(10 marks) Run the k-means clustering algorithm you implemented in part (1) to cluster the given instances. Vary the value of k from 1 to 9 and compute the Silhouette coefficient for each set of clusters. Plot k in the horizontal axis and the Silhouette coefficient in the vertical axis in the same plot.

instances:

elephant -0.015926 -0.079864 -0.33218 0.034246 0.11045 0.060519 -1.183 -0.70995 -0.15361 -0.17446 0.93593 0.0078221 0.031727 -0.7217 0.43359 0.36841 -0.43511 -0.39504 -0.69145 0.33355 0.17485 -0.10389 0.080768 -0.036019 0.2124 0.031662 -0.43299 0.28058 0.12105 0.23591 0.13806 -0.27256 0.9741 0.1831 0.020634 0.16359 0.7219 0.47769 0.047734 0.10662 0.2102 0.25111 -0.076861 0.40305 -0.33216 0.2655 -0.037451 -0.32964 0.03962 -0.098675 0.48829 -0.42426 -0.27531 0.1097 -0.31698 -0.34979 0.31296 -0.51136 0.41804 -0.49106 -0.59535 -0.50308 -0.1489 0.42512 -0.35379 0.039517 0.22683 -0.16585 0.28121 -0.29296 -0.27428 0.47738 0.010245 -0.23463 0.1659 -0.3689 -0.21445 0.11882 0.41136 0.28073 0.18518 0.45989 0.022551 -0.46109 -0.58158 -0.23942 0.27799 0.37867 0.25308 -0.10543 0.068478 -0.30065 0.38811 0.079914 0.037283 -0.51332 -1.3874 0.4043 -0.017022 -0.90614 0.19555 0.88258 -0.30933 -0.0085321 -0.46503 0.085026 -0.21927 0.27334 -0.00052822 -0.12662 -0.033887 0.22253 0.6525 -0.11693 0.59406 0.36398 0.27413 0.055859 -0.49671 -0.085198 -0.19137 0.42368 -0.26391 0.37165 0.053663 0.10106 -0.091299 -0.04479 -1.1109 -0.076544 0.17498 -0.020006 -0.24345 -0.36349 0.20398 0.12332 -0.029493 -0.44119 -0.1401 -0.060824 -0.40138 0.21532 -0.047053 0.22744 -0.33961 0.45507 0.49286 0.43621 0.41356 -0.3203 -0.24414 -0.30016 0.02418 -0.28821 -0.013389 0.12331 -0.21648 0.36268 0.62189 0.11865 -0.37222 -0.055275 -0.29719 0.69072 -0.23592 0.40409 -0.36423 0.0016781 -0.26082 0.27827 -0.32556 -0.30349 0.40435 0.46626 0.16651 0.12758 0.22869 -0.40285 -0.2055 0.52496 0.070154 -0.22629 -0.31621 0.22349 -0.010595 0.0035198 -0.20594 0.18188 0.53412 -0.0122 0.016205 -0.11435 -0.2725 0.15001 0.034643 0.22791 0.44768 -0.00030027 0.3703 0.063559 -0.0022745 0.14503 -0.37531 -0.08861 -0.36186 0.42031 0.062992 0.42979 0.27918 0.456 0.008074 0.069419 0.38417 -0.018479 -0.0096825 -0.061138 -0.34379 0.13292 0.4005 0.62487 0.17413 0.19394 -0.00104 -0.31137 -2.122 -0.8791 -0.40388 0.59427 -0.14781 -0.017978 0.47091 0.033585 0.055236 0.16153 0.13545 0.020583 0.10521 0.1027 -0.081522 0.58213 0.29933 0.41688 -0.15343 -0.089436 0.13767 -0.51928 0.45975 -0.18187 0.2158 -0.11597 -0.020845 -0.25547 0.17674 0.19649 0.14257 -0.44722 -0.86471 0.22632 0.20872 -0.09886 -0.38476 -0.19554 0.16728 -0.24257 0.58669 0.1582 0.21623 0.47024 -0.44538 -0.25146 0.15605 0.16139 -0.2738 -0.20377 -0.36825 0.22075 0.12964 0.57046 0.15933 -0.60507 0.99795 0.099976 -0.34553 0.24908 0.064574 -0.082871 -0.39993 -0.19822 -0.2159 -0.076771 -0.13267 0.46735 0.086454 0.24495 -0.62127 0.37799 0.70906 -0.023002 0.0039075 -0.035713

leopard 0.47727 -0.91587 -0.2977 -0.22489 0.55337 0.17772 -1.5603 -0.4058 -0.37523 -0.30488 0.45484 0.18073 1.065 -0.12454 -0.017987 -0.17293 -0.60042 -0.65417 -0.62527 -0.41468 -0.23069 -0.44733 -0.078435 0.25037 0.66601 -0.058046 -0.17356 0.4892 -0.11465 0.6862 -0.48702 0.073542 0.7561 0.38503 0.033083 0.37265 0.61407 0.19114 0.20129 -0.31367 0.2116 -0.17352 0.16515 -0.19704 -0.088211 -0.16415 -0.7457 -0.095694 0.11241 0.21467 0.060748 -0.046807 -0.18299 0.060798 0.46598 1.0234 -0.11825 -0.21405 0.65965 -0.84678 -0.092909 0.096912 -0.31338 0.68928 -0.52609 -0.37685 0.25258 0.37184 -0.51236 -0.15685 -0.169 0.59754 -0.45033 -0.013394 -0.015144 -0.20477 0.48002 -0.28724 0.57997 0.70833 0.25624 0.38215 -0.10612 -0.016959 0.19252 -0.048299 -0.11453 0.086922 0.41209 -0.29981 0.149 -0.65507 0.05678 -0.16212 0.59809 -0.49826 -1.1014 -0.224 -0.56247 -0.59904 0.56867 -0.62703 -0.1907 -0.69609 -0.90926 0.48525 -0.26552 1.8189 -0.24093 -0.040318 0.50771 -0.11344 0.48149 -0.087669 -0.27704 0.76473 0.12286 -0.078563 -0.46025 0.010155 -0.53681 0.6575 -0.0067907 0.727 0.1808 0.3111 -0.04129 0.33441 0.30128 0.33277 -0.089382 -0.32726 -0.14145 -0.56331 0.0026564 -0.22227 -0.042816 0.284 0.18983 0.16488 -0.81327 0.24068 0.3082 -0.34852 -0.25067 -0.44684 0.64408 -0.19655 -0.021284 0.075418 -0.2736 -0.11707 -0.026532 -0.076436 0.2906 -0.20111 0.54335 0.087591 0.84843 -0.046216 -0.25161 -0.13894 -0.38518 0.80928 0.043223 0.33801 0.75492 0.14838 -0.082548 -0.12171 -0.53773 -0.035368 -0.074539 0.64088 -0.24902 0.1716 0.13996 -0.25874 -0.73774 0.29913 -0.36709 -0.5926 0.21545 0.15125 0.15954 0.045751 -0.12953 1.0478 -0.13825 -0.23885 0.16589 -0.37044 -0.4627 0.2606 -0.23615 0.42047 0.18098 -0.058899 0.3001 0.27328 -0.058294 -0.14154 -0.38401 0.072529 -0.31949 0.077209 0.032745 0.74006 0.53936 0.17571 0.62872 -0.17703 0.099995 0.2872 0.37005 -0.050739 -0.31043 0.4118 1.1062 0.49014 -0.3923 -0.35836 0.10653 -0.075145 -1.5582 -0.088362 -0.11901 0.11998 0.026831 0.36402 0.21087 -0.18459 0.07094 0.22878 0.24154 -0.20994 0.03198 -0.13268 -0.17195 0.96102 0.57684 0.24384 0.12581 -0.13369 -0.30907 -0.16465 -0.29897 -0.36686 -0.37774 0.21144 -0.51351 -0.1291 0.046269 0.18504 -0.069456 -0.04263 -0.69336 -0.11557 -0.13998 -0.057086 -0.41079 -0.5127 0.37413 -0.19366 0.33239 -0.54822 -0.32037 -0.21488 0.032376 0.091991 0.13695 -0.21717 -0.19996 -0.33318 -0.013634 0.3642 -0.20312 0.31362 0.20962 0.059953 0.29663 0.090515 -0.022796 -0.16755 0.021664 -0.43714 -0.29944 0.38952 -0.24359 -0.013909 -0.10108 0.35108 0.31252 0.1623 0.022012 0.048974 -0.027862 -0.44699 -0.24957 0.02851

dog -0.33575 0.38897 -0.41929 -0.33219 0.5317 -0.25839 -2.3869 -0.43443 -0.3976 -0.99356 0.47093 -0.16265 -0.13474 -1.306 0.34694 0.1215 -0.15811 -0.011231 -0.4656 -0.18031 0.026682 -0.028445 -0.44228 0.20955 0.044307 0.27514 -0.2314 -0.10864 -0.0087113 0.20522 0.36109 -0.35431 0.25217 0.26608 0.11942 -0.21606 0.073164 0.25023 0.24612 0.20797 -0.18702 -0.038054 0.23604 0.42484 0.10187 0.058443 -0.60782 -0.52279 -0.026276 -0.14402 0.22169 -0.1585 -0.81178 0.082893 -0.022136 -0.12966 0.17201 0.62484 -0.023122 -0.15704 -0.41946 -0.49499 0.056224 -0.081352 0.35428 0.15145 -0.26535 0.10071 -1.0047 0.34271 -0.003079 0.35994 0.4007 0.1518 0.11983 -0.30275 0.13739 -0.36725 0.3665 0.31037 0.513 0.20102 -0.34841 0.28565 -0.48071 0.21667 -0.37125 0.60281 0.099829 -0.47562 -0.094234 -0.19625 -0.12658 0.025421 -0.10805 -0.95298 -2.1365 -0.25989 0.2901 -0.14846 -0.06318 -0.16572 0.0073842 -0.30222 -0.28538 0.47556 0.041736 -0.15516 0.39398 -0.60727 0.7889 -0.092844 0.32725 -0.19599 -0.21146 0.023927 -0.17896 -0.065021 0.52246 -0.38243 -0.4467 0.07913 0.82286 0.55868 0.030237 -0.3001 0.48222 0.54899 -0.3224 -0.67086 -0.61622 0.066708 0.30572 0.01517 -0.52623 0.15352 -0.66473 -0.2077 0.25136 0.36206 -0.22424 0.00085694 0.046224 -0.015066 -0.32618 -0.097696 0.021966 0.27861 0.1584 -0.2021 0.072365 -0.1957 -0.26862 0.13854 0.041905 -0.063822 -0.32484 0.055546 0.28501 0.67519 0.30155 -0.50474 -0.67976 0.51983 0.065695 0.025286 -0.096823 -0.052386 -0.057766 0.02108 -0.24691 -0.80533 -0.18712 0.47986 -0.45478 -0.076232 0.63681 -0.46249 0.23123 0.079812 -0.61783 -0.054644 -0.0015799 0.1465 0.053362 -0.04977 -0.63187 -0.11563 0.38775 0.10124 -0.0032881 0.17987 -0.06248 -0.27772 -0.48288 -0.37275 0.61105 -0.3227 0.69697 0.088196 0.44661 -0.0065324 -0.10571 0.946 -0.19661 -0.39961 0.29346 0.1364 0.42281 -0.45546 0.54213 -0.19004 0.55959 -0.39935 0.12659 -0.29526 -0.11524 0.10132 -0.16572 0.38628 -0.25172 0.30096 -0.22338 -0.093883 -3.1209 0.07981 -1.1115 0.16649 -0.23107 -0.12312 0.20972 -0.007045 -0.73021 -0.47405 -0.28147 0.0010118 0.66102 -0.011403 0.031912 0.50367 0.51864 -0.060027 -0.15285 0.73159 -0.5533 -0.16912 -0.063391 0.13858 0.28878 0.15076 -0.22552 0.28992 0.54796 0.1551 0.51603 -0.19686 -0.64146 0.50649 0.70221 -0.21417 0.35252 -0.29347 -0.19962 -0.055284 -0.10027 0.3333 0.49459 0.17876 -0.041699 0.46649 -0.3172 -0.32616 0.12663 -0.4367 -0.54299 -0.10077 -0.26449 0.10524 -0.325 -0.28024 0.49458 -0.0028948 -0.86985 -0.089116 -0.23145 -0.40411 -0.02368 0.24752 0.32651 -0.053385 -0.11501 -0.55804 0.48427 0.25167 -0.068426 0.34227 0.2684 -0.14929 -0.23516 0.039194

cat 0.2111 0.21763 -0.52638 -0.42277 0.84672 -0.038383 -1.9201 -0.30959 0.021942 -0.49525 0.77306 0.16158 -0.19716 -0.57098 -0.053608 0.070278 -0.60636 -0.12083 -0.57444 -0.037019 0.26274 -0.03365 0.12242 -0.14652 0.26033 -0.29463 0.1152 0.036812 0.0034356 -0.00021683 0.55426 -0.50978 0.23785 0.0254 -0.047775 -0.40466 0.2614 -0.34749 0.37919 -0.1943 0.071057 -0.6359 -0.1457 -0.0025429 -0.29784 0.30019 -0.5358 -0.087513 -0.021339 -0.17687 0.19113 -0.30737 -0.56812 0.46192 0.19877 0.20665 -0.093993 0.29382 0.3273 0.05805 -0.73197 -0.77637 0.43869 0.185 0.23261 0.35647 -0.36687 0.0012256 -1.2229 0.36615 -0.036965 0.36553 0.10303 0.13494 -0.032071 -0.37704 0.15676 -0.064954 -0.14425 0.4554 0.69572 0.17424 -0.10686 0.50207 -0.45237 0.18477 -0.12709 0.65327 0.029422 0.16903 -0.13607 -0.66783 -0.15619 -0.0097961 -0.092976 -0.73335 -1.8187 0.026675 0.28343 -0.20409 0.027432 -0.24477 0.1807 0.05601 -0.1484 0.10702 -0.071081 0.035108 -0.24279 -0.2471 0.35338 -0.12025 0.51993 -0.03251 -0.061425 0.27608 -0.10754 -0.058642 -0.21013 -0.32711 -0.56485 0.053328 0.8146 0.89608 0.56984 -0.3665 0.18799 0.071857 -0.24233 -0.405 -0.62646 -0.0054031 0.18839 -0.62807 -0.48526 0.20509 0.01556 -0.055592 -0.31686 0.44582 -0.74506 -0.23464 0.35697 0.27672 -0.034658 -0.29553 0.10892 0.49815 0.04539 -0.41345 0.33444 -0.032795 0.063787 -0.26493 -0.26112 -0.090767 0.1395 -0.45536 0.66697 0.83962 -0.052895 -0.14638 -0.43999 0.53076 0.080568 0.13796 -0.19015 -0.23527 -0.17632 -0.1968 -0.22669 -0.55286 -0.21735 0.55578 -0.37714 -0.17865 0.40321 -0.52347 -0.19288 -0.095479 -0.48039 0.023991 -0.086424 0.14968 -0.12867 0.32547 -0.49989 0.17529 0.39106 -0.19364 0.05909 0.032595 0.24663 -0.35267 -0.28403 -0.47115 0.48414 0.020973 0.59849 0.04387 0.0021328 -0.20931 -0.20211 0.38589 0.39548 0.23038 0.24491 0.27834 0.56828 -0.14234 0.67488 0.0064852 0.029645 -0.28274 0.053661 -0.25656 -0.028487 -0.021258 -0.017985 0.48703 -0.36394 0.11476 -0.26886 -0.28556 -2.9508 -0.25368 -0.87877 -0.041607 -0.30935 -0.2756 0.57268 -0.11079 -0.43844 -0.44036 -0.58429 0.18454 0.77725 0.49392 -0.10841 0.32613 0.35734 0.18962 -0.1369 0.67461 -0.081401 0.24326 0.40665 0.32347 0.040822 0.22333 -0.012498 0.064806 0.032215 -0.1861 0.078454 0.26412 -0.37658 0.42116 0.56942 -0.16653 -0.16693 -0.31635 -0.11354 0.16122 -0.33425 0.56519 0.30971 0.21785 0.37175 0.43842 -0.028513 -0.36783 0.72722 0.21965 -0.51812 0.33716 -0.163 0.34806 -0.12455 -0.4617 0.5857 0.34859 -0.34966 -0.13121 -0.16664 -0.50079 0.0010191 0.35112 0.024121 -0.38078 -0.15757 0.13171 0.63291 -0.32111 -0.04626 -0.17971 -0.0013804 -0.15076 -0.24064 -0.051365