Mining 3D Patterns from Gene Expression Temporal Data: A New Tricluster Evaluation Measure

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Triduster</td><td align="center">Match ratio</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">TCale<sub>1</sub></td><td align="center">91%</td></tr><tr><td align="left">TCale<sub>2</sub></td><td align="center">91%</td></tr><tr><td align="left"><span style="width: 48.587502px;"><svg height="16.450001" id="M251" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 48.587502 16.450001" width="48.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" id="x43"></path></g><g transform="matrix(.017,-0,0,-.017,21.855,12.162)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.017,-0,0,-.017,29.402,12.162)"><path d="M238 0h-223v26q48 5 60 17t12 61v473q0 50 -10.5 60.5t-58.5 15.5v24q73 8 148 35v-608q0 -49 11.5 -61t60.5 -17v-26z" id="x6C"></path></g><g transform="matrix(.017,-0,0,-.017,33.703,12.162)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g>
<g transform="matrix(.012,-0,0,-.012,42.188,16.25)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg></span></td><td align="center">90%</td></tr><tr><td align="left"><span style="width: 48.587502px;"><svg height="16.3125" id="M252" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 48.587502 16.3125" width="48.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
q2 -89 11 -177z" id="x54"></path></g><g transform="matrix(.017,-0,0,-.017,10.415,12.162)"><path d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207
q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" id="x43"></path></g><g transform="matrix(.017,-0,0,-.017,21.855,12.162)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.017,-0,0,-.017,29.402,12.162)"><path d="M238 0h-223v26q48 5 60 17t12 61v473q0 50 -10.5 60.5t-58.5 15.5v24q73 8 148 35v-608q0 -49 11.5 -61t60.5 -17v-26z" id="x6C"></path></g><g transform="matrix(.017,-0,0,-.017,33.703,12.162)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g>
<g transform="matrix(.012,-0,0,-.012,42.188,16.25)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg></span></td><td align="center">96%</td></tr><tr><td align="left"><span style="width: 48.587502px;"><svg height="16.450001" id="M253" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 48.587502 16.450001" width="48.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
q2 -89 11 -177z" id="x54"></path></g><g transform="matrix(.017,-0,0,-.017,10.415,12.162)"><path d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207
q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" id="x43"></path></g><g transform="matrix(.017,-0,0,-.017,21.855,12.162)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.017,-0,0,-.017,29.402,12.162)"><path d="M238 0h-223v26q48 5 60 17t12 61v473q0 50 -10.5 60.5t-58.5 15.5v24q73 8 148 35v-608q0 -49 11.5 -61t60.5 -17v-26z" id="x6C"></path></g><g transform="matrix(.017,-0,0,-.017,33.703,12.162)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g>
<g transform="matrix(.012,-0,0,-.012,42.188,16.25)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
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</svg></span></td><td align="center">95%</td></tr><tr><td align="left">TCale<sub>6</sub></td><td align="center">95%</td></tr><tr><td align="left"><span style="width: 48.587502px;"><svg height="16.450001" id="M254" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 48.587502 16.450001" width="48.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" id="x43"></path></g><g transform="matrix(.017,-0,0,-.017,21.855,12.162)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.017,-0,0,-.017,29.402,12.162)"><path d="M238 0h-223v26q48 5 60 17t12 61v473q0 50 -10.5 60.5t-58.5 15.5v24q73 8 148 35v-608q0 -49 11.5 -61t60.5 -17v-26z" id="x6C"></path></g><g transform="matrix(.017,-0,0,-.017,33.703,12.162)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g>
<g transform="matrix(.012,-0,0,-.012,42.188,16.25)"><path d="M447 623l8 -12l-283 -613l-74 -10l-7 11q174 283 297 551h-216q-48 0 -62.5 -12t-33.5 -63h-29q10 60 18 148h382z" id="x37"></path></g>
</svg></span></td><td align="center">95%</td></tr><tr><td align="left"><span style="width: 48.587502px;"><svg height="16.450001" id="M255" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 48.587502 16.450001" width="48.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
q2 -89 11 -177z" id="x54"></path></g><g transform="matrix(.017,-0,0,-.017,10.415,12.162)"><path d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207
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<g transform="matrix(.012,-0,0,-.012,42.188,16.25)"><path d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5
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</svg></span></td><td align="center">95%</td></tr><tr><td align="left"><span style="width: 48.587502px;"><svg height="16.487499" id="M256" style="vertical-align:-3.41933pt" version="1.1" viewbox="0 0 48.587502 16.487499" width="48.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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<g transform="matrix(.012,-0,0,-.012,42.188,16.25)"><path d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5
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</svg></span></td><td align="center">95%</td></tr><tr><td align="left"><span style="width: 54.299999px;"><svg height="16.450001" id="M257" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 54.299999 16.450001" width="54.299999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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<g transform="matrix(.012,-0,0,-.012,42.188,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.012,-0,0,-.012,47.899,16.25)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg></span></td><td align="center">95%</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The Scientific World Journal

tab2

Table 2

Table 2: Mining 3D Patterns from Gene Expression Temporal Data: A New Tricluster Evaluation Measure 