 0.033179170 -0.025633838 0.0212734376 -0.0336693087 0.128340379 -0.134579810
[15,] -0.056716624 -0.0124616596 -0.0337246175 0.176640221 -0.033120009 -0.0125217470 0.1854822841 0.225174822 -0.154728622
[16,] -0.251652375 0.2585256200 0.0915386778 -0.437709412 0.118736090 0.4715687589 0.2246257224 0.246370340 0.075443872
[17,] -0.053788999 -0.3649940748 0.0260303019 -0.098426773 0.301723437 -0.1380976529 -0.1605045362 0.014494198 -0.454664894
[18,] -0.168054657 0.0404866877 -0.0346298743 0.231054218 -0.446801247 -0.0028651656 -0.0162108639 -0.213585609 0.015600835
[19,] 0.400840841 0.0186092596 0.0144021582 0.419555609 -0.182077895 0.1676028758 0.0579420189 -0.169119821 -0.087270761
[20,] 0.006936330 -0.0308290115 0.0334841079 -0.100574253 -0.055067472 -0.0187429596 -0.2769932572 0.082118534 -0.034766383
[21,] 0.008782444 0.0492820119 -0.0362499021 0.073455148 0.152331140 -0.0009058959 0.3411967043 -0.039800765 0.114825528
[22,] 0.041952771 0.0162499027 0.0824876715 -0.131185943 -0.028943370 -0.0047444076 -0.2559065109 -0.322271327 0.084417885
[23,] 0.218475092 -0.0106121183 -0.1575933399 -0.204627313 -0.194953666 0.0473318892 -0.1613614410 -0.120959472 -0.036691046
[24,] -0.254268542 0.0117868086 0.0873158159 0.101183095 0.146036203 -0.0194374508 0.0433332945 0.146251906 0.067335312
[25,] 0.169486258 -0.0016152044 0.2104623403 -0.010127349 -0.016155517 -0.0669082569 0.1419081232 0.049412435 -0.008361872
[26,] -0.248868078 0.0631899711 0.0552265008 0.137500208 0.050035576 0.0804231365 -0.0423994134 -0.069044159 0.026556663
[27,] -0.093285779 0.0743011123 -0.2175294691 -0.134821109 -0.315300095 -0.1100453203 -0.1529670891 0.115346897 -0.225597171
[28,] 0.151408979 0.0248073414 0.1320938942 -0.075560016 0.188025810 0.1341076877 0.2368112818 -0.034257845 0.144506231
[29,] -0.032117248 -0.0080278754 0.0007732527 0.040686070 0.019540602 0.0227365864 -0.0427555415 0.003150382 0.014970079
[30,] 0.001034805 0.0017332014 -0.0002858144 -0.007025721 0.001901324 -0.0230314944 0.0226100369 -0.007143038 -0.011909036
[31,] 0.017811731 -0.0698985795 0.0189639542 0.055594835 -0.040194582 -0.1005089530 0.2073858842 -0.162181492 -0.067177502
[32,] 0.019816774 0.0069234004 0.0216072815 0.019036336 0.085866530 -0.0115550760 -0.0017548142 0.018068571 0.010663216
[33,] -0.027333534 0.0010617905 0.0036000684 0.020386392 -0.012033166 0.0052515771 0.0143763942 0.004507963 -0.017945515
B10 B11 B12 B13 B14 B15 S1 S2 S3
[1,] 0.142502082 0.088249676 0.2699982679 -0.120711763 -0.1637561229 -0.330460944 -0.0056316090 -0.0319349691 -0.018087237
[2,] -0.223798633 -0.178480665 -0.3899322464 0.062379931 0.1587992194 0.082270903 0.0647868582 0.0968300676 -0.141342405
[3,] -0.069106468 0.042166274 0.2031929810 -0.138602397 -0.0446705826 -0.141350480 0.1132644247 -0.0492784351 -0.033730336
[4,] 0.161280250 0.021359191 0.0032263403 -0.067317553 -0.0276428050 0.032767746 0.0165747967 -0.0788123497 0.029106723
[5,] -0.033872543 0.003286565 -0.0005974046 0.040828543 0.0105508406 -0.004644338 -0.0011564380 -0.0224890476 0.006516181
[6,] 0.030495474 0.082483427 -0.0689398379 0.071691444 -0.1305410092 -0.022412424 0.0815066171 0.0210256326 -0.073737939
[7,] 0.050820414 -0.060910975 0.0463787656 -0.041960525 0.0691468016 -0.125895142 0.0131114716 0.0045436541 0.126165826
[8,] 0.008734050 0.020973123 0.0095044592 0.017916446 0.0003234039 0.096580431 -0.0074084272 -0.0795431302 -0.084183291
[9,] -0.255513858 -0.014685815 -0.2325578076 -0.060763321 0.3143004422 0.145875555 0.0189895927 0.0167244391 0.164987305
[10,] 0.005831813 0.048578871 0.1796583347 -0.042751266 0.0255553764 -0.051115695 0.0005203644 0.0807758005 0.103093380
[11,] 0.041175609 -0.087644506 -0.1129978336 0.051723198 -0.0677448488 0.030508787 -0.0473158276 0.0886687123 -0.103357886
[12,] -0.146175538 -0.107117623 -0.2920478447 -0.159890298 -0.0150222371 -0.055454623 -0.1405745387 -0.0656760579 -0.085219520
[13,] 0.182758321 -0.040936113 0.2549904936 0.018912834 -0.2438643783 0.004571821 -0.0344526022 0.0079602908 -0.016982828
[14,] 0.006198222 0.064688291 0.1114619781 0.028059585 -0.0098429642 -0.024990888 -0.0046226664 -0.0501490603 -0.021977130
[15,] 0.391857113 -0.088640045 -0.0471962595 -0.237516308 -0.4062912283 -0.098545207 -0.1353793336 -0.0489483538 0.278339644
[16,] -0.064073917 -0.274035828 -0.0250288587 0.121214764 -0.0382512299 0.155239782 -0.0643447960 0.0411896354 -0.030854006
[17,] 0.104825363 0.156621352 -0.1028704597 0.068834178 0.2474862961 0.095189847 0.0077185573 -0.0629885910 0.081061589
[18,] 0.106585751 0.161103052 -0.1996562263 0.131433098 -0.1143643757 0.063000454 -0.0989652367 0.0431915641 -0.033548808
[19,] -0.197024162 -0.025727254 0.0579424364 -0.096113920 0.0032028361 -0.031803230 -0.1204915847 0.0057601159 -0.019705896
[20,] -0.153350122 0.026081230 0.1067689021 0.169545245 -0.2155819848 0.076099388 0.0057793917 0.0003825203 0.005211441
[21,] -0.116172389 0.042626257 -0.1338693859 -0.177091124 0.3223688255 -0.029575120 0.0559650379 -0.0205363537 0.035649099
[22,] -0.072657262 -0.019594554 0.0555244592 0.259386407 0.2630145317 0.134717996 0.1027405991 0.0541734434 -0.274841777
[23,] 0.089004242 -0.032065680 0.0741662978 -0.280402172 -0.0343800126 -0.047433146 0.0962839112 0.1164739273 0.072845843
[24,] -0.061967792 0.019402745 -0.0710843769 0.220986509 0.0859986424 0.108616823 -0.0733075366 -0.0854903939 -0.061663494
[25,] 0.080012413 0.152739105 0.3067393429 0.173071656 0.0295953358 -0.046613046 0.1437505347 0.0207164006 0.108449838
[26,] -0.150154610 0.239333465 0.3385831006 0.230863845 0.0292606905 0.176143220 0.2062384202 0.1423788664 0.021603865
[27,] 0.329542883 -0.073416158 0.0064963985 0.173313143 -0.3025525968 -0.405337667 0.0859030604 -0.1779732508 -0.050319575
[28,] -0.153233879 0.485897218 -0.0712850280 -0.188099647 0.0757021188 0.233145797 -0.1670255011 0.6320005139 -0.045991855
[29,] 0.060433493 -0.016866171 -0.0116841328 0.006070123 0.0194828985 0.011674017 0.0655833526 -0.3427339409 -0.009802049
[30,] -0.043373018 -0.009881617 0.0045282008 0.001748168 -0.0215236529 -0.010376388 0.0061092348 -0.0057692402 -0.006528758
[31,] -0.149960574 -0.262522929 -0.0385968682 -0.054180373 0.2399860936 0.354439468 -0.1857949669 -0.2248709923 -0.023563341
[32,] 0.051804702 -0.009366860 0.1656074552 0.015708170 0.0493793651 -0.048383520 -0.0755008191 0.0198127506 0.372540909
[33,] -0.016943680 0.017996917 -0.0627105208 -0.008140490 -0.0293464806 0.004129602 0.0575652567 0.0445896900 0.034659930
S4 S5 S6 S7 S8 S9 S10 S11 S12
[1,] 0.032397740 0.027928551 0.021724610 0.062574490 0.045031970 2.759793e-02 -9.392218e-02 -0.003961133 0.170247823
[2,] 0.032279001 0.128016193 0.041958695 0.016032837 0.018853028 -8.301255e-02 1.457909e-01 -0.058718624 0.002069987
[3,] -0.043897387 0.033926475 0.037605088 -0.065593199 0.133376728 6.734788e-02 4.233751e-02 -0.040805483 0.175599242
[4,] -0.009350346 -0.030137008 0.006260226 0.002790202 -0.121529242 -1.182007e-01 -4.517796e-02 0.013639537 -0.053736648
[5,] 0.015618596 -0.021769747 0.008908243 0.061435226 -0.004945569 3.762102e-02 9.875009e-03 -0.053809920 -0.023919331
[6,] -0.030254365 -0.085974355 -0.064006709 0.054693842 0.049336696 1.459989e-02 -3.524134e-02 0.049708717 -0.033895270
[7,] 0.016239724 0.009135143 -0.032941684 -0.007402840 -0.015785814 1.648699e-02 -6.858137e-02 -0.067526092 0.058723756
[8,] 0.029624984 -0.059147239 0.002924715 -0.032472496 0.026722321 -3.805495e-02 5.337635e-02 -0.021471885 -0.056399635
[9,] 0.006254551 0.110125460 -0.125384243 -0.050397002 -0.197779262 -1.892628e-03 7.069437e-02 0.083523314 -0.120529730
[10,] 0.087406534 -0.075075814 -0.057293524 -0.025057163 0.130397214 1.173485e-01 -2.113914e-02 -0.117301787 0.109659784
[11,] -0.090394551 0.203025990 -0.078636435 0.028032862 -0.163684052 -1.491995e-01 -1.177200e-02 0.203423325 -0.088107242
[12,] 0.014884685 -0.134511975 0.190203194 -0.070685880 0.114184022 3.232846e-05 5.586852e-02 -0.070706574 0.203223227
[13,] -0.092509187 -0.058808116 0.179139362 0.069371255 0.008450157 7.965707e-02 9.637389e-05 -0.013477043 0.073612533
[14,] -0.021584344 -0.122625491 0.009312352 -0.125017630 0.121639099 -1.767063e-01 -1.274495e-01 0.042503108 0.017798919
[15,] 0.238595592 0.207665495 0.332468301 0.179030125 -0.106330799 3.620144e-01 1.285581e-01 0.317061011 0.128180184
[16,] -0.005016480 -0.020658014 -0.005208722 0.005214052 -0.004884944 1.533892e-02 2.159188e-02 0.007719444 -0.011128779
[17,] -0.023269076 0.105165453 0.016813767 -0.057501506 -0.109436673 -2.289869e-02 7.661077e-02 -0.005661647 -0.062965533
[18,] 0.047372048 -0.087155656 -0.020187818 -0.005655965 0.099084114 6.274807e-02 -1.233959e-01 0.021266103 -0.159804553
[19,] -0.008398283 0.027045639 -0.017286674 -0.011506200 0.003586142 6.429829e-03 4.159790e-02 0.030072959 0.033372091
[20,] -0.002489575 -0.082196874 -0.080657847 0.082037331 -0.022419676 -8.480345e-03 1.108202e-01 -0.016517838 -0.016379673
[21,] 0.017490493 0.079055386 0.022357963 -0.019928610 -0.115334315 -3.985091e-02 -1.367783e-01 -0.083172004 -0.001364783
[22,] -0.211831612 -0.146363601 -0.250836615 -0.135801625 0.130342725 -2.046603e-01 -3.678251e-02 -0.195923109 -0.129435404
[23,] 0.059795053 0.101785654 -0.209164087 0.003202768 0.106790451 -1.402646e-01 2.555248e-01 -0.286901875 -0.289952938
[24,] -0.059755592 -0.143993533 0.187335980 0.079273170 -0.085701521 1.371673e-01 -2.209824e-01 0.325058613 0.345578958
[25,] -0.001765055 0.062907728 -0.113566753 -0.021683577 -0.037743744 8.044682e-02 -7.915549e-02 -0.061083794 -0.268403088
[26,] -0.052646907 -0.003270730 0.062871822 0.017976232 -0.083087234 -2.406911e-02 -6.915152e-02 -0.039815068 0.010136285
[27,] 0.125319431 -0.083054823 0.058008747 0.032842186 0.039339135 2.991900e-02 -3.536447e-03 0.176116601 -0.154854844
[28,] -0.046580113 -0.172383972 -0.036114531 0.173654273 -0.118866753 1.001207e-01 -7.192745e-02 -0.109806838 0.075744985
[29,] 0.014988526 0.155730374 -0.029984502 -0.024641566 0.137853627 3.804115e-02 7.323470e-03 0.030933979 -0.007679021
[30,] 0.001160705 -0.012540696 0.003665926 -0.002252281 -0.029723075 -1.951063e-02 5.894023e-03 -0.004793704 0.002064871
[31,] -0.042498311 -0.100088042 -0.070593681 -0.091001547 0.033774484 2.364009e-02 -8.517363e-02 0.012049282 0.013623860
[32,] -0.061314437 0.025835232 -0.092857933 -0.003245076 -0.078754364 -3.549129e-02 3.156189e-02 0.026340500 -0.033367603
[33,] -0.015931955 0.043843094 0.012090727 0.021120085 -0.001831175 -4.598779e-04 1.063031e-03 -0.008497183 0.013476702
S13 S14 S15
[1,] -0.0551188009 0.020950022 0.134094614
[2,] -0.0121309247 -0.310011546 0.258914913
[3,] 0.0935653050 0.068313017 -0.126133000
[4,] -0.0654785170 0.006742449 0.026194263
[5,] 0.0340354564 -0.003914214 -0.042233454
[6,] -0.1070975548 0.019481418 -0.143584610
[7,] 0.0784315435 0.139956299 -0.014326436
[8,] 0.0314143773 -0.041772330 0.070758628
[9,] -0.2015793326 -0.223579522 0.055491069
[10,] -0.0075407576 -0.113753983 -0.063587540
[11,] 0.0222281923 0.119513193 -0.042681105
[12,] 0.0769984444 -0.085973009 -0.052525276
[13,] 0.0486116272 0.165454734 -0.101567404
[14,] 0.0505984065 -0.022391331 -0.026874550
[15,] -0.1040264369 -0.044033943 -0.073364114
[16,] 0.0179249789 -0.059561137 -0.043069980
[17,] -0.0247982394 -0.125467323 -0.048644750
[18,] 0.1697377301 0.362502641 -0.076547094
[19,] 0.0005497526 -0.062948301 0.055744376
[20,] 0.0088632966 0.027556094 0.110028401
[21,] -0.0446606408 -0.004368533 -0.074638056
[22,] 0.1327277344 -0.008768517 0.071044093
[23,] -0.1043119997 0.122748084 -0.211538630
[24,] 0.0494008682 -0.100477430 0.252336919
[25,] -0.0841578649 0.147783244 0.069943886
[26,] -0.1495845678 0.193943936 -0.002297714
[27,] -0.1380811980 0.231129305 0.142065139
[28,] 0.2280079960 -0.128482766 -0.198935497
[29,] -0.0073803328 0.018859370 0.030105425
[30,] 0.0024744451 -0.011700367 -0.008517248
[31,] -0.1820884872 -0.041138300 -0.145440493
[32,] 0.1187277207 0.097328208 0.082002927
[33,] -0.0150636249 -0.027613043 0.000546060
[ reached getOption("max.print") -- omitted 17 rows ]Once the training has been performed, the predict function can be use to predict the targets of new instances.
> x1 <- AR.data$come[1:40]
> x2 <- AR.data$five[1:40]
> new_dbcsp <- new('dbcsp',x1,x2,training=TRUE)
> t1 <- AR.data$come[41:45]
> t2 <- AR.data$five[41:45]
> test_data <- c(t1,t2)
> predictions <- predict(new_dbcsp, test_data)
Predictions:
[1] x1 x1 x1 x1 x1 x2 x2 x2 x1 x2
Levels: x1 x2And if true_labels are indicated, the obtained accuracy is also printed.
> true_labels <- c(rep('x1',length(t1)),rep('x2',length(t2)))
> predictions <- predict(new_dbcsp, test_data,true_labels)
Predictions:
[1] x1 x1 x1 x1 x1 x2 x2 x2 x1 x2
Levels: x1 x2
Predicted labels vs. Real labels
real_label
x1 x2
x1 5 1
x2 0 4
Obtained accuracy: 0.9 To help us deciding which is the best dimension to use when performing the CSP algorithm, the selectQ function can be used. The data is splitted in train and test, randomly selecting the percentage indicated by train_size for training and saving the rest of the instances for testesting. The dimensions to try are indicated by the parameter Q.
> bestQ <- selectQ(new_dbcsp)
Q acc
1 1 0.75
2 2 0.85
3 3 0.85
4 5 0.80
5 10 0.80
6 15 0.75
> print(bestQ)
Q acc
1 1 0.75
2 2 0.85
3 3 0.85
4 5 0.80
5 10 0.80
6 15 0.75By default train_size = 0.75 and Q = c(1,2,3,5,10,15), but these parameters can take othe values.
> bestQ <- selectQ(new_dbcsp,Q=c(10,15,20),train_size=0.8)
Q acc
1 10 0.8125
2 15 0.7500
3 20 0.6875
> print(bestQ)
Q acc
1 10 0.8125
2 15 0.7500
3 20 0.6875Instead of splitting data in train and test with the train_size percentage, a cross validation can be performed setting CV=TRUE and indicating the number of folds, by default folds=10 and CV=FALSE.
> bestQ <- selectQ(new_dbcsp,CV=TRUE,folds=10)
Q acc sd
1 1 0.7250 0.15365907
2 2 0.8750 0.10206207
3 3 0.9000 0.11486707
4 5 0.8375 0.14493773
5 10 0.7750 0.09860133
6 15 0.7000 0.10540926
> print(bestQ)
Q acc sd
1 1 0.7250 0.15365907
2 2 0.8750 0.10206207
3 3 0.9000 0.11486707
4 5 0.8375 0.14493773
5 10 0.7750 0.09860133
6 15 0.7000 0.10540926Both in train and selectQ functions, a seed value can be indicated as parameter in order to replicate the results. This seed value can also be specified when creating the dbcsp object.
After obtaining the bestQ values, the training and prediction process can be repeated, this time selecting the just the bestQ number of vectors when creating the classifier using the selected_q parameter of the train function.
> sel_q <- bestQ$Q[bestQ$acc == max(bestQ$acc)]
> dbcsp_bestQ <- train(new_dbcsp, selected_q=sel_q)
40 instances for x1 class and 40 instances for x2 class.
Applying DB-CSP with EUCL distance and 15 projections.
3 projections are used when training the LDA classifier.
Fold 1 - 72 training instances, 8 test instances - Acc: 0.875
Fold 2 - 72 training instances, 8 test instances - Acc: 0.75
Fold 3 - 72 training instances, 8 test instances - Acc: 1
Fold 4 - 72 training instances, 8 test instances - Acc: 0.875
Fold 5 - 72 training instances, 8 test instances - Acc: 1
Fold 6 - 72 training instances, 8 test instances - Acc: 1
Fold 7 - 72 training instances, 8 test instances - Acc: 0.625
Fold 8 - 72 training instances, 8 test instances - Acc: 0.875
Fold 9 - 72 training instances, 8 test instances - Acc: 0.875
Fold 10 - 72 training instances, 8 test instances - Acc: 1
Final accuracy: 0.8875
> predictions_bestQ <- predict(dbcsp_bestQ, test_data)
3 projections have been used to train the LDA classifier.
Predictions:
[1] x1 x1 x1 x1 x1 x2 x2 x2 x2 x2
Levels: x1 x2
> predictions_bestQ <- predict(dbcsp_bestQ, test_data, true_targets = true_labels)
3 projections have been used to train the LDA classifier.
Predictions:
[1] x1 x1 x1 x1 x1 x2 x2 x2 x2 x2
Levels: x1 x2
Predicted labels vs. Real labels
real_label
x1 x2
x1 5 0
x2 0 5
Obtained accuracy: 1 Using the plot command, a selected instance is plotted before and/or after the projection.
x1 <- AR.data$come
x2 <- AR.data$five
mydbcsp <- new('dbcsp', X1=x1, X2=x2)
plot(mydbcsp) By default, the first instance of the first class is plotted, before and after the projection. Class and instance index can be changed, and it can be decide whether to show the signals only before or after the projection.
plot(mydbcsp,class=2,index=30,before=FALSE)
With the vectors parameter it can be decided which dimensions to show, by default every dimension used when performing the CSP are shown. For example, if vectors=1:5 the first 5 dimensions (with their corresponding pairs) are plotted. Set legend=TRUE to show the legend.
plot(mydbcsp,class=2,index=30,before=FALSE,vectors = 1:5, legend=TRUE)
If pairs=FALSE, only the indicated vectors will be plotted. Otherwise, their pairs are also shown. By default, pairs=TRUE. The first q vectors have a line type and the last q vectors a different one. Each pair of vectors has a color, even if pairs=FALSE when two indicated vectors form a pair they are plotted with the same color.
plot(mydbcsp,class=2,index=30,before=FALSE,vectors = c(1,16,24), pairs=FALSE,legend=TRUE)
In order to better understand what the features used for classification look like, there is a function to show them with boxplots.
X1 <- AR.data$hello
X2 <- AR.data$ignore
mydbcsp <- new('dbcsp',X1,X2)
boxplot(mydbcsp)
The function has the option of selecting the indices of the vectors you want to see, if you want to see them in pairs and if the pairs should be ordered (each one next to its pair). By default: index=1, pairs=TRUE and ordered_pairs=TRUE.
boxplot(mydbcsp, vectors=c(2,4,8))
boxplot(mydbcsp, vectors=c(2,4,8), pairs=FALSE)
boxplot(mydbcsp, vectors=c(2,4,8), ordered_pairs=FALSE)
Since the logarithms of the variances are used as features for the classification after performing the CSP, these are displayed by default, because they provide better visual information than the variances. However, using show_log=FALSE the values of the variances are plotted.
boxplot(mydbcsp, vectors=c(2,4,8), show_log=FALSE)