ISYE6501x - WEEK 1 HW1

uestion 2.1 Describe a situation or problem from your job, everyday life, current events, etc., for which a classification model would be appropriate. List some (up to 5) predictors that you might use.

For a bank, determine whether a customer will reorder a category of products or not. The predictors used are: 1. average cart size 2. average money spent per cart 3. the time of the week customer is shopping 4. the time of the day customer is shopping 5. the frequency customer bought this category

Question 2.2 1. Using the support vector machine function ksvm contained in the R package kernlab, find a good classifier for this data. Show the equation of your classifier, and how well it classifies the data points in the full data set. (Don’t worry about test/validation data yet; we’ll cover that topic soon.)

library(class)
Data = read.csv("data 2.2/credit_card_data-headers.txt",sep = "\t")
Data

model <- ksvm(as.matrix(Data[,1:10]), as.factor(Data[,11]), type="C-svc",C=100,scaled=TRUE)
pred <- predict(model, Data[,1:10])
model_accuracy <- sum(pred == Data[,11]) /nrow(Data)
model_accuracy

[1] 0.9541284

#calculate a1...am
a <-colSums(model@xmatrix[[1]] * model@coef[[1]])
#calculate a0
a0 <- -model@b
a0

[1] 0.7387083

pred <- predict(model, Data[,1:10])
sum(pred == Data[,11]) /nrow(Data)

[1] 0.9541284

Below are the coefficients of all the dependent variables #A1 A2 A3 A8 A9 A10 A11 A12 #-18.932467 -38.000465 -8.715265 56.493891 49.912693 -23.741485 14.088852 -23.803404 #A14 A15 #-58.430619 50.928425

The equation will look like: -19A1 - 38A2 - 9A3 + 56A8 +50A9 - 24A10 + 14A12 - 58A14 + 51A15 + 0.73 = y

# Create a funciton to test out different  λ (C)
accuracy_svm_lamda = function(X){
  model <- ksvm(as.matrix(Data[,1:10]), as.factor(Data[,11]), type="C-svc",C=X,scaled=TRUE)
  pred <- predict(model, Data[,1:10])
  model_accuracy <- sum(pred == Data[,11]) /nrow(Data)
  return(model_accuracy)
}
svm_accuracy_result = rep(0,100)
for (x in 1:100){
  svm_accuracy_result[x] <- accuracy_svm_lamda(x)
}
max(svm_accuracy_result)

[1] 0.9587156

which.max(svm_accuracy_result)

[1] 93

After trying out C=0…100, C= 99 gives the best accuracy of 95.9%

2. You are welcome, but not required, to try other (nonlinear) kernels as well; we’re not covering them in this course, but they can sometimes be useful and might provide better predictions than vanilladot.

# Try a new kernel
accuracy_svm_lamda = function(X){
  model <- ksvm(as.matrix(Data[,1:10]), as.factor(Data[,11]), type="C-svc",C=X,scaled=TRUE, kernel = "polydot")
  pred <- predict(model, Data[,1:10])
  model_accuracy <- sum(pred == Data[,11]) /nrow(Data)
  return(model_accuracy)
}
svm_accuracy_result = rep(0,100)
for (x in 1:100){
  svm_accuracy_result[x] <- accuracy_svm_lamda(x)
}

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cv

[[1]]
    y        yhat
1   1 0.697980502
3   1 0.384830265
4   1 0.789218552
5   1 0.387423756
6   1 0.505539061
7   1 0.867918565
8   1 0.617344789
9   1 0.227045930
10  1 0.434463027
14  1 0.045110556
16  1 0.947177531
18  1 0.886946404
19  1 0.404482349
20  1 0.892480077
21  1 0.903992813
23  1 0.857142823
25  1 0.729284725
26  1 0.752130723
28  1 0.951911619
29  1 0.831395832
32  1 0.986430103
35  1 0.830610557
36  1 0.915387788
37  1 0.910883564
38  1 0.748507067
40  1 0.916299242
43  1 0.674048898
44  1 0.868289864
45  1 0.940548012
47  1 0.888994249
48  1 0.855599120
49  1 0.024584336
50  1 0.081600109
52  1 0.428854264
54  1 0.399427520
56  1 0.537891659
59  1 0.115089712
61  1 0.765214814
67  1 0.860616370
68  1 0.802933679
70  1 0.478375075
71  0 0.528523191
72  0 0.543660632
73  0 0.565595037
75  0 0.799794460
77  0 0.365023061
78  0 0.715178722
79  0 0.438466056
80  0 0.680119532
81  0 0.443446285
86  0 0.530124805
87  0 0.284338395
88  0 0.510355077
89  0 0.379515577
90  0 0.579246994
91  0 0.471499224
92  0 0.357967794
93  0 0.343581324
94  0 0.523660442
95  0 0.660068350
96  0 0.487320200
97  0 0.473797445
99  0 0.892425054
101 0 0.962726850
102 0 0.388257856
104 0 0.614478866
105 0 0.657399673
106 0 0.886839471
108 0 0.551284984
109 0 0.701012152
110 0 0.788933416
112 0 0.922690022
113 1 0.970880942
114 1 0.831320464
115 1 0.715928769
119 1 0.850472904
121 1 0.851424578
122 1 0.945232394
123 1 0.838505339
124 1 0.821874799
125 1 0.432414222
126 1 0.763353798
127 1 0.688306157
128 1 0.971175637
129 1 0.929475716
130 1 0.895122946
131 1 0.390239163
132 1 0.761362585
133 1 0.909596712
135 1 0.913301872
137 1 0.859144245
138 1 0.901275186
139 1 0.771128371
140 1 0.914699207
141 1 0.876679701
143 1 0.927210576
146 1 0.874695612
147 1 0.911140686
149 1 0.873994189
150 1 0.831338461
151 1 0.795766207
154 1 0.743193215
155 1 0.773531408
157 1 0.746398637
158 1 0.695315097
159 1 0.474662273
160 1 0.753511693
161 1 0.595838791
162 1 0.522158839
163 1 0.444520792
164 1 0.497857781
165 1 0.060961531
166 1 0.419200551
167 1 0.690587175
168 1 0.673595131
170 1 0.395975632
171 1 0.428040503
172 1 0.530021879
173 1 0.560991159
174 1 0.865165284
175 1 0.933298235
177 1 0.769772954
178 1 0.772432708
181 1 0.953565112
185 1 0.874071999
186 1 0.565902483
187 1 0.339219684
189 1 0.852280024
190 1 0.814341107
191 1 0.830570146
193 1 0.962936611
195 1 0.904733602
196 1 0.763634455
198 1 0.820244242
199 1 0.731468148
200 1 0.918406649
202 1 0.940708846
204 1 0.895523322
206 1 0.936511216
207 1 0.925447691
210 1 0.940587130
211 1 0.835388219
212 1 0.890592176
213 1 0.743921002
214 1 0.808572588
215 1 0.918741829
216 1 0.429431278
220 1 0.318028077
221 1 0.024520817
222 1 0.668336951
223 1 0.401826381
225 1 0.625434394
226 1 0.838903127
228 1 0.952399820
229 1 0.858226249
230 1 0.399629929
231 1 0.791115129
233 1 0.915200912
234 1 0.426660587
236 1 0.534409675
240 1 0.844760692
241 1 0.830694545
242 1 0.943133503
246 0 0.031354571
249 0 0.092393015
250 0 0.026332962
251 0 0.095728637
252 0 0.078135670
254 0 0.051963590
255 0 0.059925649
256 0 0.111004088
258 0 0.024729011
259 1 0.456607931
260 1 0.097487377
261 0 0.086430973
264 0 0.105761800
265 0 0.105001857
266 0 0.049638018
267 0 0.076902026
268 0 0.229150538
269 0 0.098152375
271 0 0.101419213
272 0 0.173522000
273 0 0.177862850
277 0 0.035295024
278 0 0.043447363
279 0 0.265563046
280 0 0.090399684
281 0 0.142911945
284 0 0.323327196
285 0 0.325211903
286 0 0.079718554
288 0 0.318567632
289 0 0.045095781
290 0 0.038524154
291 0 0.036110432
292 0 0.124038802
294 0 0.120460655
295 0 0.068146057
296 0 0.051261579
297 0 0.030070989
299 0 0.066383573
301 0 0.089927850
302 0 0.212241360
305 1 0.854830166
307 1 0.041963609
308 1 0.082565426
309 1 0.025109980
312 0 0.041504021
313 0 0.028236279
314 0 0.051413936
315 0 0.119213464
316 0 0.010661388
317 0 0.051362748
318 0 0.045360352
319 0 0.015069685
320 0 0.052905625
322 0 0.012571322
324 0 0.033405996
325 0 0.072475624
326 0 0.087058226
327 0 0.164302981
328 0 0.045058454
330 0 0.158154196
331 0 0.067353058
332 0 0.879634918
333 0 0.095006963
337 0 0.084296983
338 0 0.102014475
339 0 0.072280651
340 0 0.064148522
342 0 0.044239197
343 0 0.037072161
344 0 0.072749028
345 0 0.043627188
346 0 0.120327530
348 0 0.047855007
350 0 0.092557559
352 0 0.099951140
353 0 0.045891159
354 0 0.095312943
357 0 0.084924281
358 0 0.048719601
359 0 0.066681161
360 0 0.027154408
361 0 0.141366304
363 0 0.062362222
366 0 0.027505652
367 0 0.101207466
368 0 0.052763367
369 0 0.041027303
370 0 0.139496545
371 0 0.077084402
373 0 0.074299765
374 0 0.041740935
375 0 0.145891568
377 0 0.079856498
378 0 0.008855860
379 0 0.063304517
381 0 0.125023999
382 0 0.035654829
388 0 0.116860944
389 0 0.372955347
390 0 0.078621969
391 0 0.090771080
392 0 0.174649025
393 0 0.091975240
394 0 0.031009437
395 0 0.043319505
397 0 0.085587304
398 0 0.099812898
399 0 0.056308732
400 0 0.102460482
401 0 0.001035882
403 0 0.195184760
404 0 0.067979384
405 0 0.136676815
406 0 0.062676042
407 0 0.070488666
408 0 0.000000000
410 0 0.076651262
413 0 0.128811354
414 0 0.048209963
415 0 0.081448932
416 0 0.161299396
417 0 0.086985571
418 0 0.079566404
419 0 0.023084080
420 0 0.200691490
421 0 0.044831262
422 0 0.310187187
424 0 0.044002926
426 0 0.034563477
427 0 0.169335910
428 0 0.070091346
429 0 0.052624989
430 0 0.096673657
433 0 0.089323876
435 0 0.030096361
436 0 0.024375983
437 0 0.057777059
438 0 0.033065859
439 0 0.086538882
440 0 0.049850984
441 0 0.365396454
442 0 0.097605751
443 0 0.079509545
447 0 0.031494423
448 0 0.087291610
450 0 0.075543894
454 0 0.037567130
456 0 0.079958201
457 0 0.119633911
458 0 0.052126633
459 0 0.540325239
460 0 0.071867759
462 0 0.457893924
463 0 0.048779830
466 1 0.846792719
467 1 0.760286908
468 1 0.963775316
469 1 0.573416923
472 1 0.263336676
473 1 0.752689274
474 1 0.755700376
475 1 0.763966640
477 1 0.672276644
478 1 0.852366520
479 1 0.595013512
480 1 0.917521136
483 1 0.914333186
484 1 0.622445940
487 1 0.465508354
491 1 0.808936510
492 1 0.818575749
493 1 0.863936416
494 1 0.765739880
496 0 0.977388209
498 0 0.523198317
499 0 0.284105957
501 0 0.825588558
502 0 0.520397988
503 0 0.444928822
505 0 0.433905329
506 0 0.248877248
509 0 0.521036803
510 0 0.569741949
511 0 0.479585403
512 0 0.411698643
513 0 0.582647839
515 0 0.573131916
518 0 0.462080744
519 0 0.894610029
521 1 0.877172287
522 1 0.753511587
523 1 0.874657875
525 1 0.904351650
527 1 0.887491617
529 1 0.814433117
531 1 0.276990549
534 1 0.364794108
535 1 0.369813840
540 1 0.438922774
542 1 0.866772487
543 1 0.779093342
544 1 0.787982333
545 1 0.602265701
546 1 0.891839855
548 1 0.861714056
553 1 0.893277255
554 1 0.129213272
556 1 0.550372186
557 1 0.598422420
558 1 0.454714867
560 1 0.955947934
562 1 0.792747315
564 1 0.782164979
566 1 0.448855671
568 1 0.778663130
569 1 0.896906344
570 1 0.914762024
571 1 0.811988180
572 0 0.052973567
573 0 0.162889969
575 0 0.032217231
576 1 0.109628527
579 0 0.144665640
580 0 0.231360085
583 0 0.040597789
585 0 0.147526700
588 0 0.444533110
589 0 0.138560920
590 1 0.022778908
591 0 0.189346469
593 0 0.079656707
595 0 0.047642030
597 0 0.000000000
599 0 0.031927069
600 0 0.049127283
601 0 0.041199056
603 0 0.081321506
604 0 0.051659571
605 0 0.026235385
606 0 0.121603465
607 0 0.081311670
608 0 0.103576571
610 0 0.151710604
611 0 0.061973997
613 0 0.045864802
616 0 0.115063106
617 0 0.244577043
618 0 0.007988405
620 0 0.058421620
621 0 0.036564527
622 0 0.174833995
624 0 0.039547622
626 0 0.056157150
627 0 0.045107475
628 0 0.000000000
629 0 0.040695312
630 0 0.054186166
632 0 0.017907929
633 0 0.103384972
635 0 0.094120971
636 0 0.077335888
638 0 0.036208508
640 0 0.032520361
643 0 0.084874180
644 0 0.040257985
645 0 0.075178306
646 0 0.087435119
647 0 0.046311117
649 0 0.169622760
650 0 0.029119058
653 0 0.078771765
654 0 0.128520058

[[2]]
[1] 0.2378725 0.1149316

cv

[[1]]
    y        yhat
1   1 0.697980502
3   1 0.384830265
4   1 0.789218552
5   1 0.387423756
6   1 0.505539061
7   1 0.867918565
8   1 0.617344789
9   1 0.227045930
10  1 0.434463027
14  1 0.045110556
16  1 0.947177531
18  1 0.886946404
19  1 0.404482349
20  1 0.892480077
21  1 0.903992813
23  1 0.857142823
25  1 0.729284725
26  1 0.752130723
28  1 0.951911619
29  1 0.831395832
32  1 0.986430103
35  1 0.830610557
36  1 0.915387788
37  1 0.910883564
38  1 0.748507067
40  1 0.916299242
43  1 0.674048898
44  1 0.868289864
45  1 0.940548012
47  1 0.888994249
48  1 0.855599120
49  1 0.024584336
50  1 0.081600109
52  1 0.428854264
54  1 0.399427520
56  1 0.537891659
59  1 0.115089712
61  1 0.765214814
67  1 0.860616370
68  1 0.802933679
70  1 0.478375075
71  0 0.528523191
72  0 0.543660632
73  0 0.565595037
75  0 0.799794460
77  0 0.365023061
78  0 0.715178722
79  0 0.438466056
80  0 0.680119532
81  0 0.443446285
86  0 0.530124805
87  0 0.284338395
88  0 0.510355077
89  0 0.379515577
90  0 0.579246994
91  0 0.471499224
92  0 0.357967794
93  0 0.343581324
94  0 0.523660442
95  0 0.660068350
96  0 0.487320200
97  0 0.473797445
99  0 0.892425054
101 0 0.962726850
102 0 0.388257856
104 0 0.614478866
105 0 0.657399673
106 0 0.886839471
108 0 0.551284984
109 0 0.701012152
110 0 0.788933416
112 0 0.922690022
113 1 0.970880942
114 1 0.831320464
115 1 0.715928769
119 1 0.850472904
121 1 0.851424578
122 1 0.945232394
123 1 0.838505339
124 1 0.821874799
125 1 0.432414222
126 1 0.763353798
127 1 0.688306157
128 1 0.971175637
129 1 0.929475716
130 1 0.895122946
131 1 0.390239163
132 1 0.761362585
133 1 0.909596712
135 1 0.913301872
137 1 0.859144245
138 1 0.901275186
139 1 0.771128371
140 1 0.914699207
141 1 0.876679701
143 1 0.927210576
146 1 0.874695612
147 1 0.911140686
149 1 0.873994189
150 1 0.831338461
151 1 0.795766207
154 1 0.743193215
155 1 0.773531408
157 1 0.746398637
158 1 0.695315097
159 1 0.474662273
160 1 0.753511693
161 1 0.595838791
162 1 0.522158839
163 1 0.444520792
164 1 0.497857781
165 1 0.060961531
166 1 0.419200551
167 1 0.690587175
168 1 0.673595131
170 1 0.395975632
171 1 0.428040503
172 1 0.530021879
173 1 0.560991159
174 1 0.865165284
175 1 0.933298235
177 1 0.769772954
178 1 0.772432708
181 1 0.953565112
185 1 0.874071999
186 1 0.565902483
187 1 0.339219684
189 1 0.852280024
190 1 0.814341107
191 1 0.830570146
193 1 0.962936611
195 1 0.904733602
196 1 0.763634455
198 1 0.820244242
199 1 0.731468148
200 1 0.918406649
202 1 0.940708846
204 1 0.895523322
206 1 0.936511216
207 1 0.925447691
210 1 0.940587130
211 1 0.835388219
212 1 0.890592176
213 1 0.743921002
214 1 0.808572588
215 1 0.918741829
216 1 0.429431278
220 1 0.318028077
221 1 0.024520817
222 1 0.668336951
223 1 0.401826381
225 1 0.625434394
226 1 0.838903127
228 1 0.952399820
229 1 0.858226249
230 1 0.399629929
231 1 0.791115129
233 1 0.915200912
234 1 0.426660587
236 1 0.534409675
240 1 0.844760692
241 1 0.830694545
242 1 0.943133503
246 0 0.031354571
249 0 0.092393015
250 0 0.026332962
251 0 0.095728637
252 0 0.078135670
254 0 0.051963590
255 0 0.059925649
256 0 0.111004088
258 0 0.024729011
259 1 0.456607931
260 1 0.097487377
261 0 0.086430973
264 0 0.105761800
265 0 0.105001857
266 0 0.049638018
267 0 0.076902026
268 0 0.229150538
269 0 0.098152375
271 0 0.101419213
272 0 0.173522000
273 0 0.177862850
277 0 0.035295024
278 0 0.043447363
279 0 0.265563046
280 0 0.090399684
281 0 0.142911945
284 0 0.323327196
285 0 0.325211903
286 0 0.079718554
288 0 0.318567632
289 0 0.045095781
290 0 0.038524154
291 0 0.036110432
292 0 0.124038802
294 0 0.120460655
295 0 0.068146057
296 0 0.051261579
297 0 0.030070989
299 0 0.066383573
301 0 0.089927850
302 0 0.212241360
305 1 0.854830166
307 1 0.041963609
308 1 0.082565426
309 1 0.025109980
312 0 0.041504021
313 0 0.028236279
314 0 0.051413936
315 0 0.119213464
316 0 0.010661388
317 0 0.051362748
318 0 0.045360352
319 0 0.015069685
320 0 0.052905625
322 0 0.012571322
324 0 0.033405996
325 0 0.072475624
326 0 0.087058226
327 0 0.164302981
328 0 0.045058454
330 0 0.158154196
331 0 0.067353058
332 0 0.879634918
333 0 0.095006963
337 0 0.084296983
338 0 0.102014475
339 0 0.072280651
340 0 0.064148522
342 0 0.044239197
343 0 0.037072161
344 0 0.072749028
345 0 0.043627188
346 0 0.120327530
348 0 0.047855007
350 0 0.092557559
352 0 0.099951140
353 0 0.045891159
354 0 0.095312943
357 0 0.084924281
358 0 0.048719601
359 0 0.066681161
360 0 0.027154408
361 0 0.141366304
363 0 0.062362222
366 0 0.027505652
367 0 0.101207466
368 0 0.052763367
369 0 0.041027303
370 0 0.139496545
371 0 0.077084402
373 0 0.074299765
374 0 0.041740935
375 0 0.145891568
377 0 0.079856498
378 0 0.008855860
379 0 0.063304517
381 0 0.125023999
382 0 0.035654829
388 0 0.116860944
389 0 0.372955347
390 0 0.078621969
391 0 0.090771080
392 0 0.174649025
393 0 0.091975240
394 0 0.031009437
395 0 0.043319505
397 0 0.085587304
398 0 0.099812898
399 0 0.056308732
400 0 0.102460482
401 0 0.001035882
403 0 0.195184760
404 0 0.067979384
405 0 0.136676815
406 0 0.062676042
407 0 0.070488666
408 0 0.000000000
410 0 0.076651262
413 0 0.128811354
414 0 0.048209963
415 0 0.081448932
416 0 0.161299396
417 0 0.086985571
418 0 0.079566404
419 0 0.023084080
420 0 0.200691490
421 0 0.044831262
422 0 0.310187187
424 0 0.044002926
426 0 0.034563477
427 0 0.169335910
428 0 0.070091346
429 0 0.052624989
430 0 0.096673657
433 0 0.089323876
435 0 0.030096361
436 0 0.024375983
437 0 0.057777059
438 0 0.033065859
439 0 0.086538882
440 0 0.049850984
441 0 0.365396454
442 0 0.097605751
443 0 0.079509545
447 0 0.031494423
448 0 0.087291610
450 0 0.075543894
454 0 0.037567130
456 0 0.079958201
457 0 0.119633911
458 0 0.052126633
459 0 0.540325239
460 0 0.071867759
462 0 0.457893924
463 0 0.048779830
466 1 0.846792719
467 1 0.760286908
468 1 0.963775316
469 1 0.573416923
472 1 0.263336676
473 1 0.752689274
474 1 0.755700376
475 1 0.763966640
477 1 0.672276644
478 1 0.852366520
479 1 0.595013512
480 1 0.917521136
483 1 0.914333186
484 1 0.622445940
487 1 0.465508354
491 1 0.808936510
492 1 0.818575749
493 1 0.863936416
494 1 0.765739880
496 0 0.977388209
498 0 0.523198317
499 0 0.284105957
501 0 0.825588558
502 0 0.520397988
503 0 0.444928822
505 0 0.433905329
506 0 0.248877248
509 0 0.521036803
510 0 0.569741949
511 0 0.479585403
512 0 0.411698643
513 0 0.582647839
515 0 0.573131916
518 0 0.462080744
519 0 0.894610029
521 1 0.877172287
522 1 0.753511587
523 1 0.874657875
525 1 0.904351650
527 1 0.887491617
529 1 0.814433117
531 1 0.276990549
534 1 0.364794108
535 1 0.369813840
540 1 0.438922774
542 1 0.866772487
543 1 0.779093342
544 1 0.787982333
545 1 0.602265701
546 1 0.891839855
548 1 0.861714056
553 1 0.893277255
554 1 0.129213272
556 1 0.550372186
557 1 0.598422420
558 1 0.454714867
560 1 0.955947934
562 1 0.792747315
564 1 0.782164979
566 1 0.448855671
568 1 0.778663130
569 1 0.896906344
570 1 0.914762024
571 1 0.811988180
572 0 0.052973567
573 0 0.162889969
575 0 0.032217231
576 1 0.109628527
579 0 0.144665640
580 0 0.231360085
583 0 0.040597789
585 0 0.147526700
588 0 0.444533110
589 0 0.138560920
590 1 0.022778908
591 0 0.189346469
593 0 0.079656707
595 0 0.047642030
597 0 0.000000000
599 0 0.031927069
600 0 0.049127283
601 0 0.041199056
603 0 0.081321506
604 0 0.051659571
605 0 0.026235385
606 0 0.121603465
607 0 0.081311670
608 0 0.103576571
610 0 0.151710604
611 0 0.061973997
613 0 0.045864802
616 0 0.115063106
617 0 0.244577043
618 0 0.007988405
620 0 0.058421620
621 0 0.036564527
622 0 0.174833995
624 0 0.039547622
626 0 0.056157150
627 0 0.045107475
628 0 0.000000000
629 0 0.040695312
630 0 0.054186166
632 0 0.017907929
633 0 0.103384972
635 0 0.094120971
636 0 0.077335888
638 0 0.036208508
640 0 0.032520361
643 0 0.084874180
644 0 0.040257985
645 0 0.075178306
646 0 0.087435119
647 0 0.046311117
649 0 0.169622760
650 0 0.029119058
653 0 0.078771765
654 0 0.128520058

[[2]]
[1] 0.2378725 0.1149316

max(svm_accuracy_result)

[1] 0.8639144

which.max(svm_accuracy_result)

[1] 1

Using a differet kernel “polydot”, this took a while to run. After trying out C=0…100, C= 1 gives the best accuracy of 86% which is much lower than the best result I got for linear kernel.

3. Using the k-nearest-neighbors classification function kknn contained in the R kknn package, suggest a good value of k, and show how well it classifies that data points in the full data set. Don’t forget to scale the data (scale=TRUE in kknn).

library(kknn)
# parameter for the function is k = number of nearest neighbors
accuracy_knn = function(X){
  predicted <- rep(0,(nrow(Data))) 
  for (i in 1:nrow(Data)){
    model=kknn(R1~.,Data[-i,],Data[i,],k=X, scale = TRUE) 
    predicted[i] <- as.integer(fitted(model)) 
  }
  
  acc = sum(predicted == Data[,11]) / nrow(Data)
  return(acc)
}
accuracy = rep(0,100)
for (x in 1:100){
  accuracy[x] = accuracy_knn(x)
}
test_result = cv
test_result <- cv
cv

[[1]]
    y        yhat
1   1 0.697980502
3   1 0.384830265
4   1 0.789218552
5   1 0.387423756
6   1 0.505539061
7   1 0.867918565
8   1 0.617344789
9   1 0.227045930
10  1 0.434463027
14  1 0.045110556
16  1 0.947177531
18  1 0.886946404
19  1 0.404482349
20  1 0.892480077
21  1 0.903992813
23  1 0.857142823
25  1 0.729284725
26  1 0.752130723
28  1 0.951911619
29  1 0.831395832
32  1 0.986430103
35  1 0.830610557
36  1 0.915387788
37  1 0.910883564
38  1 0.748507067
40  1 0.916299242
43  1 0.674048898
44  1 0.868289864
45  1 0.940548012
47  1 0.888994249
48  1 0.855599120
49  1 0.024584336
50  1 0.081600109
52  1 0.428854264
54  1 0.399427520
56  1 0.537891659
59  1 0.115089712
61  1 0.765214814
67  1 0.860616370
68  1 0.802933679
70  1 0.478375075
71  0 0.528523191
72  0 0.543660632
73  0 0.565595037
75  0 0.799794460
77  0 0.365023061
78  0 0.715178722
79  0 0.438466056
80  0 0.680119532
81  0 0.443446285
86  0 0.530124805
87  0 0.284338395
88  0 0.510355077
89  0 0.379515577
90  0 0.579246994
91  0 0.471499224
92  0 0.357967794
93  0 0.343581324
94  0 0.523660442
95  0 0.660068350
96  0 0.487320200
97  0 0.473797445
99  0 0.892425054
101 0 0.962726850
102 0 0.388257856
104 0 0.614478866
105 0 0.657399673
106 0 0.886839471
108 0 0.551284984
109 0 0.701012152
110 0 0.788933416
112 0 0.922690022
113 1 0.970880942
114 1 0.831320464
115 1 0.715928769
119 1 0.850472904
121 1 0.851424578
122 1 0.945232394
123 1 0.838505339
124 1 0.821874799
125 1 0.432414222
126 1 0.763353798
127 1 0.688306157
128 1 0.971175637
129 1 0.929475716
130 1 0.895122946
131 1 0.390239163
132 1 0.761362585
133 1 0.909596712
135 1 0.913301872
137 1 0.859144245
138 1 0.901275186
139 1 0.771128371
140 1 0.914699207
141 1 0.876679701
143 1 0.927210576
146 1 0.874695612
147 1 0.911140686
149 1 0.873994189
150 1 0.831338461
151 1 0.795766207
154 1 0.743193215
155 1 0.773531408
157 1 0.746398637
158 1 0.695315097
159 1 0.474662273
160 1 0.753511693
161 1 0.595838791
162 1 0.522158839
163 1 0.444520792
164 1 0.497857781
165 1 0.060961531
166 1 0.419200551
167 1 0.690587175
168 1 0.673595131
170 1 0.395975632
171 1 0.428040503
172 1 0.530021879
173 1 0.560991159
174 1 0.865165284
175 1 0.933298235
177 1 0.769772954
178 1 0.772432708
181 1 0.953565112
185 1 0.874071999
186 1 0.565902483
187 1 0.339219684
189 1 0.852280024
190 1 0.814341107
191 1 0.830570146
193 1 0.962936611
195 1 0.904733602
196 1 0.763634455
198 1 0.820244242
199 1 0.731468148
200 1 0.918406649
202 1 0.940708846
204 1 0.895523322
206 1 0.936511216
207 1 0.925447691
210 1 0.940587130
211 1 0.835388219
212 1 0.890592176
213 1 0.743921002
214 1 0.808572588
215 1 0.918741829
216 1 0.429431278
220 1 0.318028077
221 1 0.024520817
222 1 0.668336951
223 1 0.401826381
225 1 0.625434394
226 1 0.838903127
228 1 0.952399820
229 1 0.858226249
230 1 0.399629929
231 1 0.791115129
233 1 0.915200912
234 1 0.426660587
236 1 0.534409675
240 1 0.844760692
241 1 0.830694545
242 1 0.943133503
246 0 0.031354571
249 0 0.092393015
250 0 0.026332962
251 0 0.095728637
252 0 0.078135670
254 0 0.051963590
255 0 0.059925649
256 0 0.111004088
258 0 0.024729011
259 1 0.456607931
260 1 0.097487377
261 0 0.086430973
264 0 0.105761800
265 0 0.105001857
266 0 0.049638018
267 0 0.076902026
268 0 0.229150538
269 0 0.098152375
271 0 0.101419213
272 0 0.173522000
273 0 0.177862850
277 0 0.035295024
278 0 0.043447363
279 0 0.265563046
280 0 0.090399684
281 0 0.142911945
284 0 0.323327196
285 0 0.325211903
286 0 0.079718554
288 0 0.318567632
289 0 0.045095781
290 0 0.038524154
291 0 0.036110432
292 0 0.124038802
294 0 0.120460655
295 0 0.068146057
296 0 0.051261579
297 0 0.030070989
299 0 0.066383573
301 0 0.089927850
302 0 0.212241360
305 1 0.854830166
307 1 0.041963609
308 1 0.082565426
309 1 0.025109980
312 0 0.041504021
313 0 0.028236279
314 0 0.051413936
315 0 0.119213464
316 0 0.010661388
317 0 0.051362748
318 0 0.045360352
319 0 0.015069685
320 0 0.052905625
322 0 0.012571322
324 0 0.033405996
325 0 0.072475624
326 0 0.087058226
327 0 0.164302981
328 0 0.045058454
330 0 0.158154196
331 0 0.067353058
332 0 0.879634918
333 0 0.095006963
337 0 0.084296983
338 0 0.102014475
339 0 0.072280651
340 0 0.064148522
342 0 0.044239197
343 0 0.037072161
344 0 0.072749028
345 0 0.043627188
346 0 0.120327530
348 0 0.047855007
350 0 0.092557559
352 0 0.099951140
353 0 0.045891159
354 0 0.095312943
357 0 0.084924281
358 0 0.048719601
359 0 0.066681161
360 0 0.027154408
361 0 0.141366304
363 0 0.062362222
366 0 0.027505652
367 0 0.101207466
368 0 0.052763367
369 0 0.041027303
370 0 0.139496545
371 0 0.077084402
373 0 0.074299765
374 0 0.041740935
375 0 0.145891568
377 0 0.079856498
378 0 0.008855860
379 0 0.063304517
381 0 0.125023999
382 0 0.035654829
388 0 0.116860944
389 0 0.372955347
390 0 0.078621969
391 0 0.090771080
392 0 0.174649025
393 0 0.091975240
394 0 0.031009437
395 0 0.043319505
397 0 0.085587304
398 0 0.099812898
399 0 0.056308732
400 0 0.102460482
401 0 0.001035882
403 0 0.195184760
404 0 0.067979384
405 0 0.136676815
406 0 0.062676042
407 0 0.070488666
408 0 0.000000000
410 0 0.076651262
413 0 0.128811354
414 0 0.048209963
415 0 0.081448932
416 0 0.161299396
417 0 0.086985571
418 0 0.079566404
419 0 0.023084080
420 0 0.200691490
421 0 0.044831262
422 0 0.310187187
424 0 0.044002926
426 0 0.034563477
427 0 0.169335910
428 0 0.070091346
429 0 0.052624989
430 0 0.096673657
433 0 0.089323876
435 0 0.030096361
436 0 0.024375983
437 0 0.057777059
438 0 0.033065859
439 0 0.086538882
440 0 0.049850984
441 0 0.365396454
442 0 0.097605751
443 0 0.079509545
447 0 0.031494423
448 0 0.087291610
450 0 0.075543894
454 0 0.037567130
456 0 0.079958201
457 0 0.119633911
458 0 0.052126633
459 0 0.540325239
460 0 0.071867759
462 0 0.457893924
463 0 0.048779830
466 1 0.846792719
467 1 0.760286908
468 1 0.963775316
469 1 0.573416923
472 1 0.263336676
473 1 0.752689274
474 1 0.755700376
475 1 0.763966640
477 1 0.672276644
478 1 0.852366520
479 1 0.595013512
480 1 0.917521136
483 1 0.914333186
484 1 0.622445940
487 1 0.465508354
491 1 0.808936510
492 1 0.818575749
493 1 0.863936416
494 1 0.765739880
496 0 0.977388209
498 0 0.523198317
499 0 0.284105957
501 0 0.825588558
502 0 0.520397988
503 0 0.444928822
505 0 0.433905329
506 0 0.248877248
509 0 0.521036803
510 0 0.569741949
511 0 0.479585403
512 0 0.411698643
513 0 0.582647839
515 0 0.573131916
518 0 0.462080744
519 0 0.894610029
521 1 0.877172287
522 1 0.753511587
523 1 0.874657875
525 1 0.904351650
527 1 0.887491617
529 1 0.814433117
531 1 0.276990549
534 1 0.364794108
535 1 0.369813840
540 1 0.438922774
542 1 0.866772487
543 1 0.779093342
544 1 0.787982333
545 1 0.602265701
546 1 0.891839855
548 1 0.861714056
553 1 0.893277255
554 1 0.129213272
556 1 0.550372186
557 1 0.598422420
558 1 0.454714867
560 1 0.955947934
562 1 0.792747315
564 1 0.782164979
566 1 0.448855671
568 1 0.778663130
569 1 0.896906344
570 1 0.914762024
571 1 0.811988180
572 0 0.052973567
573 0 0.162889969
575 0 0.032217231
576 1 0.109628527
579 0 0.144665640
580 0 0.231360085
583 0 0.040597789
585 0 0.147526700
588 0 0.444533110
589 0 0.138560920
590 1 0.022778908
591 0 0.189346469
593 0 0.079656707
595 0 0.047642030
597 0 0.000000000
599 0 0.031927069
600 0 0.049127283
601 0 0.041199056
603 0 0.081321506
604 0 0.051659571
605 0 0.026235385
606 0 0.121603465
607 0 0.081311670
608 0 0.103576571
610 0 0.151710604
611 0 0.061973997
613 0 0.045864802
616 0 0.115063106
617 0 0.244577043
618 0 0.007988405
620 0 0.058421620
621 0 0.036564527
622 0 0.174833995
624 0 0.039547622
626 0 0.056157150
627 0 0.045107475
628 0 0.000000000
629 0 0.040695312
630 0 0.054186166
632 0 0.017907929
633 0 0.103384972
635 0 0.094120971
636 0 0.077335888
638 0 0.036208508
640 0 0.032520361
643 0 0.084874180
644 0 0.040257985
645 0 0.075178306
646 0 0.087435119
647 0 0.046311117
649 0 0.169622760
650 0 0.029119058
653 0 0.078771765
654 0 0.128520058

[[2]]
[1] 0.2378725 0.1149316

cv

[[1]]
    y        yhat
1   1 0.697980502
3   1 0.384830265
4   1 0.789218552
5   1 0.387423756
6   1 0.505539061
7   1 0.867918565
8   1 0.617344789
9   1 0.227045930
10  1 0.434463027
14  1 0.045110556
16  1 0.947177531
18  1 0.886946404
19  1 0.404482349
20  1 0.892480077
21  1 0.903992813
23  1 0.857142823
25  1 0.729284725
26  1 0.752130723
28  1 0.951911619
29  1 0.831395832
32  1 0.986430103
35  1 0.830610557
36  1 0.915387788
37  1 0.910883564
38  1 0.748507067
40  1 0.916299242
43  1 0.674048898
44  1 0.868289864
45  1 0.940548012
47  1 0.888994249
48  1 0.855599120
49  1 0.024584336
50  1 0.081600109
52  1 0.428854264
54  1 0.399427520
56  1 0.537891659
59  1 0.115089712
61  1 0.765214814
67  1 0.860616370
68  1 0.802933679
70  1 0.478375075
71  0 0.528523191
72  0 0.543660632
73  0 0.565595037
75  0 0.799794460
77  0 0.365023061
78  0 0.715178722
79  0 0.438466056
80  0 0.680119532
81  0 0.443446285
86  0 0.530124805
87  0 0.284338395
88  0 0.510355077
89  0 0.379515577
90  0 0.579246994
91  0 0.471499224
92  0 0.357967794
93  0 0.343581324
94  0 0.523660442
95  0 0.660068350
96  0 0.487320200
97  0 0.473797445
99  0 0.892425054
101 0 0.962726850
102 0 0.388257856
104 0 0.614478866
105 0 0.657399673
106 0 0.886839471
108 0 0.551284984
109 0 0.701012152
110 0 0.788933416
112 0 0.922690022
113 1 0.970880942
114 1 0.831320464
115 1 0.715928769
119 1 0.850472904
121 1 0.851424578
122 1 0.945232394
123 1 0.838505339
124 1 0.821874799
125 1 0.432414222
126 1 0.763353798
127 1 0.688306157
128 1 0.971175637
129 1 0.929475716
130 1 0.895122946
131 1 0.390239163
132 1 0.761362585
133 1 0.909596712
135 1 0.913301872
137 1 0.859144245
138 1 0.901275186
139 1 0.771128371
140 1 0.914699207
141 1 0.876679701
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[[2]]
[1] 0.2378725 0.1149316

accuracy

  [1] 0.8149847 0.7859327 0.7675841 0.7415902 0.7171254 0.7003058 0.6850153
  [8] 0.6773700 0.6651376 0.6620795 0.6544343 0.6452599 0.6360856 0.6314985
 [15] 0.6238532 0.6192661 0.6039755 0.5963303 0.5886850 0.5840979 0.5779817
 [22] 0.5764526 0.5764526 0.5764526 0.5764526 0.5733945 0.5718654 0.5718654
 [29] 0.5703364 0.5657492 0.5626911 0.5626911 0.5626911 0.5611621 0.5596330
 [36] 0.5565749 0.5565749 0.5565749 0.5565749 0.5565749 0.5550459 0.5550459
 [43] 0.5550459 0.5550459 0.5550459 0.5535168 0.5535168 0.5535168 0.5519878
 [50] 0.5504587 0.5489297 0.5489297 0.5489297 0.5489297 0.5489297 0.5474006
 [57] 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006
 [64] 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006
 [71] 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006
 [78] 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006
 [85] 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006
 [92] 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006 0.5474006
 [99] 0.5474006 0.5474006

max(accuracy)

[1] 0.8149847

which.max(accuracy)

[1] 1

Question 3.1 Using the same data set (credit_card_data.txt or credit_card_data-headers.txt) as in Question 2.2, use the ksvm or kknn function to find a good classifier: (a) using cross-validation(do this for thek-nearest-neighbors model; SVM is optional); and (b) splitting the data into training,validation,and testdatasets (pickeither KNN or SVM; the other is optional).

set.seed(123)
 #random selection of 66% data as training + validation
 # 33% as test set
m <- nrow(Data)
test <- sample(1:m,size=round(m/3), replace=FALSE)
Data.train <- Data[-test,]
Data.test <- Data[test,]
#Train of kknn method via leave-one-out cv to find the optimal k
knn_result <-train.kknn(R1 ~ ., data = Data.train, kmax = 30, kernel = c("optimal","rectangular","gaussian"), scale = TRUE, kcv=5) 
#Try KNN on the test dataset
Data.kknn <- kknn(R1~., Data.train, Data.test, k=16, kernel="rectangular")
summary(Data.kknn)

Call:
kknn(formula = R1 ~ ., train = Data.train, test = Data.test,     k = 16, kernel = "rectangular")

Response: "continuous"

fit <- fitted(Data.kknn)
table(Data.test$R1,fit)

   fit
     0 0.0625 0.125 0.1875 0.25 0.3125 0.375 0.4375 0.5 0.5625 0.625 0.6875 0.75
  0 18     36    24     11    2      1     4      4   9      7     2      2    2
  1  2      2     1      0    0      0     0      3   6      7     4      5    3
   fit
    0.8125 0.875 0.9375  1
  0      1     1      0  0
  1     13    19     20  9

pcol <- as.character(as.numeric(Data.test$R1))
acc = sum(pcol == Data[,11]) / nrow(Data)

Using train.kknn, the best k is 16 given the best kernel is rectangular.

Accuracy of the test set is 48%.