(10 marks) Run the Bisecting k-Means algorithm to compute a hierarchy of clusterings that refines the initial single cluster to 9 clusters. For each s from 1 to 9, extract from the hierarchy of clusterings the clustering with s clusters and compute the Silhouette coefficient for this clustering. Plot s in the horizontal axis and the Silhouette coefficient in the vertical axis in the same plot.

Instances:

fish -0.25734 -0.20404 -0.2104 -0.50661 0.24957 -0.23918 -2.3018 -0.19739 0.0022438 -0.39468 0.9025 -0.44758 -0.14589 -0.27937 0.22605 -0.29183 -0.336 -0.53768 -0.20243 0.25019 0.13393 -0.6373 0.0091077 -0.69793 0.34235 0.46521 0.024239 0.1078 0.4064 -0.14167 0.542 -0.05906 -0.33914 0.19435 0.10871 0.26484 -0.083715 -0.076245 -0.16798 0.20501 -0.054161 -0.10698 0.21333 -0.54237 -0.38149 0.88802 -0.29054 0.27447 -0.17883 0.24233 -0.17695 0.15471 -0.28032 0.75492 -0.017927 0.32276 -0.14711 -0.1572 -0.42107 0.13529 0.29172 -0.073847 -0.43617 0.20702 -0.63773 -0.019453 0.0725 -0.13104 0.032509 -0.45923 -0.96404 -0.29365 0.46691 -0.059232 0.30528 0.22414 0.083959 -0.33893 0.42387 0.27279 -0.21767 0.019987 0.19037 0.53578 -0.28011 0.42011 -0.3901 -0.096659 0.2619 -0.53628 0.69896 -0.45547 0.37001 -0.25577 -0.21121 -0.85306 -1.7389 -0.65624 -0.27564 0.014518 0.1304 0.6413 0.26551 -0.11149 -0.54092 0.11691 -0.062281 0.27659 0.25001 -0.12133 0.33996 -0.43425 0.36733 0.082764 0.053541 0.26526 -0.50298 -0.54868 0.21784 0.088729 0.40434 0.019209 0.028484 0.29547 0.2381 0.49535 -0.37138 0.38478 0.41554 -0.16575 -0.37288 0.31284 0.071741 -0.39757 0.72522 -0.068002 0.475 -1.0193 0.42327 0.6767 -0.62211 0.66711 -0.031731 0.09029 0.40514 -0.64351 0.13113 0.25314 1.1083 -0.87524 -0.38302 -0.0079048 -0.35292 0.16845 -0.13551 0.13177 -0.33335 -0.083003 0.31274 0.084201 -0.08278 0.031993 -0.61147 -0.0019557 -0.29313 -0.033595 -0.42393 -0.14161 -0.22582 0.84171 -0.29591 -0.2861 -0.2342 0.013774 -0.31554 0.016476 -0.09024 -0.21439 -0.24798 -0.28771 -0.1256 -0.43941 0.096667 0.072804 -0.071676 0.54044 -0.12258 0.79429 0.20544 0.081429 -0.12372 0.32965 -0.019678 -0.24451 -0.5993 -0.30791 0.34061 -0.31602 -0.32509 -0.75343 -0.095728 -0.35135 -0.36012 -0.35143 -0.25918 -0.099191 0.43088 0.093315 0.26017 0.56379 -0.38064 0.64447 0.39317 -0.092335 0.24828 0.83071 -0.34974 -0.20368 -0.22343 0.00061357 -0.3142 0.65958 0.39349 0.0060193 -2.8533 -0.2371 0.25431 0.3184 -0.3882 0.23563 0.43359 0.018576 -0.28645 -0.50609 0.35533 -0.36502 0.18519 0.11675 -0.21378 0.023044 0.43335 0.18221 -0.63717 -0.39387 -0.4574 -0.070239 0.46305 -0.18641 0.45431 0.47442 -0.70352 -0.066314 -0.1646 0.49888 0.58088 0.27743 -0.37607 0.054575 0.059415 0.40728 -0.054691 -0.40379 0.38234 -0.30989 -0.31296 0.49543 0.086751 0.43 -0.16597 0.61008 -0.12635 -0.34553 0.86741 -0.11999 -0.050206 -0.057519 0.21902 0.46359 -0.73589 -0.22356 1.0696 -0.31751 0.39121 -0.16195 0.27868 0.13581 -0.070814 0.16045 0.65002 -0.41509 0.058333 -0.5752 0.20029 0.33518 -0.15763 -0.17595 -0.44322 0.046904 0.23154 0.61955

cow -0.28264 -0.52206 -0.057515 -0.046203 0.42852 0.18715 -1.6037 -0.20396 0.26914 -0.54596 0.57356 -0.17478 0.39408 -0.66132 0.15689 0.3146 -0.36423 -0.4805 -0.51935 -0.085512 0.085881 -0.22161 0.23926 0.14309 -0.59948 -0.083865 -0.31903 0.45446 -0.63427 -0.23123 0.29398 0.26633 0.7906 0.10044 0.24117 -0.14258 -0.2513 0.47551 0.41902 -0.14044 0.32691 0.081145 0.051303 0.082221 -0.1961 0.49478 0.4128 -0.33741 -0.1345 0.21732 -0.074274 -0.42265 -0.43881 0.0040548 0.092628 -0.015363 0.089286 0.17525 0.11661 -0.39634 -0.46183 -0.13227 -0.090263 0.26541 -0.0010086 0.26284 0.25336 -0.073051 0.24735 0.21734 0.012256 0.087475 0.32997 0.215 0.15111 -0.40227 -0.25026 -0.25636 0.14128 0.34212 -0.17441 0.26789 0.14686 -0.10851 -0.45176 0.096066 -0.59244 -0.0092919 -0.20186 -0.43321 0.64152 -0.062933 -0.15238 -0.2395 -0.21921 -0.54885 -0.96932 -0.37029 0.31508 -0.038554 0.47611 0.96237 -0.20167 0.32259 -0.21616 -0.0054525 -0.14458 0.14277 0.15234 0.025315 -0.39478 0.029387 0.48784 -0.32138 0.36812 0.096794 0.0279 -0.26777 0.079224 0.4051 -0.27672 0.55215 0.038832 0.38618 -0.044174 -0.20756 0.10781 0.012276 -0.82885 -0.27864 -0.19644 0.22983 0.46409 -0.084096 0.19701 -0.20071 -0.2449 -0.54272 -0.2019 -0.054359 -0.43263 -0.4248 -0.39685 0.23398 -0.26355 -0.86817 0.31941 0.18353 -0.0056986 -0.071959 0.068195 0.43662 -0.20929 -0.018696 -0.26657 -0.05584 0.30303 -0.05105 0.45107 -0.09796 0.17969 -0.23728 -0.55559 0.44475 -0.13288 -0.32353 0.11357 -0.37897 0.3311 0.38907 0.012085 -0.23972 0.48466 0.11806 0.070535 -0.032391 0.17186 -0.078087 -0.80888 -0.24273 -0.38044 -0.17037 -0.19722 -0.148 -0.12127 0.12961 -0.41751 -0.31511 0.90589 0.12572 -0.15288 0.27983 0.14581 0.25761 0.1468 0.11981 0.61981 -0.050846 0.22291 -0.01866 0.1844 -0.32211 0.19161 0.34594 0.088649 -0.37038 -0.41676 0.24322 0.13694 -0.1314 0.06057 -0.09142 0.33404 -0.12324 -0.018774 -0.018926 -0.10954 0.53319 -0.30854 0.47923 -0.23093 0.091152 -0.11467 -0.14628 -2.2657 -0.79672 -0.17886 -0.38848 -0.073568 -0.37251 0.42776 -0.17531 0.0087038 0.10057 0.07479 -0.069471 0.086145 -0.10238 0.18856 0.18487 0.51768 0.18732 -0.13319 0.25407 -0.72778 -0.13598 0.25286 -0.45354 0.39805 0.35138 -0.025679 -0.46771 0.82798 0.13641 0.46384 0.37284 -0.7607 -0.06877 0.081846 -0.068692 0.16578 -0.083899 0.02854 -0.63279 0.093204 0.30183 0.435 0.066057 -0.25038 0.64005 -0.042531 0.26094 -0.1918 -0.27586 -0.7043 0.40784 0.090379 0.37074 0.030338 -0.77282 0.82711 0.25709 -0.3561 -0.1124 0.51866 -0.24023 0.12403 -0.30316 0.12111 -0.46393 -0.27261 0.16176 0.09249 0.35451 0.020918 0.0068084 0.38184 -0.11375 -0.11734 0.53307

crow 0.052183 0.091772 -0.70613 0.33547 0.10826 0.39206 -1.0351 -0.34601 -0.13659 -0.44888 0.94158 0.0039346 -0.044592 0.18039 0.67368 0.63128 -0.10683 0.22979 0.14159 0.085601 0.089113 -0.30065 -0.10755 -0.41771 -0.002551 -0.26821 -0.47786 0.3023 0.19232 -0.22755 0.089309 -0.19144 -0.042454 -0.085245 -0.024971 -0.36981 0.39469 0.19566 0.24925 -0.25725 0.15356 0.60287 -0.075987 -0.099604 -0.50878 0.61831 -0.044961 0.24892 0.25356 0.23132 0.42305 -0.29727 0.16703 -0.37548 0.35458 0.19794 0.2389 0.55745 0.41081 0.4327 -0.076776 -0.045716 -0.18791 -0.35231 -0.90918 0.14791 0.52305 0.18488 0.46856 -0.023686 -0.35724 -0.30802 0.30058 0.16249 0.036885 0.0062658 -0.37117 0.15196 -0.0061479 0.40991 -0.056456 -0.11148 0.029691 -0.72238 0.19631 -0.77543 0.1309 0.15281 -0.34701 -0.37132 0.37202 0.12904 0.093277 0.15692 -0.18801 -0.29862 -0.7267 0.40095 0.015185 -0.2214 -0.028096 0.30858 -0.3533 0.16835 -0.3975 -0.25862 -0.077292 0.21483 0.0046498 -0.077936 0.24041 0.084183 0.44491 0.42926 0.072223 0.030185 -0.52119 0.12667 0.00028612 -0.049418 0.012681 -0.035375 -0.028402 0.59802 0.20345 -0.55685 0.093571 -0.20145 0.24713 0.32574 -0.2473 0.28996 0.28902 0.67897 0.52942 0.44808 0.19822 -0.49164 0.13752 0.10589 -0.010877 -0.44098 0.1534 0.45945 -0.26099 -0.051324 -0.38808 0.31164 0.49547 -0.11734 0.19232 -0.31019 -0.076041 0.19484 0.25431 0.26341 0.24316 0.23291 0.1667 -0.085126 0.11132 -0.22315 -0.26569 0.057868 -0.13259 0.53362 0.18685 0.32123 0.33882 -0.12865 0.030727 -0.079176 -0.96787 -0.49539 0.02642 0.087324 0.15903 -0.68851 -0.18391 0.17846 0.048309 -0.17182 0.14566 0.35128 0.39945 -0.11376 -0.13916 -0.40915 -0.57938 0.30353 0.087352 -0.57169 0.29555 0.44339 -0.70417 -0.23768 0.085321 -0.030279 -0.10204 0.20315 -0.40805 -0.054317 0.059591 0.052038 0.31928 -0.44118 -0.33193 0.40435 0.25738 0.050469 0.27802 -0.32141 0.28077 0.10845 0.076427 0.62239 0.63603 0.35667 -0.16751 0.5952 0.27165 0.025198 -0.2271 -0.20224 -2.1506 -0.28332 -0.16026 0.040776 0.012901 0.33355 0.24952 0.12334 -0.23304 -0.25179 0.084298 0.018361 0.17671 0.069967 -0.12433 0.12158 -0.13676 -0.025464 0.2108 -0.12971 -0.1194 0.32027 -0.40048 0.55322 0.22105 0.42175 -0.60972 -0.30964 -0.17736 0.40582 -0.40236 0.19833 -0.22966 0.12083 0.40049 -0.090828 -0.39898 -0.39039 -0.0044927 -0.18254 -0.23291 0.6339 0.22438 -0.54738 0.13701 0.17348 0.53424 0.57284 0.0059235 0.18008 -0.53083 -0.12106 -0.056237 -0.29619 -0.16568 -0.45747 0.58426 -0.17267 0.24315 0.30125 -0.02617 0.40517 0.36164 0.14551 -0.083385 -0.10968 0.24564 0.48979 -0.23875 0.38213 -0.078177 -0.48097 0.02018 -0.039414 -0.013537 0.64763

boa 0.67519 -0.21722 0.058598 -0.23958 0.0057921 0.1886 -0.78074 -0.057971 -0.02723 -0.5748 0.028708 0.13951 0.6913 0.069534 0.033883 -0.11194 0.26859 -0.37794 0.21473 -0.21768 0.298 -0.21174 0.30964 -0.22837 -0.063364 -0.044219 0.085032 -0.76016 -0.31426 0.70249 -0.57482 -0.23984 -0.23864 0.33093 0.51053 0.2649 0.9534 0.14484 0.43933 0.77562 0.45671 0.78449 -0.031476 -0.58256 -0.1533 0.25155 -0.19637 0.64708 0.073688 0.032637 -0.20744 -0.18428 -0.46809 0.2852 0.21552 0.36719 0.061013 -0.1727 0.41851 -0.017141 -0.057794 -0.22341 -0.2765 -0.17753 -1.0824 0.69224 0.013197 0.27915 -0.93404 -0.20052 -0.053208 -0.39874 -0.37486 -0.18137 -0.51987 -0.50837 0.20892 0.47754 0.14121 0.059631 0.50565 0.55538 -0.25143 0.62828 0.24744 -0.16056 0.51756 -0.33274 0.23569 0.034159 0.59202 -0.1194 0.16719 -0.093278 0.10983 -0.17998 -0.60969 -0.13725 -0.08303 -0.13266 0.0069843 0.46303 0.47839 -0.32015 -0.32291 -0.42336 -0.022272 0.9681 -0.33521 0.29557 0.34322 -0.21559 0.50668 -0.11039 -0.16034 0.096994 0.1183 -0.085892 -0.061437 -0.7497 -0.16505 0.62781 -0.4372 0.39897 -0.033967 0.064191 -0.010369 -0.13971 0.059427 -0.016393 -0.17592 0.25724 0.0090074 0.11693 0.47763 0.11193 -0.046527 0.40093 0.20593 0.21195 -0.30585 -0.67847 0.3411 -0.105 0.22135 -0.57561 0.73237 -0.37915 -0.31047 -0.33066 0.16478 0.049638 0.30793 -0.16453 -0.14518 -0.51622 -0.28842 -0.24373 -0.32714 0.72181 -0.12185 -0.038524 -0.72556 0.08443 0.71406 0.38621 0.031046 -0.29324 -0.072214 -0.12814 -0.20978 0.51152 -0.22422 0.13972 -0.20151 0.0044072 0.0052126 -0.69412 -0.017229 0.043323 -0.14386 -0.60877 0.29846 0.13032 0.083568 0.082235 -0.39397 0.71538 0.25943 0.10283 -0.74979 -0.087132 0.45524 -0.36764 -0.55751 0.53272 0.075578 -0.11536 0.52378 -0.064386 -0.88792 -0.04256 -0.15928 -0.26836 -0.26602 0.51696 -0.22178 -0.103 0.16162 0.12875 -0.078279 -0.30794 0.51888 0.74139 0.15684 0.055898 -0.50409 -0.20793 -0.3029 -1.0464 0.15055 -0.28109 0.50025 -0.44448 -1.4515 -0.29259 -0.62692 -0.60055 -0.033962 0.21185 0.12051 -0.25855 0.091754 0.14676 -0.093178 0.74923 -0.44082 -0.33758 -0.13856 0.81758 0.13906 -0.36832 0.52619 -0.018318 -0.50623 -0.16063 -0.067944 -0.022289 -0.020941 0.43519 -0.063411 -0.12659 -0.36255 0.35263 -0.09418 -0.268 -0.45933 0.091004 0.5647 0.10451 -0.031036 0.42085 0.20439 -0.1607 0.21127 -0.1569 -0.3947 0.51096 0.18595 -0.14298 0.59774 0.82259 0.34498 0.0015242 0.64356 -0.54961 -0.16186 -0.10386 0.17084 -0.55044 0.2428 -0.22748 0.20629 -0.093986 -0.19708 0.084143 0.29029 0.068381 -0.19398 0.018866 0.37933 0.099567 -0.35414 0.055159 -0.3732 0.53614 -0.15798 -0.017546 0.25428 0.226

dolphin 0.12634 -0.57323 -0.23157 -0.0064088 0.15373 0.32413 -0.83706 -0.45095 0.27585 -0.44858 0.91139 -0.25322 -0.12528 -0.69553 -0.15809 -0.1794 -0.46547 -0.58404 -0.24709 0.51607 -0.11074 -0.81524 -0.015062 -0.53023 0.76601 0.17728 -0.047357 -0.4466 0.72676 0.22234 0.42804 -0.061732 -0.09918 0.23948 0.40484 -0.75476 1.0922 -0.0092765 0.10382 0.14573 0.25441 -0.11846 0.47334 -0.60166 0.064981 -0.14507 -0.33631 0.026841 0.0015462 -0.055389 0.079654 0.028954 0.38918 0.50827 0.20846 0.13145 0.22177 -0.21216 -0.15187 -0.60437 0.20589 -0.34622 -0.1416 0.086821 -0.37739 0.005585 0.033577 -0.74788 -0.19813 0.010209 -0.35003 0.052451 0.17073 -0.20823 -0.56045 -0.15536 0.24263 0.46391 0.68396 -0.059725 -0.49225 0.21625 0.022981 -6.1758e-05 -0.37421 0.25548 -0.54484 0.16954 0.43027 -0.22468 0.13808 -0.67774 0.55023 -0.13231 0.26097 -0.72733 -1.3004 0.63113 -0.22316 -0.16572 0.038888 0.36846 0.0023957 -0.11962 -0.31596 0.094968 -0.33321 0.28262 0.38595 -0.44067 0.21984 -0.24626 0.60354 -0.21798 -0.10475 0.15837 0.19556 0.29802 0.16988 0.38362 -0.30472 0.51137 -0.23731 0.16498 0.25458 0.44052 -0.34848 0.19594 -0.28571 -0.28329 -0.049861 -0.121 0.23752 -0.41657 0.50632 -0.1867 -0.22486 -0.52264 0.18008 0.64049 -0.45115 -0.2822 -0.3602 0.029721 -0.033961 0.01356 0.24533 0.078801 0.014729 -0.16594 -0.91633 -0.22352 -0.50946 0.37677 0.46714 0.27282 -0.35828 0.18833 -0.31582 -0.0025759 -0.19396 0.84891 -0.46719 0.55185 0.34607 0.05967 -0.36653 0.09895 0.21285 -0.099296 -0.29937 -0.19944 0.35841 -0.094338 -0.045039 -0.5048 -0.011728 -0.22456 0.093479 0.23267 0.3996 -0.4252 -0.14895 -0.0035811 0.38723 -0.16502 -0.45733 0.54782 -0.051453 -0.10816 0.25785 0.36397 -0.023376 -0.0016745 -0.57609 0.44793 0.34785 -0.037385 0.18383 -0.5195 0.23327 -0.074757 0.056401 0.2067 -0.53168 -0.051628 0.26454 0.52203 0.45023 0.50326 0.089421 0.41961 -0.23864 0.28418 0.48484 0.23769 -0.744 -0.08651 0.56566 0.54427 0.20823 -0.21047 0.045882 0.19572 -1.8614 -0.57801 0.23683 0.29911 -0.56126 0.59681 0.44447 -0.25253 -0.14753 -0.0086074 0.15875 -0.21652 0.08908 0.11717 0.065307 0.63002 0.091524 0.64542 -0.19491 -0.077075 -0.15532 -0.038733 0.27428 -0.19757 0.33282 0.086568 -0.1776 -0.25923 -0.16705 0.13526 -0.14772 -0.4025 -0.66873 0.12173 0.034703 -0.19732 -0.5668 0.20617 -0.13627 0.12618 -0.39119 0.38849 -0.26606 0.095902 0.19136 0.073374 0.12694 0.066848 0.47955 -0.17101 -0.05385 -0.065278 -0.12166 0.45418 -0.30926 -0.12134 -0.012967 -0.088999 -0.3141 -0.45551 0.62712 0.46768 0.18093 0.034089 -0.29081 0.34871 0.0090876 0.86533 -0.52578 -0.022145 -0.75856 0.37705 0.3462 -0.15604 0.56428 -0.29634