ActivityU10-by-John-Smith.Rmd
Cornelius
6/11/2022
Hierarchical Clustering
Hirarchichal clustering is one of the unsupervised non-linear algorithm where clusters are made with a hierarchy. An example is given of a family where all the family members are grouped together to form a hierachchy. The hierarchical clustering is has two branches the Agglomerative Hierarchichal clustering which is also known as the bottom up approach and the Divisive clustering which is the top down approach. The Agglomerative Hierarchical clustering starts at individual leaves and successfully merges clusters together while the Divisive Hierarchical clustering commence at the root and recursively split the clusters. The hierarchical clustering analysis practice was performed on the Rstudio datasets and the output displayed as follows;
## Warning: package 'dplyr' was built under R version 4.1.3##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10Finding distance matrix
## 1 2 3 4 5 6 7
## 2 8.000000
## 3 3.605551 6.708204
## 4 20.223748 12.369317 18.000000
## 5 14.560220 7.211103 12.041595 6.082763
## 6 9.433981 5.000000 6.324555 12.165525 6.082763
## 7 17.088007 10.000000 14.317821 5.000000 2.828427 8.062258
## 8 24.738634 17.088007 22.203603 5.000000 10.198039 16.031220 8.000000
## 9 32.557641 24.738634 30.149627 12.369317 18.110770 24.020824 16.000000
## 10 16.552945 9.899495 13.601471 6.403124 3.162278 7.280110 1.414214
## 11 26.925824 19.313208 24.331050 7.211103 12.369317 18.110770 10.049876
## 12 14.422205 8.944272 11.180340 9.433981 4.472136 5.000000 4.472136
## 13 19.697716 12.806248 16.763055 5.385165 5.656854 10.440307 2.828427
## 14 23.409400 16.124515 20.615528 5.385165 8.944272 14.317821 6.324555
## 15 27.202941 19.697716 24.515301 7.810250 12.649111 18.248288 10.198039
## 16 25.632011 18.357560 22.803509 7.211103 11.180340 16.492423 8.544004
## 17 33.241540 25.632011 30.594117 13.416408 18.681542 24.331050 16.278821
## 18 33.241540 25.632011 30.594117 13.416408 18.681542 24.331050 16.278821
## 19 44.911023 37.107951 42.426407 24.738634 30.413813 36.221541 28.160256
## 20 26.000000 18.867962 23.086793 8.062258 11.661904 16.763055 8.944272
## 21 35.440090 27.856777 32.756679 15.652476 20.880613 26.476405 18.439089
## 22 58.855756 50.990195 56.435804 38.639358 44.407207 50.249378 42.190046
## 23 78.638413 70.710678 76.321688 58.420887 64.280635 70.178344 62.128898
## 24 21.095023 14.866069 17.888544 8.246211 8.062258 11.661904 5.385165
## 25 26.400758 19.416488 23.409400 8.944272 12.206556 17.088007 9.433981
## 26 53.150729 45.354162 50.635956 32.984845 38.639358 44.407207 36.345564
## 27 32.310989 25.059928 29.410882 13.453624 17.888544 23.086793 15.231546
## 28 39.849718 32.310989 37.107951 20.124612 25.298221 30.805844 22.803509
## 29 32.695565 25.553865 29.732137 14.142136 18.357560 23.409400 15.652476
## 30 40.162171 32.695565 37.363083 20.591260 25.632011 31.048349 23.086793
## 31 49.729267 42.059482 47.074409 29.732137 35.171011 40.792156 32.756679
## 32 42.379240 34.928498 39.560081 22.825424 27.856777 33.241540 25.298221
## 33 55.785303 48.083261 53.150729 35.735137 41.231056 46.872167 38.832976
## 34 75.312682 67.468511 72.835431 55.108983 60.827625 66.610810 58.549125
## 35 83.186537 75.312682 80.752709 62.968246 68.731361 74.545288 66.483081
## 36 37.161808 30.016662 34.176015 18.439089 22.825424 27.856777 20.124612
## 37 46.486557 39.000000 43.680659 26.832816 31.953091 37.363083 29.410882
## 38 67.683085 59.908263 65.115282 47.539457 53.150729 58.855756 50.803543
## 39 34.000000 27.202941 30.870698 16.401219 20.000000 24.596748 17.204651
## 40 48.703183 41.231056 45.880279 29.068884 34.176015 39.560081 31.622777
## 41 52.497619 44.944410 49.729267 32.695565 37.947332 43.416587 35.440090
## 42 56.320511 48.703183 53.600373 36.400549 41.761226 47.296934 39.293765
## 43 64.031242 56.320511 61.392182 43.965896 49.477268 55.108983 47.074409
## 44 66.483081 58.821765 63.788714 46.486557 51.923020 57.489129 49.477268
## 45 55.362442 47.927028 52.497619 35.777088 40.853396 46.173586 38.275318
## 46 70.880181 63.245553 68.154237 50.921508 56.320511 61.846584 53.851648
## 47 92.195445 84.403791 89.627005 72.034714 77.665951 83.360662 75.312682
## 48 93.171884 85.375641 90.609050 73.006849 78.644771 84.344532 76.295478
## 49 119.682914 111.803399 117.239072 99.463561 105.223572 111.018017 102.956301
## 50 85.615419 77.884530 82.975900 65.520989 71.063352 76.687678 68.658576
## 8 9 10 11 12 13 14
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9 8.000000
## 10 9.055385 17.029386
## 11 2.236068 6.082763 11.000000
## 12 12.165525 20.099751 3.162278 14.035669
## 13 6.324555 14.142136 3.162278 8.062258 6.000000
## 14 2.828427 10.198039 7.071068 4.123106 10.000000 4.000000
## 15 2.828427 6.324555 11.045361 1.000000 14.000000 8.000000 4.000000
## 16 3.000000 8.544004 9.219544 2.828427 12.041595 6.082763 2.236068
## 17 8.544004 3.000000 17.117243 6.324555 20.024984 14.035669 10.049876
## 18 8.544004 3.000000 17.117243 6.324555 20.024984 14.035669 10.049876
## 19 20.223748 12.369317 29.068884 18.110770 32.015621 26.019224 22.022716
## 20 4.000000 8.944272 9.486833 3.605551 12.165525 6.324555 2.828427
## 21 10.770330 4.472136 19.235384 8.544004 22.090722 16.124515 12.165525
## 22 34.234486 26.305893 43.104524 32.140317 46.043458 40.049969 36.055513
## 23 54.147945 46.173586 63.071388 52.086467 66.030296 60.033324 56.035703
## 24 7.810250 14.866069 5.000000 8.944272 6.708204 3.000000 5.000000
## 25 5.000000 9.433981 9.848858 4.472136 12.369317 6.708204 3.605551
## 26 28.442925 20.615528 37.215588 26.305893 40.112342 34.132096 30.149627
## 27 8.485281 6.324555 15.811388 6.403124 18.439089 12.649111 8.944272
## 28 15.231546 8.485281 23.537205 13.000000 26.305893 20.396078 16.492423
## 29 9.219544 7.280110 16.155494 7.211103 18.681542 13.000000 9.433981
## 30 15.652476 9.219544 23.769729 13.416408 26.476405 20.615528 16.763055
## 31 25.000000 17.464249 33.541020 22.803509 36.345564 30.413813 26.476405
## 32 17.888544 11.313708 25.961510 15.652476 28.635642 22.803509 18.973666
## 33 31.048349 23.409400 39.623226 28.861739 42.426407 36.496575 32.557641
## 34 50.635956 42.755117 59.413803 48.507731 62.289646 56.320511 52.345009
## 35 58.549125 50.635956 67.364679 56.435804 70.256672 64.280635 60.299254
## 36 13.453624 9.219544 20.615528 11.313708 23.086793 17.464249 13.892444
## 37 21.931712 15.000000 30.083218 19.697716 32.756679 26.925824 23.086793
## 38 42.953463 35.171011 51.623638 40.792156 54.451814 48.507731 44.553339
## 39 11.661904 10.198039 17.492856 9.848858 19.697716 14.422205 11.313708
## 40 24.166092 17.204651 32.280025 21.931712 34.928498 29.120440 25.298221
## 41 27.856777 20.591260 36.138622 25.632011 38.832976 32.984845 29.120440
## 42 31.622777 24.166092 40.024992 29.410882 42.755117 36.878178 32.984845
## 43 39.293765 31.622777 47.853944 37.107951 50.635956 44.721360 40.792156
## 44 41.761226 34.176015 50.219518 39.560081 52.952809 47.074409 43.174066
## 45 30.870698 23.853721 38.897301 28.635642 41.484937 35.735137 31.953091
## 46 46.173586 38.626416 54.571055 43.965896 57.271284 51.419841 47.539457
## 47 67.468511 59.665736 76.118329 65.306967 78.917679 72.993150 69.050706
## 48 68.447060 60.638272 77.103826 66.287254 79.906195 73.979727 70.035705
## 49 95.036835 87.132084 103.817147 92.913939 106.677083 100.717426 96.747093
## 50 60.876925 53.160135 69.426220 58.694122 72.180330 66.287254 62.369865
## 15 16 17 18 19 20 21
## 2
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## 16 2.236068
## 17 6.082763 8.000000
## 18 6.082763 8.000000 0.000000
## 19 18.027756 20.000000 12.000000 12.000000
## 20 2.828427 1.000000 8.062258 8.062258 20.024984
## 21 8.246211 10.049876 2.236068 2.236068 10.049876 10.000000
## 22 32.062439 34.014703 26.019224 26.019224 14.035669 34.000000 24.000000
## 23 52.038447 54.009258 46.010868 46.010868 34.014703 54.000000 44.000000
## 24 8.544004 6.324555 14.142136 14.142136 26.076810 6.082763 16.031220
## 25 3.605551 2.000000 8.246211 8.246211 20.099751 1.000000 10.049876
## 26 26.172505 28.071338 20.099751 20.099751 8.246211 28.017851 18.027756
## 27 5.656854 6.708204 3.605551 3.605551 14.317821 6.324555 4.472136
## 28 12.649111 14.317821 6.708204 6.708204 6.708204 14.142136 4.472136
## 29 6.403124 7.211103 4.472136 4.472136 14.560220 6.708204 5.000000
## 30 13.000000 14.560220 7.211103 7.211103 7.211103 14.317821 5.000000
## 31 22.561028 24.331050 16.492423 16.492423 5.656854 24.186773 14.317821
## 32 15.231546 16.763055 9.433981 9.433981 6.403124 16.492423 7.211103
## 33 28.635642 30.413813 22.561028 22.561028 11.180340 30.265492 20.396078
## 34 48.373546 50.249378 42.296572 42.296572 30.413813 50.159745 40.199502
## 35 56.320511 58.215118 50.249378 50.249378 38.327536 58.137767 48.166378
## 36 10.630146 11.661904 6.324555 6.324555 11.661904 11.180340 5.000000
## 37 19.313208 20.880613 13.416408 13.416408 6.000000 20.615528 11.180340
## 38 40.607881 42.426407 34.525353 34.525353 22.803509 42.296572 32.388269
## 39 8.944272 9.219544 7.280110 7.280110 15.652476 8.485281 7.211103
## 40 21.540659 23.086793 15.652476 15.652476 7.280110 22.803509 13.416408
## 41 25.298221 26.925824 19.313208 19.313208 9.219544 26.683328 17.088007
## 42 29.120440 30.805844 23.086793 23.086793 12.206556 30.594117 20.880613
## 43 36.878178 38.639358 30.805844 30.805844 19.313208 38.470768 28.635642
## 44 39.293765 41.000000 33.241540 33.241540 21.931712 40.792156 31.048349
## 45 28.231188 29.732137 22.360680 22.360680 12.806248 29.410882 20.124612
## 46 43.680659 45.354162 37.643060 37.643060 26.400758 45.122057 35.440090
## 47 65.115282 66.910388 59.033889 59.033889 47.296934 66.753277 56.885851
## 48 66.098411 67.896981 60.016664 60.016664 48.270074 67.742158 57.870545
## 49 92.779308 94.641429 86.700634 86.700634 74.813100 94.530418 84.593144
## 50 58.463664 60.207973 52.392748 52.392748 40.804412 60.016664 50.219518
## 22 23 24 25 26 27 28
## 2
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## 23 20.000000
## 24 40.012498 60.008333
## 25 34.014703 54.009258 6.000000
## 26 6.082763 26.019224 34.000000 28.000000
## 27 28.071338 48.041649 12.041595 6.082763 22.022716
## 28 20.099751 40.049969 20.024984 14.035669 14.035669 8.000000
## 29 28.160256 48.093659 12.165525 6.324555 22.090722 1.000000 8.062258
## 30 20.223748 40.112342 20.099751 14.142136 14.142136 8.062258 1.000000
## 31 10.440307 30.149627 30.066593 24.083189 4.472136 18.027756 10.049876
## 32 18.439089 38.209946 22.203603 16.278821 12.369317 10.198039 2.828427
## 33 5.656854 24.331050 36.124784 30.149627 3.605551 24.083189 16.124515
## 34 16.492423 5.656854 56.080300 50.089919 22.203603 44.045431 36.055513
## 35 24.331050 5.656854 64.070274 58.077534 30.149627 52.038447 44.045431
## 36 24.515301 44.283180 16.492423 10.770330 18.439089 5.000000 5.000000
## 37 14.866069 34.365681 26.305893 20.396078 8.944272 14.317821 6.708204
## 38 9.433981 13.000000 48.166378 42.190046 14.560220 36.124784 28.160256
## 39 28.635642 48.373546 13.000000 7.810250 22.561028 4.000000 8.944272
## 40 13.416408 32.557641 28.442925 22.561028 7.810250 16.492423 8.944272
## 41 10.000000 28.635642 32.388269 26.476405 5.385165 20.396078 12.649111
## 42 7.211103 24.738634 36.345564 30.413813 5.385165 24.331050 16.492423
## 43 7.211103 17.088007 44.283180 38.327536 11.180340 32.249031 24.331050
## 44 10.000000 16.124515 46.529560 40.607881 13.892444 34.525353 26.683328
## 45 10.816654 27.513633 34.928498 29.120440 8.000000 23.086793 15.652476
## 46 14.142136 14.142136 50.803543 44.911023 18.357560 38.832976 31.048349
## 47 33.526109 15.620499 72.560320 66.610810 39.051248 60.530984 52.611786
## 48 34.481879 16.401219 73.552702 67.601775 40.024992 61.522354 53.600373
## 49 60.827625 41.231056 100.404183 94.429868 66.610810 88.362888 80.399005
## 50 27.313001 12.083046 65.764732 59.841457 32.572995 53.758720 45.891176
## 29 30 31 32 33 34 35
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## 30 8.000000
## 31 18.000000 10.000000
## 32 10.049876 2.236068 8.062258
## 33 24.020824 16.031220 6.082763 14.000000
## 34 44.011362 36.013886 26.019224 34.000000 20.000000
## 35 52.009614 44.011362 34.014703 42.000000 28.000000 8.000000
## 36 4.472136 4.472136 14.142136 6.082763 20.024984 40.012498 48.010416
## 37 14.142136 6.324555 4.472136 4.123106 10.049876 30.016662 38.013156
## 38 36.055513 28.071338 18.110770 26.019224 12.041595 8.062258 16.031220
## 39 3.000000 8.544004 18.248288 10.198039 24.083189 44.045431 52.038447
## 40 16.278821 8.544004 3.605551 6.324555 8.246211 28.071338 36.055513
## 41 20.223748 12.369317 3.605551 10.198039 4.472136 24.083189 32.062439
## 42 24.186773 16.278821 6.708204 14.142136 2.000000 20.099751 28.071338
## 43 32.140317 24.186773 14.317821 22.090722 8.246211 12.165525 20.099751
## 44 34.365681 26.476405 16.763055 24.331050 10.770330 10.770330 18.439089
## 45 22.803509 15.231546 7.211103 13.000000 5.385165 22.561028 30.413813
## 46 38.639358 30.805844 21.189620 28.635642 15.231546 8.485281 15.231546
## 47 60.406953 52.469038 42.579338 50.358713 36.496575 17.088007 10.000000
## 48 61.400326 53.460266 43.566042 51.351728 37.483330 18.027756 10.816654
## 49 88.277970 80.305666 70.349129 78.230429 64.280635 44.407207 36.496575
## 50 53.600373 45.705580 35.902646 43.566042 29.832868 11.401754 7.071068
## 36 37 38 39 40 41 42
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## 37 10.000000
## 38 32.000000 22.000000
## 39 4.123106 14.035669 36.013886
## 40 12.041595 2.236068 20.024984 16.000000
## 41 16.031220 6.082763 16.031220 20.000000 4.000000
## 42 20.024984 10.049876 12.041595 24.000000 8.000000 4.000000
## 43 28.017851 18.027756 4.123106 32.000000 16.000000 12.000000 8.000000
## 44 30.149627 20.223748 3.605551 34.058773 18.110770 14.142136 10.198039
## 45 18.439089 8.944272 14.560220 22.203603 6.708204 3.605551 3.605551
## 46 34.365681 24.515301 5.385165 38.209946 22.360680 18.439089 14.560220
## 47 56.222771 46.270941 24.515301 60.133186 44.181444 40.199502 36.221541
## 48 57.218878 47.265209 25.495098 61.131007 45.177428 41.194660 37.215588
## 49 84.148678 74.168727 52.239832 88.090862 72.111026 68.117545 64.124878
## 50 49.365980 39.458839 18.027756 53.235327 37.336309 33.376639 29.427878
## 43 44 45 46 47 48 49
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## 44 2.828427
## 45 10.440307 12.041595
## 46 7.211103 4.472136 16.031220
## 47 28.284271 26.076810 38.013156 22.000000
## 48 29.274562 27.073973 39.012818 23.000000 1.000000
## 49 56.142675 54.037024 66.007575 50.000000 28.000000 27.000000
## 50 21.587033 19.235384 31.064449 15.033296 7.071068 8.062258 35.014283Fitting Hierarchical clustering Model
##
## Call:
## hclust(d = distance_mat, method = "average")
##
## Cluster method : average
## Distance : euclidean
## Number of objects: 50The model has it that, the cluster method is average, distance is euclidean and no. of objects are 50. ## Plotting dendrogram
The plot dendrogram is shown with x-axis as distance matrix and y-axis as height.
Differences between HCA and k means
HCA can’t handle big data as well as kmeans
Results are responsible in hierarchical clustering unlike kmeans.
*K means mostly works well with globular clusters.
## Linkage The linkage methods in statistics is applied by evaluating the distances or similarities between all objects. Then the closest pair of clusters are combined into a single cluster, reducing the number of clusters remaining. The process is then repeated until there is only a single cluster left.
MARKET BASKET ANALYSIS
It is the investigation of any collection of commodities to uncover affinities that may be exploited.
Market Basket Analysis uses the information to:
Capable of recognizing customer purchasing patterns
To identify who customers are(not by name)
Understand why you buy certain items.
The Groceries Dataset
The Groceries dataset has been used in this analysis and all the out put generetad accordingly.
## Warning: package 'arules' was built under R version 4.1.3## Loading required package: Matrix##
## Attaching package: 'arules'## The following object is masked from 'package:dplyr':
##
## recode## The following objects are masked from 'package:base':
##
## abbreviate, write## Warning: package 'arulesViz' was built under R version 4.1.3## Formal class 'transactions' [package "arules"] with 3 slots
## ..@ data :Formal class 'ngCMatrix' [package "Matrix"] with 5 slots
## .. .. ..@ i : int [1:43367] 13 60 69 78 14 29 98 24 15 29 ...
## .. .. ..@ p : int [1:9836] 0 4 7 8 12 16 21 22 27 28 ...
## .. .. ..@ Dim : int [1:2] 169 9835
## .. .. ..@ Dimnames:List of 2
## .. .. .. ..$ : NULL
## .. .. .. ..$ : NULL
## .. .. ..@ factors : list()
## ..@ itemInfo :'data.frame': 169 obs. of 3 variables:
## .. ..$ labels: chr [1:169] "frankfurter" "sausage" "liver loaf" "ham" ...
## .. ..$ level2: Factor w/ 55 levels "baby food","bags",..: 44 44 44 44 44 44 44 42 42 41 ...
## .. ..$ level1: Factor w/ 10 levels "canned food",..: 6 6 6 6 6 6 6 6 6 6 ...
## ..@ itemsetInfo:'data.frame': 0 obs. of 0 variablesCreate an item frequency plot for the top 20 items
Lets explore the data before we make any rules 
## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 0.001 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 9
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [157 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.02s].
## writing ... [410 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 0.001 1
## maxlen target ext
## 3 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 9
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.01s].
## sorting and recoding items ... [157 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3## Warning in apriori(Groceries, parameter = list(supp = 0.001, conf = 0.8, :
## Mining stopped (maxlen reached). Only patterns up to a length of 3 returned!## done [0.01s].
## writing ... [29 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].Redundancies
Rules will be repeated sometimes. Redundancy means one item could be specified. You have the option of removing the item from the dataset. Otherwise, redundant rules generated can be removed. These repeated rules can be deleted using the following code snippet.
## Warning in `[<-`(`*tmp*`, as.vector(i), value = NA): x[.] <- val: x is
## "ngTMatrix", val not in {TRUE, FALSE} is coerced; NA |--> TRUE.Targeting Items
Since we can generate rules then we minimize the output, we therefore look at the rules. For example we can choose our interested target “all milk”
## lhs rhs support confidence coverage lift count
## [1] {rice,
## sugar} => {whole milk} 0.001220132 1 0.001220132 3.913649 12
## [2] {canned fish,
## hygiene articles} => {whole milk} 0.001118454 1 0.001118454 3.913649 11
## [3] {root vegetables,
## butter,
## rice} => {whole milk} 0.001016777 1 0.001016777 3.913649 10
## [4] {root vegetables,
## whipped/sour cream,
## flour} => {whole milk} 0.001728521 1 0.001728521 3.913649 17
## [5] {butter,
## soft cheese,
## domestic eggs} => {whole milk} 0.001016777 1 0.001016777 3.913649 10## lhs rhs support confidence coverage lift
## [1] {whole milk} => {other vegetables} 0.07483477 0.2928770 0.255516 1.513634
## [2] {whole milk} => {rolls/buns} 0.05663447 0.2216474 0.255516 1.205032
## [3] {whole milk} => {yogurt} 0.05602440 0.2192598 0.255516 1.571735
## [4] {whole milk} => {root vegetables} 0.04890696 0.1914047 0.255516 1.756031
## [5] {whole milk} => {tropical fruit} 0.04229792 0.1655392 0.255516 1.577595
## count
## [1] 736
## [2] 557
## [3] 551
## [4] 481
## [5] 416Visualization
