2. Data Inspection.
library(data.table)
df<-fread("http://bit.ly/CarreFourDataset")
head(df)
## Invoice ID Branch Customer type Gender Product line Unit price
## 1: 750-67-8428 A Member Female Health and beauty 74.69
## 2: 226-31-3081 C Normal Female Electronic accessories 15.28
## 3: 631-41-3108 A Normal Male Home and lifestyle 46.33
## 4: 123-19-1176 A Member Male Health and beauty 58.22
## 5: 373-73-7910 A Normal Male Sports and travel 86.31
## 6: 699-14-3026 C Normal Male Electronic accessories 85.39
## Quantity Tax Date Time Payment cogs gross margin percentage
## 1: 7 26.1415 1/5/2019 13:08 Ewallet 522.83 4.761905
## 2: 5 3.8200 3/8/2019 10:29 Cash 76.40 4.761905
## 3: 7 16.2155 3/3/2019 13:23 Credit card 324.31 4.761905
## 4: 8 23.2880 1/27/2019 20:33 Ewallet 465.76 4.761905
## 5: 7 30.2085 2/8/2019 10:37 Ewallet 604.17 4.761905
## 6: 7 29.8865 3/25/2019 18:30 Ewallet 597.73 4.761905
## gross income Rating Total
## 1: 26.1415 9.1 548.9715
## 2: 3.8200 9.6 80.2200
## 3: 16.2155 7.4 340.5255
## 4: 23.2880 8.4 489.0480
## 5: 30.2085 5.3 634.3785
## 6: 29.8865 4.1 627.6165
Checking for missing values
# Checking for missing values
any(is.na.data.frame(df))
## [1] FALSE
# There are no missing values
Checking for duplicated values
# Checking for duplicated data
any(duplicated.data.frame(df))
## [1] FALSE
# There are no duplicates in our dataset
Encoding categorical variables to nominal to perform PCA
library("dplyr")
## Warning: package 'dplyr' was built under R version 4.0.5
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:data.table':
##
## between, first, last
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
numerical<-select_if(df,is.numeric)
numerical
## Unit price Quantity Tax cogs gross margin percentage gross income
## 1: 74.69 7 26.1415 522.83 4.761905 26.1415
## 2: 15.28 5 3.8200 76.40 4.761905 3.8200
## 3: 46.33 7 16.2155 324.31 4.761905 16.2155
## 4: 58.22 8 23.2880 465.76 4.761905 23.2880
## 5: 86.31 7 30.2085 604.17 4.761905 30.2085
## ---
## 996: 40.35 1 2.0175 40.35 4.761905 2.0175
## 997: 97.38 10 48.6900 973.80 4.761905 48.6900
## 998: 31.84 1 1.5920 31.84 4.761905 1.5920
## 999: 65.82 1 3.2910 65.82 4.761905 3.2910
## 1000: 88.34 7 30.9190 618.38 4.761905 30.9190
## Rating Total
## 1: 9.1 548.9715
## 2: 9.6 80.2200
## 3: 7.4 340.5255
## 4: 8.4 489.0480
## 5: 5.3 634.3785
## ---
## 996: 6.2 42.3675
## 997: 4.4 1022.4900
## 998: 7.7 33.4320
## 999: 4.1 69.1110
## 1000: 6.6 649.2990
# Selecting non numeric columns
head(df)
## Invoice ID Branch Customer type Gender Product line Unit price
## 1: 750-67-8428 A Member Female Health and beauty 74.69
## 2: 226-31-3081 C Normal Female Electronic accessories 15.28
## 3: 631-41-3108 A Normal Male Home and lifestyle 46.33
## 4: 123-19-1176 A Member Male Health and beauty 58.22
## 5: 373-73-7910 A Normal Male Sports and travel 86.31
## 6: 699-14-3026 C Normal Male Electronic accessories 85.39
## Quantity Tax Date Time Payment cogs gross margin percentage
## 1: 7 26.1415 1/5/2019 13:08 Ewallet 522.83 4.761905
## 2: 5 3.8200 3/8/2019 10:29 Cash 76.40 4.761905
## 3: 7 16.2155 3/3/2019 13:23 Credit card 324.31 4.761905
## 4: 8 23.2880 1/27/2019 20:33 Ewallet 465.76 4.761905
## 5: 7 30.2085 2/8/2019 10:37 Ewallet 604.17 4.761905
## 6: 7 29.8865 3/25/2019 18:30 Ewallet 597.73 4.761905
## gross income Rating Total
## 1: 26.1415 9.1 548.9715
## 2: 3.8200 9.6 80.2200
## 3: 16.2155 7.4 340.5255
## 4: 23.2880 8.4 489.0480
## 5: 30.2085 5.3 634.3785
## 6: 29.8865 4.1 627.6165
# Caret package for dummy variables
library(caret)
## Loading required package: lattice
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 4.0.5
# Encoding using Dummy variables and excluding unique ID and date time data
dums<-dummyVars("~.",data=df[,c(-1,-9,-10)])
dums
## Dummy Variable Object
##
## Formula: ~.
## <environment: 0x00000000343ef040>
## 13 variables, 0 factors
## Variables and levels will be separated by '.'
## A less than full rank encoding is used
# Encoding.
new_df<-data.frame(predict(dums,newdata =df[,c(-1,-9,-10)]))
new_df
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## X.Product.line.Sports.and.travel X.Unit.price. Quantity Tax
## 1 0 74.69 7 26.1415
## 2 0 15.28 5 3.8200
## 3 0 46.33 7 16.2155
## 4 0 58.22 8 23.2880
## 5 1 86.31 7 30.2085
## 6 0 85.39 7 29.8865
## 7 0 68.84 6 20.6520
## 8 0 73.56 10 36.7800
## 9 0 36.26 2 3.6260
## 10 0 54.84 3 8.2260
## 11 0 14.48 4 2.8960
## 12 0 25.51 4 5.1020
## 13 0 46.95 5 11.7375
## 14 0 43.19 10 21.5950
## 15 0 71.38 10 35.6900
## 16 1 93.72 6 28.1160
## 17 0 68.93 7 24.1255
## 18 1 72.61 6 21.7830
## 19 0 54.67 3 8.2005
## 20 0 40.30 2 4.0300
## 21 0 86.04 5 21.5100
## 22 0 87.98 3 13.1970
## 23 0 33.20 2 3.3200
## 24 0 34.56 5 8.6400
## 25 1 88.63 3 13.2945
## 26 0 52.59 8 21.0360
## 27 0 33.52 1 1.6760
## 28 0 87.67 2 8.7670
## 29 0 88.36 5 22.0900
## 30 0 24.89 9 11.2005
## 31 0 94.13 5 23.5325
## 32 1 78.07 9 35.1315
## 33 1 83.78 8 33.5120
## 34 0 96.58 2 9.6580
## 35 0 99.42 4 19.8840
## 36 1 68.12 1 3.4060
## 37 1 62.62 5 15.6550
## 38 0 60.88 9 27.3960
## 39 0 54.92 8 21.9680
## 40 0 30.12 8 12.0480
## 41 0 86.72 1 4.3360
## 42 0 56.11 2 5.6110
## 43 1 69.12 6 20.7360
## 44 0 98.70 8 39.4800
## 45 0 15.37 2 1.5370
## 46 0 93.96 4 18.7920
## 47 0 56.69 9 25.5105
## 48 0 20.01 9 9.0045
## 49 0 18.93 6 5.6790
## 50 0 82.63 10 41.3150
## 51 0 91.40 7 31.9900
## 52 0 44.59 5 11.1475
## 53 0 17.87 4 3.5740
## 54 0 15.43 1 0.7715
## 55 0 16.16 2 1.6160
## 56 0 85.98 8 34.3920
## 57 0 44.34 2 4.4340
## 58 0 89.60 8 35.8400
## 59 0 72.35 10 36.1750
## 60 0 30.61 6 9.1830
## 61 1 24.74 3 3.7110
## 62 0 55.73 6 16.7190
## 63 1 55.07 9 24.7815
## 64 1 15.81 10 7.9050
## 65 0 75.74 4 15.1480
## 66 0 15.87 10 7.9350
## 67 0 33.47 2 3.3470
## 68 0 97.61 6 29.2830
## 69 1 78.77 10 39.3850
## 70 0 18.33 1 0.9165
## 71 0 89.48 10 44.7400
## 72 0 62.12 10 31.0600
## 73 0 48.52 3 7.2780
## 74 0 75.91 6 22.7730
## 75 0 74.67 9 33.6015
## 76 0 41.65 10 20.8250
## 77 0 49.04 9 22.0680
## 78 0 20.01 9 9.0045
## 79 0 78.31 10 39.1550
## 80 0 20.38 5 5.0950
## 81 0 99.19 6 29.7570
## 82 0 96.68 3 14.5020
## 83 0 19.25 8 7.7000
## 84 0 80.36 4 16.0720
## 85 1 48.91 5 12.2275
## 86 1 83.06 7 29.0710
## 87 0 76.52 5 19.1300
## 88 0 49.38 7 17.2830
## 89 1 42.47 1 2.1235
## 90 0 76.99 6 23.0970
## 91 0 47.38 4 9.4760
## 92 1 44.86 10 22.4300
## 93 1 21.98 7 7.6930
## 94 0 64.36 9 28.9620
## 95 0 89.75 1 4.4875
## 96 0 97.16 1 4.8580
## 97 0 87.87 10 43.9350
## 98 0 12.45 6 3.7350
## 99 0 52.75 3 7.9125
## 100 0 82.70 6 24.8100
## 101 0 48.71 1 2.4355
## 102 0 78.55 9 35.3475
## 103 0 23.07 9 10.3815
## 104 0 58.26 6 17.4780
## 105 0 30.35 7 10.6225
## 106 0 88.67 10 44.3350
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## 435 0 1 0 47.44
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## 437 0 0 1 331.72
## 438 0 1 0 203.94
## 439 0 0 1 68.16
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## 441 1 0 0 87.20
## 442 0 1 0 707.44
## 443 0 1 0 802.89
## 444 0 0 1 12.78
## 445 1 0 0 133.70
## 446 0 1 0 19.15
## 447 0 1 0 276.60
## 448 0 1 0 137.22
## 449 0 1 0 27.07
## 450 0 1 0 39.12
## 451 1 0 0 448.26
## 452 1 0 0 132.06
## 453 0 0 1 318.05
## 454 0 0 1 25.00
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## 456 1 0 0 147.80
## 457 0 1 0 696.60
## 458 1 0 0 793.90
## 459 1 0 0 465.70
## 460 0 1 0 35.89
## 461 1 0 0 202.60
## 462 0 1 0 730.50
## 463 1 0 0 295.80
## 464 1 0 0 22.62
## 465 0 1 0 256.70
## 466 0 1 0 545.50
## 467 0 1 0 260.05
## 468 1 0 0 222.12
## 469 0 0 1 21.58
## 470 1 0 0 98.84
## 471 0 0 1 502.62
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## 473 0 1 0 431.30
## 474 1 0 0 580.56
## 475 1 0 0 322.20
## 476 0 1 0 195.54
## 477 0 1 0 166.30
## 478 0 0 1 336.28
## 479 0 0 1 343.70
## 480 0 0 1 38.60
## 481 1 0 0 527.76
## 482 1 0 0 328.00
## 483 0 0 1 185.70
## 484 1 0 0 603.80
## 485 0 1 0 369.80
## 486 0 0 1 197.96
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## 488 0 0 1 148.60
## 489 1 0 0 22.96
## 490 0 0 1 699.12
## 491 0 0 1 69.40
## 492 0 1 0 196.60
## 493 0 0 1 202.56
## 494 0 1 0 121.20
## 495 0 0 1 199.78
## 496 1 0 0 607.36
## 497 1 0 0 126.44
## 498 1 0 0 541.44
## 499 1 0 0 98.13
## 500 1 0 0 412.16
## 501 0 1 0 73.97
## 502 0 0 1 31.90
## 503 0 0 1 138.80
## 504 1 0 0 186.62
## 505 0 1 0 88.45
## 506 0 0 1 193.44
## 507 1 0 0 145.50
## 508 0 1 0 504.30
## 509 1 0 0 306.45
## 510 0 1 0 95.70
## 511 0 1 0 635.18
## 512 0 0 1 214.55
## 513 0 0 1 379.96
## 514 1 0 0 696.85
## 515 0 1 0 408.73
## 516 0 0 1 51.47
## 517 0 0 1 274.30
## 518 0 1 0 196.95
## 519 0 0 1 69.46
## 520 0 1 0 359.60
## 521 0 1 0 137.13
## 522 1 0 0 499.02
## 523 0 1 0 224.64
## 524 1 0 0 125.74
## 525 0 1 0 490.26
## 526 0 0 1 457.05
## 527 0 1 0 156.84
## 528 0 0 1 119.72
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## 530 1 0 0 882.81
## 531 0 0 1 152.58
## 532 0 1 0 693.44
## 533 0 0 1 229.50
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## 535 0 0 1 141.60
## 536 0 0 1 116.69
## 537 0 1 0 73.96
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## 539 0 1 0 292.20
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## 541 0 0 1 92.04
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## 543 0 1 0 80.72
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## 549 1 0 0 257.70
## 550 1 0 0 396.36
## 551 0 0 1 171.81
## 552 1 0 0 488.79
## 553 1 0 0 524.16
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## 555 1 0 0 135.24
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## 557 1 0 0 144.08
## 558 0 0 1 985.20
## 559 0 0 1 249.96
## 560 0 0 1 217.26
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## 563 0 0 1 339.36
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## 566 0 1 0 812.10
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## 568 1 0 0 591.66
## 569 0 1 0 559.02
## 570 0 0 1 517.86
## 571 0 1 0 410.20
## 572 1 0 0 266.70
## 573 0 0 1 70.91
## 574 0 1 0 144.78
## 575 0 1 0 429.55
## 576 0 0 1 569.17
## 577 1 0 0 241.20
## 578 0 0 1 127.08
## 579 1 0 0 257.08
## 580 0 0 1 139.02
## 581 1 0 0 81.66
## 582 1 0 0 310.72
## 583 0 1 0 185.96
## 584 0 1 0 72.32
## 585 0 0 1 189.18
## 586 0 1 0 206.84
## 587 1 0 0 157.02
## 588 0 0 1 215.30
## 589 1 0 0 596.10
## 590 1 0 0 73.10
## 591 0 1 0 279.18
## 592 0 0 1 169.68
## 593 1 0 0 45.58
## 594 0 0 1 225.60
## 595 1 0 0 290.40
## 596 0 1 0 44.46
## 597 0 1 0 156.60
## 598 0 0 1 419.94
## 599 1 0 0 184.25
## 600 0 0 1 140.64
## 601 0 0 1 83.08
## 602 0 1 0 64.99
## 603 0 0 1 775.60
## 604 0 0 1 327.06
## 605 1 0 0 363.23
## 606 1 0 0 127.00
## 607 0 0 1 375.55
## 608 0 1 0 199.16
## 609 0 0 1 30.61
## 610 0 0 1 115.78
## 611 0 1 0 28.96
## 612 1 0 0 890.73
## 613 1 0 0 279.66
## 614 0 1 0 80.93
## 615 0 0 1 674.50
## 616 0 0 1 348.48
## 617 1 0 0 435.60
## 618 0 0 1 439.55
## 619 0 1 0 591.18
## 620 0 0 1 260.76
## 621 0 1 0 215.04
## 622 1 0 0 91.61
## 623 0 1 0 662.13
## 624 0 1 0 832.50
## 625 1 0 0 91.35
## 626 1 0 0 157.76
## 627 0 0 1 121.74
## 628 1 0 0 825.80
## 629 0 0 1 159.90
## 630 0 1 0 12.09
## 631 0 1 0 641.90
## 632 0 0 1 234.93
## 633 0 1 0 167.54
## 634 0 0 1 299.10
## 635 0 1 0 239.73
## 636 0 1 0 664.70
## 637 0 1 0 202.65
## 638 1 0 0 46.20
## 639 1 0 0 88.15
## 640 0 0 1 157.26
## 641 0 0 1 296.37
## 642 0 0 1 708.40
## 643 0 0 1 111.34
## 644 0 1 0 580.16
## 645 0 0 1 60.25
## 646 0 0 1 174.24
## 647 1 0 0 421.26
## 648 1 0 0 33.63
## 649 1 0 0 30.98
## 650 1 0 0 247.40
## 651 0 0 1 378.30
## 652 1 0 0 334.86
## 653 1 0 0 727.80
## 654 0 0 1 335.88
## 655 0 1 0 240.72
## 656 0 1 0 47.07
## 657 0 1 0 99.69
## 658 0 0 1 264.45
## 659 1 0 0 139.65
## 660 0 1 0 55.45
## 661 1 0 0 128.91
## 662 0 1 0 119.98
## 663 0 1 0 352.50
## 664 0 1 0 871.00
## 665 1 0 0 197.60
## 666 0 0 1 194.52
## 667 0 0 1 173.22
## 668 0 0 1 71.88
## 669 0 0 1 286.26
## 670 0 1 0 81.24
## 671 0 0 1 560.40
## 672 1 0 0 186.80
## 673 0 0 1 220.23
## 674 0 1 0 269.12
## 675 0 1 0 454.80
## 676 1 0 0 167.54
## 677 0 1 0 448.56
## 678 1 0 0 293.88
## 679 0 0 1 589.50
## 680 0 0 1 291.00
## 681 1 0 0 39.48
## 682 0 1 0 34.81
## 683 0 0 1 295.92
## 684 0 0 1 42.96
## 685 0 0 1 138.48
## 686 0 1 0 98.20
## 687 0 1 0 129.66
## 688 1 0 0 635.60
## 689 1 0 0 145.76
## 690 1 0 0 201.30
## 691 1 0 0 631.71
## 692 0 0 1 385.28
## 693 1 0 0 486.30
## 694 1 0 0 513.66
## 695 1 0 0 473.40
## 696 1 0 0 436.85
## 697 0 0 1 108.16
## 698 0 0 1 248.76
## 699 0 1 0 626.22
## 700 0 0 1 975.00
## 701 0 0 1 483.28
## 702 0 1 0 96.96
## 703 0 1 0 197.70
## 704 1 0 0 724.23
## 705 1 0 0 795.51
## 706 1 0 0 502.39
## 707 0 0 1 172.00
## 708 1 0 0 68.98
## 709 0 0 1 124.96
## 710 0 0 1 77.10
## 711 1 0 0 483.72
## 712 0 0 1 302.12
## 713 0 0 1 698.67
## 714 0 0 1 124.65
## 715 0 0 1 789.60
## 716 0 1 0 178.40
## 717 0 0 1 500.22
## 718 0 1 0 35.82
## 719 0 1 0 136.14
## 720 0 1 0 104.88
## 721 1 0 0 178.92
## 722 1 0 0 815.67
## 723 0 1 0 132.36
## 724 1 0 0 257.39
## 725 0 0 1 93.36
## 726 1 0 0 228.00
## 727 0 1 0 166.71
## 728 0 1 0 697.40
## 729 0 0 1 389.04
## 730 1 0 0 365.26
## 731 0 1 0 89.28
## 732 0 0 1 168.00
## 733 0 0 1 19.70
## 734 0 0 1 531.16
## 735 0 0 1 53.72
## 736 0 1 0 819.50
## 737 0 1 0 568.40
## 738 0 0 1 587.60
## 739 0 0 1 732.48
## 740 1 0 0 845.64
## 741 1 0 0 389.27
## 742 0 0 1 84.83
## 743 0 0 1 143.26
## 744 0 0 1 75.38
## 745 0 1 0 253.36
## 746 1 0 0 38.42
## 747 0 1 0 652.30
## 748 0 1 0 52.65
## 749 0 1 0 110.61
## 750 1 0 0 568.61
## 751 0 0 1 89.28
## 752 0 1 0 136.40
## 753 0 0 1 174.20
## 754 0 0 1 366.40
## 755 0 0 1 254.61
## 756 0 1 0 778.32
## 757 0 0 1 285.92
## 758 1 0 0 579.12
## 759 0 0 1 188.50
## 760 0 0 1 221.56
## 761 0 1 0 772.00
## 762 0 1 0 721.30
## 763 0 0 1 511.04
## 764 0 0 1 53.45
## 765 0 1 0 222.00
## 766 0 0 1 763.68
## 767 0 1 0 228.18
## 768 1 0 0 82.14
## 769 1 0 0 382.56
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## 771 0 0 1 382.16
## 772 0 1 0 601.09
## 773 0 0 1 475.93
## 774 0 1 0 52.42
## 775 1 0 0 131.30
## 776 0 1 0 144.30
## 777 0 1 0 457.17
## 778 1 0 0 93.38
## 779 1 0 0 126.25
## 780 0 0 1 790.83
## 781 1 0 0 174.40
## 782 0 0 1 379.04
## 783 0 1 0 30.62
## 784 1 0 0 352.08
## 785 0 0 1 50.80
## 786 0 1 0 522.06
## 787 0 0 1 575.12
## 788 0 1 0 54.95
## 789 0 1 0 181.41
## 790 0 0 1 412.37
## 791 0 1 0 46.41
## 792 0 1 0 274.20
## 793 0 1 0 973.70
## 794 0 1 0 648.20
## 795 0 1 0 93.22
## 796 0 0 1 54.36
## 797 1 0 0 60.87
## 798 1 0 0 244.90
## 799 0 1 0 92.78
## 800 0 0 1 433.45
## 801 0 0 1 138.06
## 802 0 0 1 241.60
## 803 0 0 1 471.73
## 804 1 0 0 440.64
## 805 1 0 0 680.31
## 806 1 0 0 309.88
## 807 0 1 0 186.36
## 808 1 0 0 200.92
## 809 1 0 0 17.75
## 810 0 0 1 621.80
## 811 0 0 1 86.00
## 812 0 1 0 402.60
## 813 0 1 0 324.85
## 814 1 0 0 95.15
## 815 1 0 0 388.96
## 816 0 0 1 425.68
## 817 1 0 0 318.08
## 818 0 0 1 271.04
## 819 0 1 0 384.64
## 820 0 1 0 235.80
## 821 0 0 1 211.56
## 822 0 1 0 95.36
## 823 1 0 0 10.17
## 824 1 0 0 206.13
## 825 0 1 0 420.56
## 826 0 1 0 88.04
## 827 0 1 0 648.99
## 828 0 1 0 123.84
## 829 1 0 0 649.50
## 830 0 1 0 742.20
## 831 1 0 0 84.48
## 832 1 0 0 250.28
## 833 1 0 0 94.80
## 834 0 0 1 91.30
## 835 0 0 1 285.11
## 836 1 0 0 52.38
## 837 0 0 1 192.70
## 838 0 1 0 267.78
## 839 1 0 0 558.70
## 840 0 0 1 175.32
## 841 1 0 0 155.82
## 842 1 0 0 60.30
## 843 0 1 0 78.94
## 844 0 1 0 29.74
## 845 1 0 0 21.32
## 846 0 1 0 281.34
## 847 0 0 1 73.26
## 848 0 1 0 22.38
## 849 1 0 0 655.92
## 850 1 0 0 594.60
## 851 1 0 0 74.10
## 852 0 0 1 196.96
## 853 0 0 1 372.33
## 854 0 0 1 527.90
## 855 0 0 1 479.75
## 856 1 0 0 328.59
## 857 1 0 0 168.96
## 858 1 0 0 113.24
## 859 1 0 0 345.54
## 860 1 0 0 428.67
## 861 0 0 1 86.27
## 862 0 0 1 25.52
## 863 0 1 0 101.52
## 864 1 0 0 357.49
## 865 1 0 0 238.77
## 866 0 0 1 101.43
## 867 0 1 0 724.24
## 868 0 0 1 125.64
## 869 0 1 0 72.93
## 870 0 0 1 258.36
## 871 0 1 0 173.74
## 872 0 0 1 56.50
## 873 1 0 0 214.30
## 874 1 0 0 534.36
## 875 0 1 0 93.16
## 876 0 0 1 522.08
## 877 1 0 0 52.35
## 878 1 0 0 39.75
## 879 0 1 0 720.16
## 880 0 0 1 96.80
## 881 0 0 1 332.10
## 882 0 1 0 81.44
## 883 0 1 0 319.90
## 884 0 0 1 206.52
## 885 1 0 0 166.68
## 886 1 0 0 319.06
## 887 0 0 1 87.90
## 888 0 0 1 734.70
## 889 0 0 1 97.52
## 890 0 0 1 769.20
## 891 1 0 0 418.30
## 892 1 0 0 463.28
## 893 0 1 0 462.45
## 894 1 0 0 141.90
## 895 0 1 0 302.70
## 896 0 1 0 793.28
## 897 0 0 1 425.18
## 898 1 0 0 283.62
## 899 1 0 0 599.20
## 900 0 0 1 315.36
## 901 0 1 0 403.56
## 902 0 0 1 183.88
## 903 0 1 0 138.65
## 904 1 0 0 80.71
## 905 0 0 1 116.64
## 906 1 0 0 313.52
## 907 0 1 0 846.10
## 908 0 1 0 414.40
## 909 0 0 1 159.08
## 910 0 1 0 490.10
## 911 0 1 0 87.45
## 912 0 0 1 224.52
## 913 1 0 0 744.96
## 914 0 0 1 410.72
## 915 1 0 0 298.80
## 916 1 0 0 212.94
## 917 0 1 0 42.85
## 918 1 0 0 378.68
## 919 0 0 1 206.91
## 920 0 0 1 78.78
## 921 0 1 0 322.11
## 922 1 0 0 98.22
## 923 0 1 0 25.46
## 924 0 1 0 581.98
## 925 0 0 1 211.32
## 926 0 0 1 55.12
## 927 0 1 0 88.31
## 928 0 1 0 356.58
## 929 0 1 0 794.25
## 930 0 0 1 50.62
## 931 0 0 1 599.52
## 932 0 1 0 166.70
## 933 0 0 1 744.40
## 934 0 0 1 448.56
## 935 0 0 1 378.90
## 936 0 0 1 257.16
## 937 0 0 1 552.23
## 938 1 0 0 447.40
## 939 1 0 0 276.27
## 940 0 0 1 343.74
## 941 0 0 1 266.08
## 942 1 0 0 898.38
## 943 0 0 1 456.80
## 944 0 1 0 253.95
## 945 1 0 0 70.56
## 946 0 1 0 657.16
## 947 0 1 0 168.50
## 948 0 0 1 53.78
## 949 0 0 1 179.05
## 950 0 0 1 211.44
## 951 0 0 1 119.73
## 952 0 0 1 65.70
## 953 0 0 1 251.40
## 954 1 0 0 84.16
## 955 1 0 0 395.46
## 956 1 0 0 297.99
## 957 1 0 0 454.41
## 958 1 0 0 276.12
## 959 1 0 0 158.00
## 960 1 0 0 887.94
## 961 1 0 0 91.98
## 962 1 0 0 41.78
## 963 0 1 0 15.50
## 964 1 0 0 290.46
## 965 0 1 0 66.66
## 966 0 1 0 76.54
## 967 0 0 1 299.70
## 968 0 1 0 243.03
## 969 1 0 0 47.40
## 970 0 1 0 172.45
## 971 0 1 0 846.30
## 972 0 0 1 258.37
## 973 1 0 0 609.56
## 974 1 0 0 240.24
## 975 1 0 0 172.26
## 976 0 1 0 99.84
## 977 1 0 0 298.64
## 978 0 0 1 159.60
## 979 0 1 0 25.45
## 980 0 1 0 67.77
## 981 1 0 0 238.36
## 982 1 0 0 232.60
## 983 0 0 1 877.32
## 984 1 0 0 699.72
## 985 1 0 0 674.59
## 986 0 0 1 318.55
## 987 0 0 1 29.52
## 988 0 1 0 496.00
## 989 0 0 1 823.40
## 990 0 1 0 602.96
## 991 0 1 0 282.80
## 992 0 0 1 766.00
## 993 0 0 1 116.06
## 994 0 0 1 174.90
## 995 0 0 1 60.95
## 996 0 0 1 40.35
## 997 0 0 1 973.80
## 998 1 0 0 31.84
## 999 1 0 0 65.82
## 1000 1 0 0 618.38
## X.gross.margin.percentage. X.gross.income. Rating Total
## 1 4.761905 26.1415 9.1 548.9715
## 2 4.761905 3.8200 9.6 80.2200
## 3 4.761905 16.2155 7.4 340.5255
## 4 4.761905 23.2880 8.4 489.0480
## 5 4.761905 30.2085 5.3 634.3785
## 6 4.761905 29.8865 4.1 627.6165
## 7 4.761905 20.6520 5.8 433.6920
## 8 4.761905 36.7800 8.0 772.3800
## 9 4.761905 3.6260 7.2 76.1460
## 10 4.761905 8.2260 5.9 172.7460
## 11 4.761905 2.8960 4.5 60.8160
## 12 4.761905 5.1020 6.8 107.1420
## 13 4.761905 11.7375 7.1 246.4875
## 14 4.761905 21.5950 8.2 453.4950
## 15 4.761905 35.6900 5.7 749.4900
## 16 4.761905 28.1160 4.5 590.4360
## 17 4.761905 24.1255 4.6 506.6355
## 18 4.761905 21.7830 6.9 457.4430
## 19 4.761905 8.2005 8.6 172.2105
## 20 4.761905 4.0300 4.4 84.6300
## 21 4.761905 21.5100 4.8 451.7100
## 22 4.761905 13.1970 5.1 277.1370
## 23 4.761905 3.3200 4.4 69.7200
## 24 4.761905 8.6400 9.9 181.4400
## 25 4.761905 13.2945 6.0 279.1845
## 26 4.761905 21.0360 8.5 441.7560
## 27 4.761905 1.6760 6.7 35.1960
## 28 4.761905 8.7670 7.7 184.1070
## 29 4.761905 22.0900 9.6 463.8900
## 30 4.761905 11.2005 7.4 235.2105
## 31 4.761905 23.5325 4.8 494.1825
## 32 4.761905 35.1315 4.5 737.7615
## 33 4.761905 33.5120 5.1 703.7520
## 34 4.761905 9.6580 5.1 202.8180
## 35 4.761905 19.8840 7.5 417.5640
## 36 4.761905 3.4060 6.8 71.5260
## 37 4.761905 15.6550 7.0 328.7550
## 38 4.761905 27.3960 4.7 575.3160
## 39 4.761905 21.9680 7.6 461.3280
## 40 4.761905 12.0480 7.7 253.0080
## 41 4.761905 4.3360 7.9 91.0560
## 42 4.761905 5.6110 6.3 117.8310
## 43 4.761905 20.7360 5.6 435.4560
## 44 4.761905 39.4800 7.6 829.0800
## 45 4.761905 1.5370 7.2 32.2770
## 46 4.761905 18.7920 9.5 394.6320
## 47 4.761905 25.5105 8.4 535.7205
## 48 4.761905 9.0045 4.1 189.0945
## 49 4.761905 5.6790 8.1 119.2590
## 50 4.761905 41.3150 7.9 867.6150
## 51 4.761905 31.9900 9.5 671.7900
## 52 4.761905 11.1475 8.5 234.0975
## 53 4.761905 3.5740 6.5 75.0540
## 54 4.761905 0.7715 6.1 16.2015
## 55 4.761905 1.6160 6.5 33.9360
## 56 4.761905 34.3920 8.2 722.2320
## 57 4.761905 4.4340 5.8 93.1140
## 58 4.761905 35.8400 6.6 752.6400
## 59 4.761905 36.1750 5.4 759.6750
## 60 4.761905 9.1830 9.3 192.8430
## 61 4.761905 3.7110 10.0 77.9310
## 62 4.761905 16.7190 7.0 351.0990
## 63 4.761905 24.7815 10.0 520.4115
## 64 4.761905 7.9050 8.6 166.0050
## 65 4.761905 15.1480 7.6 318.1080
## 66 4.761905 7.9350 5.8 166.6350
## 67 4.761905 3.3470 6.7 70.2870
## 68 4.761905 29.2830 9.9 614.9430
## 69 4.761905 39.3850 6.4 827.0850
## 70 4.761905 0.9165 4.3 19.2465
## 71 4.761905 44.7400 9.6 939.5400
## 72 4.761905 31.0600 5.9 652.2600
## 73 4.761905 7.2780 4.0 152.8380
## 74 4.761905 22.7730 8.7 478.2330
## 75 4.761905 33.6015 9.4 705.6315
## 76 4.761905 20.8250 5.4 437.3250
## 77 4.761905 22.0680 8.6 463.4280
## 78 4.761905 9.0045 5.7 189.0945
## 79 4.761905 39.1550 6.6 822.2550
## 80 4.761905 5.0950 6.0 106.9950
## 81 4.761905 29.7570 5.5 624.8970
## 82 4.761905 14.5020 6.4 304.5420
## 83 4.761905 7.7000 6.6 161.7000
## 84 4.761905 16.0720 8.3 337.5120
## 85 4.761905 12.2275 6.6 256.7775
## 86 4.761905 29.0710 4.0 610.4910
## 87 4.761905 19.1300 9.9 401.7300
## 88 4.761905 17.2830 7.3 362.9430
## 89 4.761905 2.1235 5.7 44.5935
## 90 4.761905 23.0970 6.1 485.0370
## 91 4.761905 9.4760 7.1 198.9960
## 92 4.761905 22.4300 8.2 471.0300
## 93 4.761905 7.6930 5.1 161.5530
## 94 4.761905 28.9620 8.6 608.2020
## 95 4.761905 4.4875 6.6 94.2375
## 96 4.761905 4.8580 7.2 102.0180
## 97 4.761905 43.9350 5.1 922.6350
## 98 4.761905 3.7350 4.1 78.4350
## 99 4.761905 7.9125 9.3 166.1625
## 100 4.761905 24.8100 7.4 521.0100
## 101 4.761905 2.4355 4.1 51.1455
## 102 4.761905 35.3475 7.2 742.2975
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## 901 4.761905 20.1780 7.5 423.7380
## 902 4.761905 9.1940 5.1 193.0740
## 903 4.761905 6.9325 4.2 145.5825
## 904 4.761905 4.0355 8.1 84.7455
## 905 4.761905 5.8320 6.0 122.4720
## 906 4.761905 15.6760 7.9 329.1960
## 907 4.761905 42.3050 8.8 888.4050
## 908 4.761905 20.7200 6.6 435.1200
## 909 4.761905 7.9540 6.2 167.0340
## 910 4.761905 24.5050 4.2 514.6050
## 911 4.761905 4.3725 7.3 91.8225
## 912 4.761905 11.2260 8.6 235.7460
## 913 4.761905 37.2480 6.8 782.2080
## 914 4.761905 20.5360 7.6 431.2560
## 915 4.761905 14.9400 5.8 313.7400
## 916 4.761905 10.6470 4.1 223.5870
## 917 4.761905 2.1425 9.3 44.9925
## 918 4.761905 18.9340 6.8 397.6140
## 919 4.761905 10.3455 8.7 217.2555
## 920 4.761905 3.9390 6.3 82.7190
## 921 4.761905 16.1055 5.1 338.2155
## 922 4.761905 4.9110 7.0 103.1310
## 923 4.761905 1.2730 5.2 26.7330
## 924 4.761905 29.0990 6.6 611.0790
## 925 4.761905 10.5660 6.5 221.8860
## 926 4.761905 2.7560 9.0 57.8760
## 927 4.761905 4.4155 5.2 92.7255
## 928 4.761905 17.8290 6.8 374.4090
## 929 4.761905 39.7125 7.6 833.9625
## 930 4.761905 2.5310 7.2 53.1510
## 931 4.761905 29.9760 7.1 629.4960
## 932 4.761905 8.3350 9.5 175.0350
## 933 4.761905 37.2200 5.1 781.6200
## 934 4.761905 22.4280 7.6 470.9880
## 935 4.761905 18.9450 9.8 397.8450
## 936 4.761905 12.8580 5.1 270.0180
## 937 4.761905 27.6115 7.5 579.8415
## 938 4.761905 22.3700 7.4 469.7700
## 939 4.761905 13.8135 4.2 290.0835
## 940 4.761905 17.1870 5.9 360.9270
## 941 4.761905 13.3040 6.9 279.3840
## 942 4.761905 44.9190 6.6 943.2990
## 943 4.761905 22.8400 5.7 479.6400
## 944 4.761905 12.6975 5.3 266.6475
## 945 4.761905 3.5280 4.2 74.0880
## 946 4.761905 32.8580 7.3 690.0180
## 947 4.761905 8.4250 5.3 176.9250
## 948 4.761905 2.6890 4.7 56.4690
## 949 4.761905 8.9525 7.9 188.0025
## 950 4.761905 10.5720 8.9 222.0120
## 951 4.761905 5.9865 9.3 125.7165
## 952 4.761905 3.2850 4.7 68.9850
## 953 4.761905 12.5700 8.7 263.9700
## 954 4.761905 4.2080 7.6 88.3680
## 955 4.761905 19.7730 5.7 415.2330
## 956 4.761905 14.8995 6.8 312.8895
## 957 4.761905 22.7205 5.4 477.1305
## 958 4.761905 13.8060 7.1 289.9260
## 959 4.761905 7.9000 7.8 165.9000
## 960 4.761905 44.3970 8.4 932.3370
## 961 4.761905 4.5990 9.8 96.5790
## 962 4.761905 2.0890 9.8 43.8690
## 963 4.761905 0.7750 7.4 16.2750
## 964 4.761905 14.5230 6.7 304.9830
## 965 4.761905 3.3330 6.4 69.9930
## 966 4.761905 3.8270 5.8 80.3670
## 967 4.761905 14.9850 7.2 314.6850
## 968 4.761905 12.1515 9.3 255.1815
## 969 4.761905 2.3700 9.5 49.7700
## 970 4.761905 8.6225 9.0 181.0725
## 971 4.761905 42.3150 9.0 888.6150
## 972 4.761905 12.9185 6.7 271.2885
## 973 4.761905 30.4780 5.5 640.0380
## 974 4.761905 12.0120 5.4 252.2520
## 975 4.761905 8.6130 8.2 180.8730
## 976 4.761905 4.9920 7.0 104.8320
## 977 4.761905 14.9320 8.5 313.5720
## 978 4.761905 7.9800 4.9 167.5800
## 979 4.761905 1.2725 5.1 26.7225
## 980 4.761905 3.3885 6.5 71.1585
## 981 4.761905 11.9180 9.8 250.2780
## 982 4.761905 11.6300 8.4 244.2300
## 983 4.761905 43.8660 7.4 921.1860
## 984 4.761905 34.9860 6.1 734.7060
## 985 4.761905 33.7295 6.0 708.3195
## 986 4.761905 15.9275 8.5 334.4775
## 987 4.761905 1.4760 4.3 30.9960
## 988 4.761905 24.8000 6.2 520.8000
## 989 4.761905 41.1700 4.3 864.5700
## 990 4.761905 30.1480 8.4 633.1080
## 991 4.761905 14.1400 4.5 296.9400
## 992 4.761905 38.3000 6.0 804.3000
## 993 4.761905 5.8030 8.8 121.8630
## 994 4.761905 8.7450 6.6 183.6450
## 995 4.761905 3.0475 5.9 63.9975
## 996 4.761905 2.0175 6.2 42.3675
## 997 4.761905 48.6900 4.4 1022.4900
## 998 4.761905 1.5920 7.7 33.4320
## 999 4.761905 3.2910 4.1 69.1110
## 1000 4.761905 30.9190 6.6 649.2990
# Dimensionality Reduction technique
# Will use PCA so as to understand the variance displayed by each feature
reduced_df<-prcomp(new_df,center = TRUE)
# Since prcomp uses single value decomposition that tests each points covariance and correlation to each other.
reduced_df$sdev
## [1] 3.403819e+02 2.053220e+01 1.719967e+00 1.246753e+00 7.268821e-01
## [6] 6.944099e-01 5.945089e-01 5.811926e-01 5.690861e-01 5.568613e-01
## [11] 4.180209e-01 4.106769e-01 4.077796e-01 4.004978e-01 3.904585e-01
## [16] 3.316253e-14 3.958663e-15 3.729380e-15 4.310238e-16 1.295179e-16
## [21] 1.009774e-16 7.798827e-17 1.648208e-17 1.265091e-33
# Checking the standard deviation of each PC
plot(reduced_df$sdev,main="Standard deviation of each Principal Component",ylab = "Standard Deviation",xlab = "Princial Components",type = "bar",col="blue")
## Warning in plot.xy(xy, type, ...): plot type 'bar' will be truncated to first
## character
### We can observe that the first three Principal components have a significant standard deviation in our dataset
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
# Getting the sum of square distances from the projected point in our data
eigen_values<-get_eigenvalue(reduced_df)
eigen_values
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 1.158598e+05 9.963088e+01 99.63088
## Dim.2 4.215713e+02 3.625202e-01 99.99340
## Dim.3 2.958285e+00 2.543907e-03 99.99595
## Dim.4 1.554394e+00 1.336664e-03 99.99728
## Dim.5 5.283577e-01 4.543485e-04 99.99774
## Dim.6 4.822052e-01 4.146608e-04 99.99815
## Dim.7 3.534408e-01 3.039330e-04 99.99846
## Dim.8 3.377848e-01 2.904700e-04 99.99875
## Dim.9 3.238590e-01 2.784948e-04 99.99903
## Dim.10 3.100945e-01 2.666584e-04 99.99929
## Dim.11 1.747415e-01 1.502648e-04 99.99944
## Dim.12 1.686555e-01 1.450313e-04 99.99959
## Dim.13 1.662842e-01 1.429921e-04 99.99973
## Dim.14 1.603985e-01 1.379309e-04 99.99987
## Dim.15 1.524578e-01 1.311025e-04 100.00000
## Dim.16 1.099753e-27 9.457064e-31 100.00000
## Dim.17 1.567101e-29 1.347591e-32 100.00000
## Dim.18 1.390828e-29 1.196009e-32 100.00000
## Dim.19 1.857815e-31 1.597584e-34 100.00000
## Dim.20 1.677488e-32 1.442516e-35 100.00000
## Dim.21 1.019644e-32 8.768181e-36 100.00000
## Dim.22 6.082171e-33 5.230218e-36 100.00000
## Dim.23 2.716589e-34 2.336066e-37 100.00000
## Dim.24 1.600456e-66 1.376274e-69 100.00000
# We get to understand from these that dimension 1 or PCA 1 explains almost 99 % of all the variance in my dataset
summary(reduced_df)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 340.3819 20.53220 1.71997 1.24675 0.7269 0.6944 0.5945
## Proportion of Variance 0.9963 0.00363 0.00003 0.00001 0.0000 0.0000 0.0000
## Cumulative Proportion 0.9963 0.99993 0.99996 0.99997 1.0000 1.0000 1.0000
## PC8 PC9 PC10 PC11 PC12 PC13 PC14 PC15
## Standard deviation 0.5812 0.5691 0.5569 0.418 0.4107 0.4078 0.4005 0.3905
## Proportion of Variance 0.0000 0.0000 0.0000 0.000 0.0000 0.0000 0.0000 0.0000
## Cumulative Proportion 1.0000 1.0000 1.0000 1.000 1.0000 1.0000 1.0000 1.0000
## PC16 PC17 PC18 PC19 PC20
## Standard deviation 3.316e-14 3.959e-15 3.729e-15 4.31e-16 1.295e-16
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.00e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.00e+00 1.000e+00
## PC21 PC22 PC23 PC24
## Standard deviation 1.01e-16 7.799e-17 1.648e-17 1.265e-33
## Proportion of Variance 0.00e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.00e+00 1.000e+00 1.000e+00 1.000e+00
New PCA
# Columns that are numeric are more thus i will exclude non numeric columns
pca_d<-prcomp(df[,c(6,7,8,12,14,15,16)],scale. = TRUE)
summary(pca_d)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 2.2185 1.0002 0.9939 0.30001 1.499e-16 1.095e-16
## Proportion of Variance 0.7031 0.1429 0.1411 0.01286 0.000e+00 0.000e+00
## Cumulative Proportion 0.7031 0.8460 0.9871 1.00000 1.000e+00 1.000e+00
## PC7
## Standard deviation 1.298e-17
## Proportion of Variance 0.000e+00
## Cumulative Proportion 1.000e+00
# PC1 explains about 70% of variation in our dataset followed by PC2
# Plotting a scree plot of the Principle components explained variance
library(factoextra)
fviz_eig(pca_d)
# From the scree plot above we can see that only PC1 ,PC2 and PC3 contain core information about our set that we will concentrate on that
# Getting the variables that contributed to the principle components
library(ggbiplot)
## Loading required package: plyr
## ------------------------------------------------------------------------------
## You have loaded plyr after dplyr - this is likely to cause problems.
## If you need functions from both plyr and dplyr, please load plyr first, then dplyr:
## library(plyr); library(dplyr)
## ------------------------------------------------------------------------------
##
## Attaching package: 'plyr'
## The following objects are masked from 'package:dplyr':
##
## arrange, count, desc, failwith, id, mutate, rename, summarise,
## summarize
## Loading required package: scales
## Loading required package: grid
ggbiplot(pca_d,obs.scale = 1,var.scale = 1,varname.adjust = 0.6,circle = TRUE)
# Rating contributes positively to PC1 which holds the core information of our dataset
# Most variables are clustered together at negative value of PC1
str(df)
## Classes 'data.table' and 'data.frame': 1000 obs. of 16 variables:
## $ Invoice ID : chr "750-67-8428" "226-31-3081" "631-41-3108" "123-19-1176" ...
## $ Branch : chr "A" "C" "A" "A" ...
## $ Customer type : chr "Member" "Normal" "Normal" "Member" ...
## $ Gender : chr "Female" "Female" "Male" "Male" ...
## $ Product line : chr "Health and beauty" "Electronic accessories" "Home and lifestyle" "Health and beauty" ...
## $ Unit price : num 74.7 15.3 46.3 58.2 86.3 ...
## $ Quantity : int 7 5 7 8 7 7 6 10 2 3 ...
## $ Tax : num 26.14 3.82 16.22 23.29 30.21 ...
## $ Date : chr "1/5/2019" "3/8/2019" "3/3/2019" "1/27/2019" ...
## $ Time : chr "13:08" "10:29" "13:23" "20:33" ...
## $ Payment : chr "Ewallet" "Cash" "Credit card" "Ewallet" ...
## $ cogs : num 522.8 76.4 324.3 465.8 604.2 ...
## $ gross margin percentage: num 4.76 4.76 4.76 4.76 4.76 ...
## $ gross income : num 26.14 3.82 16.22 23.29 30.21 ...
## $ Rating : num 9.1 9.6 7.4 8.4 5.3 4.1 5.8 8 7.2 5.9 ...
## $ Total : num 549 80.2 340.5 489 634.4 ...
## - attr(*, ".internal.selfref")=<externalptr>
# Getting the distribution of our categorical columns in the reduced dimension
ggbiplot(pca_d,obs.scale = 1,var.scale = 1,varname.adjust = 0.6,circle = TRUE,groups =df$Payment)
# Payment by Credit card and E-wallet is rampant and seems to be heavily clustered across core information(one with the highest variation) in the dataset
# an attempt to extract information from the lower principal components
ggbiplot(pca_d,choice=c(3,4),obs.scale = 1,var.scale = 1,varname.adjust = 0.6,circle = TRUE,groups =df$Payment)
# Its not easily interpratable.
PartII on Feature Selection
Performing elbow method to find appropriate number of clusters so as not to get the correct weights of the Entropy weighted Kmeans feature selection function
# Normalizing so as to perform cluster based feature selection using min max scaler
normalize<-function(x){
return ((x-min(x))/(max(x)-min(x)))}
Normalizing Features
norm_df<-as.data.frame(lapply(new_df, normalize))
summary(norm_df)
## BranchA BranchB BranchC X.Customer.type.Member
## Min. :0.00 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.00 Median :0.000 Median :0.000 Median :1.000
## Mean :0.34 Mean :0.332 Mean :0.328 Mean :0.501
## 3rd Qu.:1.00 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.00 Max. :1.000 Max. :1.000 Max. :1.000
##
## X.Customer.type.Normal GenderFemale GenderMale
## Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :1.000 Median :0.000
## Mean :0.499 Mean :0.501 Mean :0.499
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000 Max. :1.000
##
## X.Product.line.Electronic.accessories X.Product.line.Fashion.accessories
## Min. :0.00 Min. :0.000
## 1st Qu.:0.00 1st Qu.:0.000
## Median :0.00 Median :0.000
## Mean :0.17 Mean :0.178
## 3rd Qu.:0.00 3rd Qu.:0.000
## Max. :1.00 Max. :1.000
##
## X.Product.line.Food.and.beverages X.Product.line.Health.and.beauty
## Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.000
## Mean :0.174 Mean :0.152
## 3rd Qu.:0.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.000
##
## X.Product.line.Home.and.lifestyle X.Product.line.Sports.and.travel
## Min. :0.00 Min. :0.000
## 1st Qu.:0.00 1st Qu.:0.000
## Median :0.00 Median :0.000
## Mean :0.16 Mean :0.166
## 3rd Qu.:0.00 3rd Qu.:0.000
## Max. :1.00 Max. :1.000
##
## X.Unit.price. Quantity Tax PaymentCash
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.2536 1st Qu.:0.2222 1st Qu.:0.1102 1st Qu.:0.000
## Median :0.5023 Median :0.4444 Median :0.2356 Median :0.000
## Mean :0.5073 Mean :0.5011 Mean :0.3026 Mean :0.344
## 3rd Qu.:0.7550 3rd Qu.:0.7778 3rd Qu.:0.4464 3rd Qu.:1.000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.000
##
## PaymentCredit.card PaymentEwallet cogs X.gross.margin.percentage.
## Min. :0.000 Min. :0.000 Min. :0.0000 Min. : NA
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.1102 1st Qu.: NA
## Median :0.000 Median :0.000 Median :0.2356 Median : NA
## Mean :0.311 Mean :0.345 Mean :0.3026 Mean :NaN
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:0.4464 3rd Qu.: NA
## Max. :1.000 Max. :1.000 Max. :1.0000 Max. : NA
## NA's :1000
## X.gross.income. Rating Total
## Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.1102 1st Qu.:0.2500 1st Qu.:0.1102
## Median :0.2356 Median :0.5000 Median :0.2356
## Mean :0.3026 Mean :0.4955 Mean :0.3026
## 3rd Qu.:0.4464 3rd Qu.:0.7500 3rd Qu.:0.4464
## Max. :1.0000 Max. :1.0000 Max. :1.0000
##
# Using the encoded set of data excluding the gross margin which is non variant. 4 are the optimum clusters
fviz_nbclust(norm_df[,c(-21)],FUNcluster = kmeans,method = "wss")
# Using Embedding methods: Entropy Weighted K means
library(wskm)
## Loading required package: latticeExtra
##
## Attaching package: 'latticeExtra'
## The following object is masked from 'package:ggplot2':
##
## layer
## Loading required package: fpc
#Setting the initial clusters as 3 first and a variable for weight distribution
# We get to see the importance of every variable to the kmeans cluster
# We will exclude the gross margin percentage as its inclusion would give us errors in distance metrics.
my_model<-ewkm(norm_df[,c(-21)],2,lambda = 2,maxiter=1000)
my_model
## K-means clustering with 2 clusters of sizes 344, 656
##
## Cluster means:
## BranchA BranchB BranchC X.Customer.type.Member X.Customer.type.Normal
## 1 0.3197674 0.3197674 0.3604651 0.4883721 0.5116279
## 2 0.3506098 0.3384146 0.3109756 0.5076220 0.4923780
## GenderFemale GenderMale X.Product.line.Electronic.accessories
## 1 0.5174419 0.4825581 0.2063953
## 2 0.4923780 0.5076220 0.1509146
## X.Product.line.Fashion.accessories X.Product.line.Food.and.beverages
## 1 0.1656977 0.1656977
## 2 0.1844512 0.1783537
## X.Product.line.Health.and.beauty X.Product.line.Home.and.lifestyle
## 1 0.1424419 0.1482558
## 2 0.1570122 0.1661585
## X.Product.line.Sports.and.travel X.Unit.price. Quantity Tax
## 1 0.1715116 0.5193478 0.5012920 0.3057288
## 2 0.1631098 0.5009145 0.5010163 0.3009795
## PaymentCash PaymentCredit.card PaymentEwallet cogs X.gross.income.
## 1 1 0.0000000 0.0000000 0.3057288 0.3057288
## 2 0 0.4740854 0.5259146 0.3009795 0.3009795
## Rating Total
## 1 0.4950097 0.3057288
## 2 0.4956809 0.3009795
##
## Clustering vector:
## [1] 2 1 2 2 2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 1 1 2 2 2 2
## [38] 2 2 1 2 1 1 1 1 1 2 2 2 2 1 1 2 2 2 1 1 2 1 1 2 2 2 2 1 1 2 2 1 1 2 1 2 1
## [75] 2 2 2 2 2 1 2 2 2 2 1 2 1 2 1 1 1 2 2 2 2 2 2 1 2 1 1 1 1 1 1 2 2 1 1 1 2
## [112] 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 1 1 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2
## [149] 2 2 2 2 2 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2 2
## [186] 2 2 1 2 2 2 2 1 2 2 1 1 2 2 2 2 1 1 2 2 2 2 2 2 2 2 1 2 2 1 2 1 1 2 2 2 2
## [223] 1 1 1 2 2 2 1 2 1 2 1 1 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 1 1 1 2 2 2
## [260] 2 2 2 1 1 2 2 2 1 2 2 2 1 2 1 2 1 1 2 1 2 2 2 1 2 1 1 1 1 2 1 2 2 1 1 2 1
## [297] 1 2 1 1 2 2 1 2 1 2 1 1 2 1 1 2 2 1 1 1 1 1 2 2 1 1 2 1 2 2 1 1 2 1 1 2 1
## [334] 2 2 2 2 1 2 2 2 2 1 2 1 2 1 1 1 2 2 1 2 1 1 2 2 1 2 1 2 1 2 1 1 1 1 1 1 2
## [371] 1 2 2 1 2 2 2 2 2 2 2 1 1 2 2 1 1 2 2 2 1 1 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2
## [408] 1 2 2 1 2 1 2 2 2 2 2 2 1 2 1 2 2 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
## [445] 1 2 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 2 2 1 2 1 2 1 2 1 1 2 2 2 2 2 1
## [482] 1 2 1 2 2 1 2 1 2 2 2 2 2 2 1 1 1 1 1 2 2 2 1 2 2 1 2 1 2 2 2 2 1 2 2 2 2
## [519] 2 2 2 1 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 1 2 1
## [556] 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 1 2 1 1 2 2 2 2 1 2 1 1 2 2
## [593] 1 2 1 2 2 2 1 2 2 2 2 2 1 1 2 2 2 2 2 1 1 2 2 2 1 2 2 2 2 1 2 2 1 1 2 1 2
## [630] 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 1 1 1 1 2 1 1 2 2 2 2 2 1 2 1 2 2 2 1 2
## [667] 2 2 2 2 2 1 2 2 2 1 2 1 2 2 1 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 2 2 2 2 2 2 2
## [704] 1 1 1 2 1 2 2 1 2 2 2 2 2 2 2 2 2 1 1 2 1 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 1
## [741] 1 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 1 2 2
## [778] 1 1 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 1 1 1 2 1 1 2 2 2 2 1
## [815] 1 2 1 2 2 2 2 2 1 1 2 2 2 2 1 2 1 1 1 2 2 1 2 2 1 2 1 1 2 2 1 2 2 2 1 1 1
## [852] 2 2 2 2 1 1 1 1 1 2 2 2 1 1 2 2 2 2 2 2 2 1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2
## [889] 2 2 1 1 2 1 2 2 2 1 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 1 1 2 1 2 2 2 1 2 2 2
## [926] 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1
## [963] 2 1 2 2 2 2 1 2 2 2 1 1 1 2 1 2 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1
## [1000] 1
##
## Within cluster sum of squares by cluster:
## [1] 1027.784 2297.495
## (between_SS / total_SS = 9.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iterations"
## [9] "total.iterations" "restarts" "weights"
library(cluster)
# Plotting the cluster with 2 as my maximum clusters
fviz_cluster(my_model,data=norm_df[,c(-21)])
# We get to the the importance of each parameter to the individual clusters
(my_model$weights)*10000
## BranchA BranchB BranchC X.Customer.type.Member
## 1 0.04347526 0.04347526 0.04347526 0.04347526
## 2 0.04347410 0.04347410 0.04347410 0.04347410
## X.Customer.type.Normal GenderFemale GenderMale
## 1 0.04347526 0.04347526 0.04347526
## 2 0.04347410 0.04347410 0.04347410
## X.Product.line.Electronic.accessories X.Product.line.Fashion.accessories
## 1 0.04347526 0.04347526
## 2 0.04347410 0.04347410
## X.Product.line.Food.and.beverages X.Product.line.Health.and.beauty
## 1 0.04347526 0.04347526
## 2 0.04347410 0.04347410
## X.Product.line.Home.and.lifestyle X.Product.line.Sports.and.travel
## 1 0.04347526 0.04347526
## 2 0.04347410 0.04347410
## X.Unit.price. Quantity Tax PaymentCash PaymentCredit.card
## 1 0.04347526 0.04347526 0.2538423 3332.763 3332.7630089
## 2 0.04347410 0.04347410 0.0434741 9999.044 0.0434741
## PaymentEwallet cogs X.gross.income. Rating Total
## 1 3332.7630089 0.2538423 0.2538423 0.04347526 0.2538423
## 2 0.0434741 0.0434741 0.0434741 0.04347410 0.0434741
Important variables to cluster one are
Important variables to cluster two are
- Price
- Quantity
- gross Income
- Total