(10 marks) Run the k-means++ clustering algorithm 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:

baboon 0.024381 -0.25704 -0.17484 0.1595 -0.10039 -0.14013 -0.14975 -0.098324 0.13771 -0.32334 0.73675 0.22851 -0.20929 -0.48092 0.26737 0.15829 -0.57243 -0.52613 -0.55734 0.14291 0.45114 -0.80091 0.28912 0.069717 0.12698 0.11443 -0.11273 -0.092734 0.0025172 0.006852 -0.17274 -0.1625 0.68705 -0.18158 0.2057 0.21783 0.10103 0.76089 0.071789 -0.73079 0.19514 0.092091 -0.14542 -0.61356 -0.045183 0.039628 0.40823 0.044321 0.057152 0.19718 0.17802 -0.37666 -0.31716 0.89145 -0.51495 0.20305 0.85553 -0.057081 0.27727 -0.50159 -0.46154 -0.62078 -0.0092805 -0.035735 -0.45353 0.16957 -0.33002 0.052288 0.075321 0.13582 -0.011073 0.11058 -0.23741 -0.57562 -0.30195 0.20553 0.1706 -0.39796 0.23519 0.072052 0.20807 0.058815 -0.18437 -0.21356 -0.21409 -0.43421 0.25475 0.28255 0.15387 -0.47699 0.0051439 0.27284 -0.44194 -0.31002 0.26096 -0.43915 -0.20059 0.55618 0.029926 0.091113 0.25856 0.38545 0.27601 -0.00078012 -0.28265 0.31195 0.31486 0.13587 0.30599 0.23861 -0.44381 -0.22208 0.10096 -0.03718 -0.014359 -0.14223 0.28411 0.35328 0.013749 0.031331 -0.7473 0.36938 0.039471 0.37993 0.11565 -0.064877 0.071188 0.61026 -0.8215 0.34785 -0.44251 -0.15766 0.10141 -0.37658 -0.16978 0.13551 -0.18864 -0.25268 0.21509 0.27291 -0.078716 0.078918 0.037612 0.22352 -0.083982 0.093558 -0.07874 0.40701 0.31904 -0.091478 -0.28537 -0.30462 0.34372 -0.73835 -0.33105 -0.11618 -0.39744 -0.15928 0.59507 0.12249 -0.21616 0.16317 -0.28482 0.28961 0.20309 0.25418 -0.28048 -0.073073 -0.28648 0.1592 0.11623 -0.31536 0.32453 0.46294 0.37358 0.16455 0.26077 -0.85493 -0.99599 0.048289 0.093838 -0.36656 -0.097094 -0.031534 -0.089378 0.23804 0.085218 -0.10688 0.48672 -0.25265 0.16502 0.13794 0.32878 -0.064312 -0.26377 -0.18715 0.046275 0.29376 0.1051 -0.40011 -0.11914 0.42404 0.10195 -0.48473 0.13258 0.43079 -0.40941 0.29434 0.50121 0.35985 -0.26469 -0.088336 -0.084051 -0.13526 -0.38032 -0.20407 0.080193 -0.40087 0.82536 0.58307 -0.50617 0.19974 -0.58824 -0.48423 -0.3152 -0.15859 -0.49027 0.0072953 -0.10747 -0.14411 -0.13865 -0.11504 0.34521 -0.22456 -0.21017 0.078437 0.24526 0.016978 0.19365 0.49317 0.16722 0.73004 0.043865 -0.18819 -0.18338 -0.29218 -0.21811 -0.30459 0.56204 1.2319 0.088727 -0.5933 -0.02688 0.86848 0.27266 -0.65837 -0.63814 0.43819 0.22543 0.25716 -0.025459 -0.34117 -0.61086 -0.11611 0.068997 0.26028 -0.82152 -0.28872 0.052731 0.097854 0.21085 0.34192 0.076079 -0.27178 0.25937 -0.025835 0.092208 0.72561 0.56336 0.17059 0.69139 -0.044171 0.038502 0.12926 0.1974 -0.055539 -0.03309 0.19822 -0.046203 -0.065178 -0.30571 0.29579 -0.63766 0.27666 -0.15911 0.37668 0.9075 -0.0444 -0.30247 0.18084

bear -0.41044 -0.19597 -0.012241 0.083717 -0.59795 -0.10726 -2.0542 -0.28523 0.32217 -0.80038 0.30767 0.28796 -0.018168 -0.54969 -0.067746 -0.11492 0.26071 0.18208 0.16057 0.14394 0.42632 -0.52072 0.25233 0.2672 -0.31511 0.13853 -0.088934 0.7419 0.27738 0.1829 -0.22921 0.1515 0.56262 0.30922 0.21134 0.47241 0.35654 0.3375 -0.54762 -0.11631 0.087479 0.0361 -0.13327 0.39181 -0.45236 -0.18059 -0.21021 -0.15297 0.2272 0.26222 0.46811 -0.21561 -0.23517 0.68993 0.36135 0.24974 -0.0060859 -0.10347 -0.097298 -0.14304 -0.41823 -0.40693 -0.35854 0.41666 -0.62661 -0.13718 0.075982 0.039974 -0.0077233 -0.011034 -0.16118 0.38357 0.46287 0.15494 0.11334 -0.49186 0.02235 -0.26287 0.83105 0.52649 -0.067135 0.49735 -0.48043 -0.076038 0.22932 -0.25599 0.0026345 0.59884 0.21157 -0.16023 0.53461 0.02659 0.43241 -0.29149 -0.025366 -0.64727 -1.8372 -0.077598 0.54179 -0.59861 -0.35948 0.29402 0.070091 -0.45013 -0.075259 0.044498 0.069899 -0.38389 -0.092545 -0.038198 0.17174 -0.17309 -0.13342 -0.24711 0.69168 0.052375 -0.12066 -0.4025 -0.63502 0.16861 -0.33054 0.24358 -0.31646 0.030893 0.69765 0.039574 0.054145 -0.10713 -0.43983 0.16706 -0.17588 -0.16741 -0.28076 0.18578 0.51079 0.19238 0.42415 -0.63652 0.11681 0.53019 -0.20604 0.032795 0.14853 -0.20142 0.29755 -0.20408 0.0088149 0.45379 0.68736 -0.12303 0.51661 -0.20863 0.16416 0.25857 0.24845 0.018574 -0.2869 0.24959 0.36225 -0.061244 -0.33474 -0.044665 -0.21157 0.55203 -0.20543 -0.013623 0.30052 0.32182 -0.21759 -0.098131 -0.16301 -0.76776 -0.19664 0.44813 0.11803 -0.13705 0.31048 -0.47909 0.041141 -0.3847 0.13652 -0.069978 -0.10926 0.32176 -0.22871 0.20088 -0.45805 0.36725 -0.18987 -0.29437 -0.12215 0.01233 -0.53627 -0.58068 -0.36588 -0.14963 0.36094 0.36647 0.40504 0.031621 0.51973 -0.048877 0.013615 0.24357 -0.010523 0.28545 0.17441 0.39911 0.40962 -0.15226 0.27253 -0.58752 0.66947 0.17536 -0.044935 -0.22277 0.2281 0.66886 0.55373 -0.010188 0.21846 0.43444 -0.18421 0.19938 -2.782 -0.33308 -0.55712 -0.17002 0.011995 -0.14979 0.54387 -0.30035 -0.41877 -0.18769 0.41164 0.094462 0.14821 -0.10714 0.027588 -0.024872 0.16376 0.10035 0.29718 0.09105 0.018737 0.10736 -0.47117 0.33764 0.49972 0.17254 -0.28546 0.38117 0.10069 0.39373 0.080213 -0.21792 -0.12956 0.25298 -0.15178 -0.090761 -0.63733 0.13816 -0.3729 0.17748 -0.0068847 0.39226 0.2585 -0.40147 -0.17444 0.44314 -0.33091 -0.22827 -0.15532 -0.10802 -0.25772 0.27866 -0.25997 0.11733 0.40366 -0.52178 0.40787 -0.069771 -0.56997 0.23473 0.058293 -0.3276 -0.60678 0.46819 -0.060487 0.32174 0.082006 0.53562 0.06701 0.52636 -0.15388 -0.021983 0.39553 -0.33171 -0.045919 0.31322

bat -0.23368 0.12823 -0.13186 0.56226 0.72904 0.076742 -1.6554 -0.086032 -0.41883 -0.057504 0.54242 0.025744 -0.22126 -0.34469 0.46576 0.068388 -0.37072 0.011167 -0.1885 -0.3465 0.22375 -0.20154 -0.029037 0.073654 -0.18157 -0.28773 -0.45881 0.025478 0.84279 0.30621 0.23221 0.26273 0.059376 -0.47045 0.38708 0.25501 0.64451 -0.029159 0.16477 -0.014281 -0.30512 0.86901 -1.1886 0.81413 -0.16084 0.10659 0.70443 0.34037 -0.33233 0.48607 0.26077 0.35454 0.17926 0.28666 -0.078171 -0.65724 0.31908 0.27482 -0.25911 -0.84436 -0.37035 -0.12726 0.1668 0.45356 -0.34444 -0.17874 0.18465 0.1721 0.21739 0.20694 -0.24376 0.16876 -0.11776 -0.40765 -0.013393 -0.3525 0.59161 0.33897 -0.24811 0.24717 -0.22136 0.26474 -0.063749 -0.090558 -0.47343 -0.31342 0.29846 0.29561 0.15655 -0.23965 -0.66214 -0.08733 0.27152 0.068733 0.23538 -0.81152 -1.1473 0.21893 -0.296 -0.62049 0.28937 -0.20592 -0.18965 0.19927 0.33309 -0.21678 -0.081617 0.07007 -0.48993 0.011982 -0.24144 0.55544 -0.30985 0.31048 0.20508 -0.076615 -0.52467 0.34498 0.22387 -0.046575 -0.15922 -0.20184 -0.24585 0.43052 0.03363 -0.43968 0.036845 0.50299 -0.43565 0.093161 0.29525 -0.23746 0.32527 -0.60145 -0.21055 -0.15451 -0.37027 0.12231 -0.29482 0.31494 0.029645 0.098646 0.0099514 0.76549 0.14866 -0.46288 -0.10088 0.56511 -0.12096 -0.36389 -0.1954 0.72885 0.4908 -0.25044 0.13553 0.16672 -0.37271 0.62627 0.22739 -0.064227 -0.46684 -0.19088 -0.4748 0.34136 -0.60755 0.21896 -0.53716 -0.66354 0.30117 0.37715 -0.43852 -0.46933 -0.1023 0.45937 0.27994 -0.035668 -0.082453 0.41415 -0.66155 0.039534 -0.052157 -0.50769 0.50464 0.54152 0.13807 0.20314 -0.016809 0.087883 0.045418 0.047816 -0.013542 -0.18727 0.4675 0.12636 -0.096819 -0.2804 -0.16199 -0.0020822 0.33256 0.087062 0.24516 0.083417 -0.44102 -0.15723 -0.43744 0.30536 0.15781 -0.094552 0.19264 0.25419 0.34477 -0.5481 0.064518 -0.17219 0.69226 0.20781 0.32596 0.036121 0.091125 0.35831 0.21137 0.021466 0.24129 0.044402 -2.2217 -0.44754 -0.09028 -0.28194 -0.036407 0.43875 -0.2354 -0.50817 -0.2172 0.024458 -0.31452 0.5186 -0.45528 0.40237 0.83851 0.097076 0.17276 0.79505 0.4693 0.17169 -0.7965 0.56543 -0.12987 0.48786 0.034357 0.46672 -0.11907 -0.8635 -0.2478 0.11528 -0.0091465 -0.59633 0.020092 -0.21874 -0.09095 -0.054318 -0.045734 0.34494 0.71151 -0.046171 -0.17727 0.17657 -0.16628 -0.061923 0.34496 0.070112 0.4434 -0.019464 0.70041 0.52434 0.46343 -0.18128 0.17271 0.4308 -0.55399 -0.66883 0.63401 0.30291 0.40579 0.012541 0.35025 -0.1843 -0.048953 0.20925 -0.50904 0.11675 -0.88846 -0.11581 -0.12398 -0.12958 0.34837 -0.17167 0.26288 -0.20873 0.091751 0.50305

butterfly 0.070648 -0.57851 -0.90726 0.10215 0.69148 0.040074 -1.1973 -0.65287 -0.1753 -0.24311 0.36115 -0.15642 0.27646 -0.046325 0.10171 -0.29059 -0.32595 0.048262 -0.39335 0.32119 0.15199 -0.45655 0.24407 -0.24379 0.89718 -0.19406 -0.087462 0.69564 -0.023637 -0.052175 0.50044 -0.35369 -0.029591 -0.1919 0.024488 0.017198 0.55724 -0.38165 0.141 0.66374 -0.080538 0.19081 0.332 -0.11475 -0.055013 -0.39443 -0.35776 -0.15986 -0.092676 -0.16471 -0.16482 -0.025144 0.37448 0.30512 0.039582 0.090394 0.30916 0.44094 0.72134 -0.34347 -0.051664 -0.14801 -0.3621 -0.074667 -0.27767 -0.34831 -0.089578 0.16454 -0.60715 0.36985 -0.5763 0.58656 0.1778 0.20209 -0.032924 -0.75922 0.068901 0.40373 0.58566 0.54161 -0.12986 0.66262 -0.24787 0.20212 -0.078725 0.33982 -0.10352 -0.4228 -0.2783 0.19236 0.45815 0.065253 0.097663 -0.081418 0.15506 -0.33226 -1.6936 0.56822 -0.083409 -0.50323 0.56953 0.0077068 0.45346 -0.52397 -0.46208 -0.43187 -0.41092 0.78749 0.29048 -0.12774 0.20324 -0.05034 0.53853 0.54914 0.27674 0.70897 0.027112 -0.086424 -0.75654 0.0068564 0.0024212 -0.21954 -0.22943 0.21641 0.29457 0.098628 -0.40742 0.041845 -0.19345 -0.2406 0.31593 0.29992 -0.45308 -0.38672 -0.18185 0.20144 0.60579 -0.53846 -0.23017 0.68163 -0.47739 0.066733 0.35619 -0.054953 0.17834 -0.40476 -0.25447 0.047845 0.88911 0.10941 -0.79818 -0.050177 0.32878 -0.26474 -0.0060458 0.23604 -0.2656 -0.55324 -0.23208 0.17016 -0.11013 0.28665 -0.21296 0.095298 -0.88637 0.17611 -0.5295 0.090866 0.25634 0.073273 -0.35426 0.27764 0.012377 0.20269 0.00060103 0.40186 0.039934 -0.011268 -0.67941 0.20729 -0.24762 -0.0452 0.24467 0.13828 0.008927 -0.26778 -0.093547 -0.53352 -0.22255 0.027586 -0.31033 0.57063 -0.021747 0.22627 0.085127 0.30571 0.27552 0.37138 0.17041 0.022938 0.045261 -0.15928 0.4136 -0.3348 -0.193 0.27552 -0.23392 0.27918 -0.24377 0.74065 -0.43198 -0.077703 0.017444 0.73499 0.46694 -0.37194 0.33282 -0.45278 -0.10594 0.29135 0.26728 -0.10813 0.20893 -0.23222 -2.0899 -0.89363 0.045515 0.63911 -0.13324 0.30047 0.06444 -0.23238 -0.22665 -0.21684 -0.43764 0.18404 -0.054769 -0.44143 0.18835 0.52008 0.55419 0.2136 0.67464 0.1365 -0.16825 -0.60275 0.5102 0.3977 0.11563 0.33214 -0.29681 -0.092345 -0.30954 -0.2347 0.6044 0.093208 -0.1267 0.37602 -0.22829 0.41265 -0.8332 -0.20613 0.15814 0.042047 -0.072134 0.28664 0.1713 -0.11328 -0.048886 0.0096486 0.17819 0.31017 0.24535 0.064199 0.47412 -0.30396 0.025289 0.49804 0.026042 0.090132 0.69798 0.06159 -0.066379 -0.37763 0.7544 -0.068795 -0.034186 0.7117 0.40201 0.2951 -0.0061702 0.50787 0.19551 -0.12818 -0.27271 -0.067378 0.29641 0.2268 -0.023719 0.53886

camel -0.0054036 -0.56333 -0.2145 0.060838 0.049263 0.53287 -0.94061 -0.47999 0.042311 -0.35047 0.56581 -0.048963 0.8984 -0.88139 0.20364 0.40131 -0.15361 -0.3181 -0.34545 -0.15474 -0.040746 -0.6502 0.075975 -0.37421 0.34818 0.016768 -0.048186 0.025694 -0.046044 0.39473 0.3488 -0.071366 0.35755 0.1135 -0.44242 -0.07911 -0.30281 0.10572 0.47017 -0.33314 -0.10178 0.099841 -0.30004 -0.20945 -0.15313 0.34446 0.35314 -0.30114 -0.072913 0.23523 0.32349 -0.67715 -0.023946 -0.14355 0.2319 0.33971 0.13888 -0.36548 0.68535 -0.43642 -0.22602 -0.22796 -0.16661 0.47827 0.15987 0.87804 0.61074 0.20497 0.60532 0.083688 -0.33019 0.12833 -0.13736 0.12569 -0.24696 -0.48385 0.056333 0.033648 -0.29165 0.32719 -0.15565 0.93422 0.14081 0.22226 -0.4222 -0.33861 -0.13154 0.43499 0.26886 -0.33257 -0.23582 0.0027932 0.31293 0.028485 -0.15301 -0.39968 -1.2737 0.094307 0.52706 -0.44263 0.8379 0.38775 -0.32271 -0.18517 -0.35827 -0.060432 0.4576 -0.14149 -0.087309 0.092532 -0.10253 0.062701 0.37817 -0.59479 0.10788 0.33133 0.37069 0.2819 -0.089027 -0.007533 0.19593 0.25043 0.12424 -0.31438 -0.011347 0.14342 0.42111 0.48861 -0.5727 0.26115 0.13081 -0.24878 -0.17921 0.043057 -0.36322 0.021669 -0.18045 -0.16827 -0.0759 0.50327 -0.56226 -0.090352 -0.073791 -0.094552 -0.60814 0.11988 0.64858 0.16278 0.22622 -0.37472 0.010588 -0.00037971 0.00067766 -0.23942 0.037741 -0.46268 -0.070566 -0.21061 0.87256 -0.35418 0.058925 -0.22605 -0.064902 0.58011 -0.039055 -0.39856 -0.077305 -0.85496 -0.04927 0.018649 -0.19778 0.25206 -0.27465 0.0038631 -0.43609 0.21872 0.3939 0.18548 -0.44338 0.29679 0.028492 -0.19765 0.10322 -0.45173 0.0776 0.13422 0.52124 0.1774 0.1117 0.18604 0.40868 -0.5161 -0.52269 0.12032 0.19516 0.081604 0.85593 -0.24842 -0.1486 0.068467 0.08277 -0.12931 0.31236 0.25279 -0.21456 0.11995 -0.7297 -0.21522 0.36477 -0.19134 0.3432 -0.21153 -0.35289 0.76849 0.39045 0.38957 -0.36081 0.37089 0.16984 0.43012 0.26903 -0.21663 -0.38402 -0.60153 -1.6358 -1.3663 -0.74934 -0.18387 -0.043273 -0.023586 -0.058104 0.12452 0.41781 0.59641 -0.0050597 -0.66816 -0.54004 0.41239 -0.52864 0.35109 0.28499 -0.47461 0.73114 0.22923 0.035117 0.12758 0.52819 -0.40953 0.19998 0.33691 0.11437 -0.10391 0.031409 -0.066146 -0.10101 -0.22149 -0.92804 -0.041475 -0.21828 0.13374 0.066746 -0.66277 0.10729 0.066336 0.53603 0.25584 -0.35871 -0.043953 -0.27164 0.061458 0.21468 0.13735 -0.18657 -0.66887 0.01812 0.16208 0.63693 -0.21263 0.14682 -0.34353 0.39509 0.22297 -0.23527 -0.52881 -0.12007 -0.40234 -0.014177 -0.19844 -0.24031 -0.93533 0.032942 0.067235 0.12171 0.26104 0.41025 0.48095 0.015652 -0.089106 0.28733 0.19007

catfish -0.35742 0.10999 0.20853 -0.49442 0.50404 0.086665 -0.48293 -0.5624 0.73622 -0.58815 0.68234 0.049176 -0.19704 -0.079342 1.0066 -0.082292 -0.44306 -0.68452 0.037116 0.23024 -0.24162 -0.10931 0.042944 -0.34711 0.15162 0.49847 0.11438 0.048285 0.31918 0.68403 0.3824 -0.17143 -0.1734 -0.11076 0.058109 0.38322 -0.087773 0.26967 -0.40914 0.14555 0.29459 -0.30186 0.064904 -0.04022 -0.3661 0.99822 -0.34212 0.004237 -0.43265 0.068742 0.28692 -0.24064 -0.16398 0.68546 0.06249 0.16163 0.2275 -0.011154 0.076975 0.6671 0.071667 0.24716 -0.24874 0.27025 -0.35197 -0.17451 0.48229 -0.25308 0.19339 -0.27742 -0.52851 -0.64609 0.080579 0.19465 0.040746 0.41098 0.0032952 -0.073493 0.88946 -0.19431 0.15309 -0.10267 0.84473 -0.10159 -0.32598 -0.24438 -0.53843 -0.34702 -0.23193 -0.37058 0.29791 -0.76792 -0.25192 -0.64799 -0.037978 -0.84814 -0.37748 -0.73075 0.12106 -0.18899 0.020654 0.38072 0.056816 -0.81918 -0.36313 0.1249 0.33378 0.20584 0.054659 -0.15582 0.32303 -0.62396 0.31083 0.65468 0.015671 0.066958 -0.15577 -0.49652 0.17708 -0.19184 0.16849 0.056219 0.14009 0.27207 0.13706 0.74732 -0.40578 -0.51668 0.12948 0.052154 0.11988 -0.039228 0.093798 -0.23395 1.0527 -0.70708 0.22099 -0.22105 0.90916 0.40095 -0.24943 0.18399 0.10077 -0.0087418 -0.10094 -0.054781 0.24104 0.36838 0.75457 -1.2007 -0.1334 -0.61339 -0.22606 0.16236 -0.24857 -0.20258 -0.54066 -0.40474 -0.32768 0.028839 0.10075 -0.26353 -0.67309 0.16664 -0.13909 -0.18254 -0.91218 0.2378 0.024663 0.47255 -0.53015 -0.21903 0.4692 -0.054716 -0.54657 0.25269 0.2332 -0.32359 -0.54629 -0.12386 -0.32904 -0.047302 0.19967 0.34355 0.26852 0.33259 -0.3937 0.31326 0.2425 0.43862 -0.47408 -0.3056 0.45356 -0.10655 0.041743 0.030686 0.202 -0.27844 -0.21838 -0.61306 -0.30534 -0.77149 -0.29197 -0.34591 0.42308 0.50578 0.18208 0.019962 0.48778 0.12868 -0.057299 0.47508 -0.076626 -0.40581 0.50145 1.0787 -0.3816 -0.41183 -0.49798 -0.13849 -0.49947 0.59601 -0.00097049 -0.82496 -1.4968 -0.2614 -0.041198 0.38383 -0.14826 0.42925 0.20691 0.17839 0.023277 -0.2022 -0.55911 -0.41961 0.13218 0.86711 -0.2884 -0.34119 0.66142 -0.055456 -0.13262 0.020062 -0.35527 0.00055615 0.29417 0.086833 -0.004127 0.17015 -0.70204 0.012589 -0.48245 0.54446 0.30868 -0.053147 -0.01233 -0.13763 0.26752 -0.40718 0.3199 -0.42179 0.36017 -0.31167 -0.0040716 0.67684 0.22875 0.3253 0.74358 -0.12485 0.010192 0.34724 0.82716 -0.22664 0.87353 0.21385 0.1984 0.57588 -0.29415 -0.20219 0.5767 -0.31421 0.48012 0.34326 0.12012 0.11175 -0.16937 0.52038 0.66516 -0.28575 -0.37457 -0.28112 0.42636 0.14493 -0.031302 -0.1741 -0.37457 -0.74464 -0.26569 0.35412