Thesis Update - Fuzzy Clustering

This week I performed a completed fuzzy clustering set upon data provided by Dr Poon. I firstly checked which number of clusters was best, using the clValid function, and then performed a fuzzy clustering analysis upon the data using this number of clusters. The results are as follows:

Clustering Determination using clValid:

Clustering Determination using clValid:

Cluster sizes:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

Validation Measures:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

fanny Connectivity 17.6429 15.6361 26.2500 38.6222 44.8575 47.1246 52.2718 86.2238 80.3901 83.1063 75.4885 99.8266 79.9262 88.6492 103.7821 141.2881 94.4425 108.0456 88.9873 109.7246 104.8306 128.4329 116.3290 96.4512 118.6901 129.3504 100.5310 137.2397 87.9849 120.8452 103.8091 131.6369 124.2206 137.7921 150.8726 140.9762 169.8508 156.1194 165.8202 179.5583 188.7667 184.4540 196.6766 194.9726 204.8901 192.5278 222.9175 219.1512 234.1079 239.3738 250.2071 255.2821 244.8940 243.3845 242.0552 251.2544 245.1659 252.9909 263.9631 285.9647 300.1361 303.7901 304.6492 310.1956 342.0210 338.8845 350.2933 360.7131 360.5933 361.4758 347.8706 357.0214 366.3710 361.6758 375.6111 355.5508 363.5639 369.8798 376.3706 380.6302 384.4921 391.0083 396.2425 400.8155 409.2960 411.4611 419.0857 422.3060 419.7639 424.0175 428.4333 419.9694 428.1302 429.0349 434.1635 423.6893 429.7310 432.2143 441.9460 451.9274 464.2226 467.7210 470.2028 474.5651 476.5817 463.7944 466.9492 471.0075 476.4484 470.1337 476.7099 477.4099 486.1218 476.2429 482.7587 487.9103 489.0440 491.6155 495.2456 497.9123 496.1159 496.8548 501.0881 497.7444 497.8548 503.6226 506.5488 509.6853 513.5020
Dunn 0.0122 0.0248 0.0280 0.0271 0.0221 0.0241 0.0250 0.0107 0.0169 0.0227 0.0201 0.0280 0.0266 0.0424 0.0180 0.0222 0.0264 0.0464 0.0521 0.0497 0.0470 0.0205 0.0392 0.0394 0.0518 0.0359 0.0389 0.0251 0.0389 0.0234 0.0389 0.0374 0.0241 0.0433 0.0209 0.0469 0.0466 0.0469 0.0433 0.0209 0.0469 0.0277 0.0389 0.0414 0.0456 0.0569 0.0418 0.0570 0.0365 0.0277 0.0363 0.0299 0.0299 0.0299 0.0639 0.0561 0.0560 0.0757 0.0547 0.0889 0.0375 0.0375 0.0375 0.0375 0.0525 0.0657 0.0298 0.0263 0.0263 0.0263 0.0525 0.0525 0.0531 0.0531 0.0531 0.0500 0.0638 0.0510 0.0633 0.0906 0.0794 0.0626 0.0626 0.0626 0.0626 0.0626 0.0309 0.0248 0.0275 0.0275 0.0257 0.0257 0.0257 0.0257 0.0259 0.0420 0.0444 0.0457 0.0457 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0271 0.0277 0.0313 0.0313 0.0357 0.0393 0.0528 0.0528 0.0565 0.0589 0.0589 0.0682 0.0682 0.0427 0.0427 0.0427 0.0427
Silhouette 0.4849 0.5735 0.4836 0.4278 0.3433 0.3887 0.3835 0.2603 0.3265 0.2677 0.2010 0.1594 0.1656 0.2525 0.2271 0.2583 0.3578 0.3457 0.3973 0.3630 0.3293 0.2901 0.3419 0.3399 0.2816 0.2861 0.3980 0.2971 0.4109 0.3093 0.3387 0.3537 0.2285 0.3295 0.3190 0.3041 0.3226 0.3264 0.3200 0.3461 0.3114 0.3143 0.2946 0.2865 0.2761 0.2809 0.2621 0.3140 0.3073 0.3025 0.2784 0.2374 0.3115 0.2992 0.3334 0.2961 0.3200 0.3064 0.3040 0.3350 0.3667 0.3669 0.3589 0.3601 0.2290 0.2255 0.2234 0.2512 0.2477 0.2503 0.2861 0.2897 0.3071 0.3324 0.3213 0.3611 0.3522 0.3544 0.3566 0.3589 0.3557 0.3503 0.3460 0.3425 0.3363 0.3387 0.1350 0.1511 0.1839 0.1924 0.1592 0.1608 0.1769 0.1797 0.1723 0.2039 0.2042 0.2087 0.2017 0.1973 0.1897 0.1964 0.1876 0.1842 0.1806 0.2261 0.2210 0.2245 0.2239 0.2377 0.2269 0.2208 0.2157 0.2408 0.2396 0.2453 0.2535 0.2478 0.2572 0.2528 0.2627 0.2542 0.2561 0.2758 0.2765 0.2736 0.2681 0.2727 0.2608

Optimal Scores:

Score Method Clusters
Connectivity 15.6361 fanny 3
Dunn 0.0906 fanny 81
Silhouette 0.5735 fanny 3

For Connectivity and Silhouette (3)

Fuzzy Clustering Results, using 3 clusters:

Fuzzy Clustering object of class 'fanny' :
m.ship.expon. 2
objective 1944560
tolerance 1e-15
iterations 32
converged 1
maxit 500
n 263
Membership coefficients (in %, rounded):
[,1] [,2] [,3]
[1,] 64 20 15
[2,] 66 19 15
[3,] 69 17 14
[4,] 70 17 13
[5,] 58 23 19
[6,] 63 20 16
[7,] 66 19 15
[8,] 68 18 15
[9,] 69 17 14
[10,] 70 17 13
[11,] 72 16 11
[12,] 73 16 11
[13,] 74 15 11
[14,] 72 17 11
[15,] 70 18 13
[16,] 74 15 12
[17,] 71 16 13
[18,] 76 14 10
[19,] 73 15 12
[20,] 75 15 11
[21,] 73 15 12
[22,] 12 84 4
[23,] 10 86 4
[24,] 10 86 4
[25,] 10 86 3
[26,] 11 85 4
[27,] 12 84 4
[28,] 12 84 4
[29,] 14 81 5
[30,] 15 81 5
[31,] 17 78 5
[32,] 18 76 6
[33,] 19 74 7
[34,] 19 75 6
[35,] 19 74 7
[36,] 21 72 7
[37,] 23 69 8
[38,] 23 69 8
[39,] 24 68 8
[40,] 24 68 8
[41,] 25 65 9
[42,] 28 62 10
[43,] 28 62 10
[44,] 18 13 69
[45,] 18 13 69
[46,] 12 8 80
[47,] 11 7 81
[48,] 12 8 80
[49,] 12 8 80
[50,] 12 8 80
[51,] 14 10 76
[52,] 16 12 72
[53,] 14 10 76
[54,] 13 9 79
[55,] 13 8 79
[56,] 14 9 78
[57,] 14 9 78
[58,] 14 9 77
[59,] 15 10 75
[60,] 16 10 74
[61,] 16 11 73
[62,] 17 11 72
[63,] 18 12 70
[64,] 20 13 67
[65,] 21 14 64
[66,] 9 88 3
[67,] 9 88 3
[68,] 9 88 3
[69,] 9 88 3
[70,] 8 89 3
[71,] 10 87 3
[72,] 11 85 4
[73,] 11 85 4
[74,] 11 85 4
[75,] 13 82 5
[76,] 14 81 5
[77,] 14 81 5
[78,] 14 81 5
[79,] 16 79 6
[80,] 14 80 5
[81,] 16 78 6
[82,] 16 78 6
[83,] 15 79 6
[84,] 15 79 6
[85,] 16 78 6
[86,] 21 71 8
[87,] 18 75 7
[88,] 74 14 12
[89,] 74 14 12
[90,] 80 12 8
[91,] 81 12 7
[92,] 78 13 9
[93,] 75 14 11
[94,] 72 14 13
[95,] 69 15 16
[96,] 56 18 26
[97,] 50 18 32
[98,] 60 17 23
[99,] 72 14 14
[100,] 65 16 18
[101,] 60 17 23
[102,] 52 18 30
[103,] 52 18 30
[104,] 52 18 30
[105,] 48 18 34
[106,] 41 17 41
[107,] 31 15 53
[108,] 36 16 48
[109,] 33 16 51
[110,] 74 19 7
[111,] 77 17 7
[112,] 72 21 7
[113,] 71 22 7
[114,] 78 16 6
[115,] 80 14 6
[116,] 80 14 6
[117,] 82 12 6
[118,] 81 12 7
[119,] 78 13 9
[120,] 78 13 9
[121,] 80 12 8
[122,] 80 12 8
[123,] 77 13 10
[124,] 78 13 9
[125,] 75 14 11
[126,] 74 16 11
[127,] 72 16 12
[128,] 70 17 13
[129,] 66 18 16
[130,] 67 19 15
[131,] 65 19 15
[132,] 33 17 50
[133,] 35 17 49
[134,] 34 17 49
[135,] 34 17 49
[136,] 32 16 53
[137,] 26 14 60
[138,] 25 14 62
[139,] 21 12 67
[140,] 18 11 71
[141,] 16 10 74
[142,] 17 10 73
[143,] 17 10 73
[144,] 16 10 74
[145,] 16 10 74
[146,] 14 9 78
[147,] 13 8 79
[148,] 13 8 80
[149,] 12 8 80
[150,] 12 8 80
[151,] 13 8 79
[152,] 13 8 79
[153,] 14 9 77
[154,] 12 84 4
[155,] 14 82 4
[156,] 16 79 5
[157,] 18 77 5
[158,] 21 73 6
[159,] 21 74 6
[160,] 25 68 6
[161,] 31 61 7
[162,] 36 56 8
[163,] 40 52 8
[164,] 44 48 9
[165,] 48 43 9
[166,] 46 46 9
[167,] 51 41 9
[168,] 58 34 9
[169,] 60 31 9
[170,] 64 28 8
[171,] 65 27 8
[172,] 68 25 8
[173,] 74 19 7
[174,] 77 16 7
[175,] 76 17 7
[176,] 63 29 8
[177,] 65 28 8
[178,] 65 28 8
[179,] 66 26 8
[180,] 68 25 7
[181,] 73 20 7
[182,] 76 18 7
[183,] 77 17 6
[184,] 77 16 6
[185,] 80 14 6
[186,] 81 13 6
[187,] 79 14 6
[188,] 77 16 7
[189,] 79 15 6
[190,] 79 14 7
[191,] 79 13 7
[192,] 77 15 8
[193,] 78 14 8
[194,] 76 15 9
[195,] 75 15 10
[196,] 71 17 12
[197,] 70 18 12
[198,] 13 83 4
[199,] 12 84 4
[200,] 12 84 4
[201,] 12 85 4
[202,] 11 85 4
[203,] 11 85 4
[204,] 10 86 3
[205,] 10 87 3
[206,] 9 88 3
[207,] 9 88 3
[208,] 9 88 3
[209,] 8 89 3
[210,] 9 88 3
[211,] 8 89 3
[212,] 9 88 3
[213,] 12 85 3
[214,] 13 83 4
[215,] 12 84 4
[216,] 15 81 4
[217,] 18 77 5
[218,] 21 73 6
[219,] 18 76 5
[220,] 48 44 8
[221,] 49 43 8
[222,] 50 42 8
[223,] 51 41 8
[224,] 38 54 8
[225,] 49 43 8
[226,] 53 38 8
[227,] 62 30 9
[228,] 64 27 9
[229,] 68 23 9
[230,] 66 25 9
[231,] 62 29 10
[232,] 57 33 10
[233,] 57 33 10
[234,] 57 32 11
[235,] 58 31 11
[236,] 58 31 11
[237,] 56 32 12
[238,] 55 31 14
[239,] 54 31 15
[240,] 54 31 15
[241,] 53 30 16
[242,] 14 81 5
[243,] 13 82 5
[244,] 13 83 5
[245,] 12 84 4
[246,] 12 84 4
[247,] 11 86 4
[248,] 10 86 3
[249,] 10 87 3
[250,] 10 87 3
[251,] 10 87 3
[252,] 9 88 3
[253,] 10 87 3
[254,] 9 88 3
[255,] 10 87 3
[256,] 12 84 4
[257,] 12 84 4
[258,] 13 83 4
[259,] 14 82 4
[260,] 15 81 4
[261,] 16 80 4
[262,] 16 79 4
[263,] 19 76 5
Fuzzyness coefficients:
dunn_coeff normalized
0.5928260 0.3892389
Closest hard clustering:
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
[60] 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1
[119] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1
[178] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
[237] 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Available components:
[1] "membership" "coeff" "memb.exp" "clustering" "k.crisp" "objective" "convergence" "diss"
[9] "call" "silinfo" "data"

[,1] [,2] [,3]
[1,] 0.64308606 0.20316617 0.15374776
[2,] 0.65740785 0.19464854 0.14794361
[3,] 0.68964138 0.17457229 0.13578633
[4,] 0.70191629 0.17154831 0.12653540
[5,] 0.58358282 0.22519072 0.19122646
[6,] 0.63167295 0.20439811 0.16392893
[7,] 0.66309979 0.18735918 0.14954103
[8,] 0.67539285 0.17845279 0.14615436
[9,] 0.68797690 0.17321485 0.13880825
[10,] 0.69953625 0.16574425 0.13471950
[11,] 0.72156444 0.16383609 0.11459947
[12,] 0.73161044 0.15862833 0.10976122
[13,] 0.73862621 0.15436670 0.10700709
[14,] 0.72366989 0.16651925 0.10981087
[15,] 0.69741765 0.17613134 0.12645101
[16,] 0.73565879 0.14930836 0.11503285
[17,] 0.71150445 0.15686307 0.13163248
[18,] 0.75831888 0.13985422 0.10182690
[19,] 0.73245812 0.14727960 0.12026229
[20,] 0.74698637 0.14557968 0.10743396
[21,] 0.72698149 0.15226343 0.12075508
[22,] 0.11629744 0.84232658 0.04137598
[23,] 0.10308109 0.86133368 0.03558524
[24,] 0.10157861 0.86291686 0.03550454
[25,] 0.10079328 0.86429341 0.03491331
[26,] 0.11365397 0.84687319 0.03947284
[27,] 0.12060269 0.83864432 0.04075298
[28,] 0.11849516 0.84103643 0.04046841
[29,] 0.13941929 0.81317712 0.04740359
[30,] 0.14529510 0.80591935 0.04878556
[31,] 0.16533660 0.78033004 0.05433336
[32,] 0.17628606 0.76437152 0.05934243
[33,] 0.19127064 0.74268905 0.06604031
[34,] 0.18641653 0.74913292 0.06445054
[35,] 0.19173206 0.74317196 0.06509598
[36,] 0.21030396 0.71723893 0.07245711
[37,] 0.23131762 0.68801667 0.08066571
[38,] 0.23195018 0.68731709 0.08073273
[39,] 0.24002253 0.67557395 0.08440353
[40,] 0.23846552 0.67756832 0.08396616
[41,] 0.25472246 0.65297482 0.09230273
[42,] 0.27901078 0.61674919 0.10424003
[43,] 0.27790511 0.61864206 0.10345283
[44,] 0.18167949 0.13058518 0.68773534
[45,] 0.17798295 0.12770224 0.69431481
[46,] 0.11920734 0.08034544 0.80044722
[47,] 0.11145960 0.07417952 0.81436088
[48,] 0.11739738 0.07926588 0.80333674
[49,] 0.11668412 0.07889987 0.80441601
[50,] 0.11877977 0.08053675 0.80068348
[51,] 0.14155474 0.09846595 0.75997931
[52,] 0.16443135 0.11687942 0.71868923
[53,] 0.14422864 0.10024070 0.75553066
[54,] 0.12729069 0.08617904 0.78653027
[55,] 0.12722387 0.08219027 0.79058586
[56,] 0.13560085 0.08686367 0.77753548
[57,] 0.13555491 0.08836465 0.77608044
[58,] 0.13706577 0.09138560 0.77154863
[59,] 0.15042665 0.09933736 0.75023599
[60,] 0.15763545 0.10382862 0.73853593
[61,] 0.16368192 0.10904375 0.72727433
[62,] 0.16825765 0.11262758 0.71911477
[63,] 0.18036661 0.12003546 0.69959792
[64,] 0.19567254 0.13055114 0.67377631
[65,] 0.21439219 0.14254268 0.64306513
[66,] 0.08715453 0.88295648 0.02988899
[67,] 0.08848089 0.88096001 0.03055911
[68,] 0.08645427 0.88430505 0.02924068
[69,] 0.09065097 0.87875719 0.03059184
[70,] 0.08133971 0.89123771 0.02742258
[71,] 0.09584413 0.87192822 0.03222765
[72,] 0.11092123 0.85087567 0.03820310
[73,] 0.11209909 0.84887277 0.03902813
[74,] 0.10818970 0.85401114 0.03779916
[75,] 0.13301014 0.81961055 0.04737931
[76,] 0.13683924 0.81384467 0.04931609
[77,] 0.13626314 0.81485039 0.04888647
[78,] 0.13933557 0.80993644 0.05072799
[79,] 0.15542585 0.78730249 0.05727166
[80,] 0.14473976 0.80199420 0.05326604
[81,] 0.15933194 0.78105112 0.05961695
[82,] 0.16085993 0.77771960 0.06142047
[83,] 0.14977784 0.79345922 0.05676293
[84,] 0.15490113 0.78650311 0.05859576
[85,] 0.15640402 0.78439286 0.05920312
[86,] 0.20650675 0.71323304 0.08026022
[87,] 0.18145480 0.74951980 0.06902540
[88,] 0.73703609 0.14386046 0.11910345
[89,] 0.74003506 0.14207153 0.11789341
[90,] 0.80116671 0.12377021 0.07506308
[91,] 0.80676073 0.12434550 0.06889377
[92,] 0.77975766 0.12748702 0.09275532
[93,] 0.75038509 0.13665745 0.11295747
[94,] 0.72477530 0.14395266 0.13127204
[95,] 0.68916099 0.15414325 0.15669576
[96,] 0.56279542 0.17678054 0.26042403
[97,] 0.50200654 0.17848797 0.31950549
[98,] 0.59675109 0.17206779 0.23118112
[99,] 0.72017167 0.14429854 0.13552979
[100,] 0.65316313 0.16219022 0.18464665
[101,] 0.59988136 0.17195477 0.22816387
[102,] 0.52275531 0.17827169 0.29897301
[103,] 0.51720598 0.17842106 0.30437296
[104,] 0.52498218 0.17880317 0.29621465
[105,] 0.47707065 0.17954689 0.34338246
[106,] 0.41369904 0.17460815 0.41169281
[107,] 0.31367463 0.15229538 0.53402999
[108,] 0.35768951 0.16151866 0.48079183
[109,] 0.33163061 0.15638283 0.51198656
[110,] 0.73960091 0.19089034 0.06950875
[111,] 0.76543339 0.16864606 0.06592054
[112,] 0.71881521 0.21048002 0.07070477
[113,] 0.70979980 0.21919479 0.07100541
[114,] 0.77912254 0.15784356 0.06303390
[115,] 0.80010221 0.13958790 0.06030989
[116,] 0.80091532 0.13791249 0.06117219
[117,] 0.82104652 0.11927401 0.05967947
[118,] 0.81193341 0.11701828 0.07104831
[119,] 0.78061010 0.12894793 0.09044197
[120,] 0.77793417 0.13199866 0.09006717
[121,] 0.80048250 0.12420835 0.07530915
[122,] 0.79988650 0.12384277 0.07627074
[123,] 0.77008120 0.13251231 0.09740650
[124,] 0.78135862 0.12970701 0.08893437
[125,] 0.75227953 0.14252068 0.10519979
[126,] 0.73508606 0.15614796 0.10876599
[127,] 0.72116942 0.16031797 0.11851261
[128,] 0.69732378 0.16949769 0.13317853
[129,] 0.65737611 0.18118377 0.16144012
[130,] 0.66707669 0.18519897 0.14772435
[131,] 0.65172457 0.19409434 0.15418108
[132,] 0.33009791 0.16557643 0.50432565
[133,] 0.34513018 0.16807636 0.48679346
[134,] 0.34382536 0.16713172 0.48904292
[135,] 0.34353438 0.16611501 0.49035061
[136,] 0.31698687 0.15776079 0.52525234
[137,] 0.25988096 0.13909361 0.60102543
[138,] 0.24885132 0.13513171 0.61601697
[139,] 0.20848195 0.11883509 0.67268296
[140,] 0.18097801 0.10641348 0.71260852
[141,] 0.16086899 0.09721563 0.74191537
[142,] 0.16867499 0.10023912 0.73108588
[143,] 0.17051616 0.10035049 0.72913335
[144,] 0.16260654 0.09667386 0.74071960
[145,] 0.16068184 0.09526815 0.74405001
[146,] 0.13679913 0.08602475 0.77717612
[147,] 0.13092360 0.08286750 0.78620890
[148,] 0.12539432 0.07906505 0.79554063
[149,] 0.12308446 0.07763445 0.79928109
[150,] 0.12060186 0.07772703 0.80167111
[151,] 0.12655846 0.08369958 0.78974196
[152,] 0.12562248 0.08308802 0.79128950
[153,] 0.13803499 0.09350853 0.76845648
[154,] 0.12457690 0.83638630 0.03903680
[155,] 0.13857533 0.81944019 0.04198448
[156,] 0.15922659 0.79407403 0.04669938
[157,] 0.18212460 0.76631372 0.05156168
[158,] 0.20974021 0.73294897 0.05731082
[159,] 0.20708132 0.73652176 0.05639692
[160,] 0.25414907 0.68111754 0.06473339
[161,] 0.31442047 0.61197345 0.07360608
[162,] 0.35877186 0.56274151 0.07848662
[163,] 0.40229917 0.51552156 0.08217927
[164,] 0.43887497 0.47612275 0.08500228
[165,] 0.48363667 0.42889612 0.08746721
[166,] 0.45522215 0.45891588 0.08586198
[167,] 0.50585359 0.40696334 0.08718307
[168,] 0.57557601 0.33822583 0.08619816
[169,] 0.60223289 0.31206333 0.08570378
[170,] 0.63960291 0.27699175 0.08340534
[171,] 0.65029768 0.26732362 0.08237870
[172,] 0.67532433 0.24587842 0.07879725
[173,] 0.73507655 0.19098357 0.07393988
[174,] 0.76880457 0.15667407 0.07452136
[175,] 0.76003222 0.16947431 0.07049347
[176,] 0.62560022 0.29396297 0.08043681
[177,] 0.64658111 0.27519109 0.07822780
[178,] 0.64626344 0.27544304 0.07829352
[179,] 0.66394946 0.25980279 0.07624775
[180,] 0.67996769 0.24602229 0.07401002
[181,] 0.73147118 0.20025500 0.06827382
[182,] 0.75857013 0.17625701 0.06517286
[183,] 0.76717200 0.16826076 0.06456723
[184,] 0.77426432 0.16169221 0.06404347
[185,] 0.80373698 0.13565977 0.06060325
[186,] 0.80518916 0.13447402 0.06033682
[187,] 0.79411302 0.14371294 0.06217405
[188,] 0.77089375 0.16377598 0.06533027
[189,] 0.78880563 0.14689928 0.06429509
[190,] 0.79155725 0.13941857 0.06902419
[191,] 0.79070715 0.13473693 0.07455593
[192,] 0.76922280 0.14675389 0.08402331
[193,] 0.77637425 0.14220477 0.08142098
[194,] 0.76436928 0.14527665 0.09035407
[195,] 0.74664828 0.15484509 0.09850663
[196,] 0.71123462 0.16916439 0.11960099
[197,] 0.69873599 0.17903303 0.12223098
[198,] 0.12817758 0.82773107 0.04409135
[199,] 0.12250023 0.83538714 0.04211263
[200,] 0.12001228 0.83839791 0.04158980
[201,] 0.11551494 0.84521163 0.03927342
[202,] 0.11346319 0.84822938 0.03830744
[203,] 0.10992590 0.85346748 0.03660662
[204,] 0.10145701 0.86471023 0.03383276
[205,] 0.09691101 0.87041884 0.03267016
[206,] 0.09314032 0.87595152 0.03090816
[207,] 0.08933258 0.88148935 0.02917807
[208,] 0.08960222 0.88138141 0.02901637
[209,] 0.08487447 0.88709391 0.02803162
[210,] 0.08790979 0.88229766 0.02979255
[211,] 0.08219806 0.89097270 0.02682924
[212,] 0.09349764 0.87751393 0.02898844
[213,] 0.11505652 0.85063492 0.03430857
[214,] 0.13098290 0.83092361 0.03809349
[215,] 0.12179686 0.84100450 0.03719865
[216,] 0.14592286 0.81019968 0.04387747
[217,] 0.18238860 0.76550624 0.05210516
[218,] 0.20867436 0.73297186 0.05835378
[219,] 0.18292691 0.76348763 0.05358546
[220,] 0.47793633 0.43956367 0.08250000
[221,] 0.48838602 0.42939311 0.08222087
[222,] 0.49939626 0.41854159 0.08206215
[223,] 0.51152121 0.40648592 0.08199287
[224,] 0.38140750 0.54077595 0.07781655
[225,] 0.48841809 0.42846120 0.08312071
[226,] 0.53256893 0.38273790 0.08469317
[227,] 0.61700503 0.29621139 0.08678358
[228,] 0.64340563 0.26871432 0.08788006
[229,] 0.67546623 0.23336461 0.09116916
[230,] 0.66102720 0.24514291 0.09382988
[231,] 0.61595888 0.28876132 0.09527980
[232,] 0.56826769 0.33202378 0.09970853
[233,] 0.57182423 0.32699107 0.10118470
[234,] 0.57022069 0.32398504 0.10579427
[235,] 0.58414216 0.30637271 0.10948513
[236,] 0.57693201 0.31006817 0.11299982
[237,] 0.55841837 0.32152166 0.12005996
[238,] 0.55428214 0.31029983 0.13541804
[239,] 0.54189660 0.31091570 0.14718771
[240,] 0.54063954 0.30591957 0.15344089
[241,] 0.53226979 0.30335155 0.16437867
[242,] 0.13825362 0.81072212 0.05102426
[243,] 0.13082769 0.82147739 0.04769492
[244,] 0.12567786 0.82899773 0.04532441
[245,] 0.11858326 0.83920074 0.04221600
[246,] 0.11537116 0.84361878 0.04101006
[247,] 0.10523988 0.85843654 0.03632357
[248,] 0.10238668 0.86263557 0.03497775
[249,] 0.09777133 0.86951819 0.03271048
[250,] 0.09516655 0.87347713 0.03135632
[251,] 0.09822792 0.87022897 0.03154310
[252,] 0.09277850 0.87676727 0.03045423
[253,] 0.09637454 0.87292209 0.03070337
[254,] 0.08893323 0.88210912 0.02895764
[255,] 0.09730386 0.87219650 0.03049964
[256,] 0.12363848 0.83980979 0.03655174
[257,] 0.11986239 0.84460158 0.03553603
[258,] 0.12883672 0.83349363 0.03766966
[259,] 0.13715618 0.82363547 0.03920835
[260,] 0.14901744 0.80911178 0.04187078
[261,] 0.16030202 0.79540713 0.04429085
[262,] 0.16330648 0.79205729 0.04463622
[263,] 0.18605354 0.76456116 0.04938530

dunn_coeff normalized
0.5928260 0.3892389

I also tried performing a switching regression test upon the data, but have so far been unable to do so. This week, however, I will attempt to cluster using 3 cycles, and determining the clusters for each cycle.

Partial Draft:
I am also working upon my partial draft, and expect to have the introduction, literature review, and data interpretation drafted by the due date.