TESI DOCTORAL - La Salle

More documents

Recommendations

Info

3.2. Random hierarchical consensus architectures λ 1 λ 11 λ 12 λ 13 … λ 1m λ 2 λ 21 λ 22 λ 23 … λ 2m λ 3 λ 31 λ 32 λ 33 … λ 3m λ 4 λ 41 λ 42 λ 43 … λ 4m λ 5 λ 51 λ 52 λ 53 … λ 5m λ 6 λ 61 λ 62 λ 63 … λ 6m λ 7 λ 71 λ 72 λ 73 … λ 7m λ 8 λ 81 λ 82 λ 83 … λ 8m λ 1 λ 11 λ 12 λ 13 … λ 1m λ 2 λ 21 λ 22 λ 23 … λ 2m λ 3 λ 31 λ 32 λ 33 … λ 3m λ 4 λ 41 λ 42 λ 43 … λ 4m λ 5 λ 51 λ 52 λ 53 … λ 5m λ 6 λ 61 λ 62 λ 63 … λ 6m λ 7 λ 71 λ 72 λ 73 … λ 7m λ 8 λ 81 λ 82 λ 83 … λ 8m λ 9 λ 91 λ 92 λ 93 … λ 9m Consensus function Consensus function Consensus function Consensus function λ λ λ λ 1 c1 1 c2 1 c3 1 c4 Consensus function Consensus function (a) Topology of a RHCA with l =8andb =2,withs =3 Consensus function Consensus function Consensus function Consensus function λ λ λ λ 1 c1 1 c2 1 c3 1 c4 Consensus function Consensus function (b) Topology of a RHCA with l =9andb =2,withs =3 1 11 12 13 … 1m 2 21 22 23 … 2m 3 31 32 33 … 3m 4 41 42 43 … 4m 5 51 52 53 … 5m 6 61 62 63 … 6m 7 71 72 73 … 7m Consensus function Consensus function Consensus function 1 c1 λ λ λ λ 2 c1 2 c2 2 c1 2 c2 Consensus function (c) Topology of a RHCA with l =7andb =2,withs =2 1 c2 Consensus function Consensus function Figure 3.2: Three examples of topologies of random hierarchical consensus architectures with distinct relationships between the cluster ensemble and mini-ensembles sizes, l and b, respectively. maximum complexity O ((2b) w ) are executed is s Ki. The value of this summation can be approximated by considering that the number of consensus per stage Ki is also bounded, as Ki ≤ l b i (see equation (3.2)), yielding: 52 i=1 1 c3 c 2 1 c λc 3 1 λc 3 1 = λ = λ c c
Chapter 3. Hierarchical consensus architectures i # inner loop iterations 1 K1 2 K2 ... ... s 1 Table 3.1: Number of inner loop iterations as a function of the outer’s loop index i. s Ki ≤ i=1 s i=1 l = l · bi s i=1 1 1 1 b − b = l · bi s+1 1 − 1 bs − 1 = l · b b s (3.6) (b − 1) . Therefore, the which equals the partial sum of a geometric series whose common ratio is 1 b upper bound of the time complexity STCRHCA can be rewritten as: bs − 1 STCRHCA Ki, ∀i ∈ [2,s]). In this case of maximum parallelism, the parallel time complexity of a RHCA (PTCRHCA) ofs stages is formulated according to equation (3.9). PTCRHCA = s i=1 max j∈[1,Ki] (O (bij w )) (3.9) That is, the parallel time complexity of a RHCA is equal to the sum of the time complexities of the most time-consuming consensus process of each RHCA stage. Notice that it is not difficult to find an upper bound to PTCRHCA, as finding the maximum of O (bij w ) just requires taking into account that bij < 2b, ∀i, j. Thus: PTCRHCA < s i=1 O ((2b) w )=s · O ((2b) w )=O (s · (2b) w ) (3.10) If the number of RHCA stages is approximated as s ≈ log b (l), and constants are dropped, equation (3.10) can be rewritten as a function of l and b: 53
Page 1:
C.I.F. G: 59069740 Universitat Ramo
Page 5:
Resum En segmentar de forma no supe
Page 9:
Abstract When facing the task of pa
Page 12 and 13:
Contents 2.2.6 Consensus functions
Page 14 and 15:
Contents A.5 Consensus functions .
Page 16 and 17:
Contents D.2.5 WDBC data set . . .
Page 18 and 19:
List of Tables 3.13 Relative percen
Page 20 and 21:
List of Tables 5.15 Relative φ (NM
Page 23 and 24:
List of Figures 1.1 Evolution of th
Page 25 and 26:
List of Figures 4.2 Decreasingly or
Page 27 and 28:
List of Figures C.18 Estimated and
Page 29 and 30:
List of Figures C.49 φ (NMI) of th
Page 31 and 32:
List of Figures D.22 φ (NMI) boxpl
Page 33:
List of Algorithms 6.1 Symbolic des
Page 36 and 37:
List of symbols OΛ: object co-asso
Page 38 and 39: Chapter 1. Framework of the thesis
Page 40 and 41: 1.1. Knowledge discovery and data m
Page 42 and 43: 1.1. Knowledge discovery and data m
Page 44 and 45: 1.2. Clustering in knowledge discov
Page 54 and 55: 1.3. Multimodal clustering in clust
Page 56 and 57: 1.4. Clustering indeterminacies exe
Page 58 and 59: 1.4. Clustering indeterminacies The
Page 60 and 61: 1.4. Clustering indeterminacies Dat
Page 62 and 63: 1.5. Motivation and contributions o
Page 64 and 65: Chapter 2. Cluster ensembles and co
Page 66 and 67: fuzzy consensus clustering solution
Page 68 and 69: 2.1. Related work on cluster ensemb
Page 70 and 71: 2.2. Related work on consensus func
Page 82 and 83: 3.1. Motivation - the computational
Page 84 and 85: 3.1. Motivation An additional and v
Page 86 and 87: 3.2. Random hierarchical consensus
Page 106 and 107: 3.3. Deterministic hierarchical con
Page 124 and 125: 3.4. Flat vs. hierarchical consensu
Page 138 and 139:
3.4. Flat vs. hierarchical consensu
Page 140 and 141:
3.5. Discussion Consensus Consensus
Page 142 and 143:
3.5. Discussion separate clustering
Page 145 and 146:
Chapter 4 Self-refining consensus a
Page 147 and 148:
Chapter 4. Self-refining consensus
Page 149 and 150:
- What do we want to measure? Chapt
Page 151 and 152:
φ (NMI) φ (NMI) φ (NMI) φ (NMI)
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
φ (NMI) 0.8 0.78 0.76 0.74 0.72 0
Page 159 and 160:
1. Given a cluster ensemble E conta
Page 161 and 162:
Page 163 and 164:
%of experiments relative % φ (NMI)
Page 165 and 166:
Page 167:
Publisher: Springer Series: Lecture
Page 170 and 171:
5.1. Generation of multimodal clust
Page 172 and 173:
5.2. Self-refining multimodal conse
Page 174 and 175:
5.3. Multimodal consensus clusterin
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
5.4. Discussion Data set Relative
Page 198 and 199:
5.5. Related publications modes joi
Page 200 and 201:
Chapter 6. Voting based consensus f
Page 202 and 203:
6.2. Adapting consensus functions t
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
6.3. Voting based consensus functio
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
6.4. Experiments λc = 1 1 1 3 3 3
Page 222 and 223:
6.4. Experiments Data set Soft clus
Page 224 and 225:
6.4. Experiments CSPA EAC HGPA MCLA
Page 226 and 227:
6.5. Discussion solutions on hard c
Page 229 and 230:
Chapter 7 Conclusions The contribut
Page 231 and 232:
Chapter 7. Conclusions of-the-art c
Page 233 and 234:
Chapter 7. Conclusions Though put f
Page 235 and 236:
Chapter 7. Conclusions clustering r
Page 237 and 238:
Chapter 7. Conclusions hardened. Ou
Page 239 and 240:
References Ben-Hur, A., D. Horn, H.
Page 241 and 242:
References Deerwester, S., S.-T. Du
Page 243 and 244:
References Fred, A. and A.K. Jain.
Page 245 and 246:
References Ingaramo, D., D. Pinto,
Page 247 and 248:
References Li, S.Z. and G. GuoDong.
Page 249 and 250:
References Sebastiani, F. 2002. Mac
Page 251 and 252:
References Topchy, A., A.K. Jain, a
Page 253 and 254:
Appendix A Experimental setup A.1 T
Page 255 and 256:
Appendix A. Experimental setup g. s
Page 257 and 258:
A.2.1 Unimodal data sets Appendix A
Page 259 and 260:
A.2.2 Multimodal data sets Appendix
Page 261 and 262:
Appendix A. Experimental setup gene
Page 263 and 264:
Appendix A. Experimental setup orig
Page 265 and 266:
Appendix A. Experimental setup Data
Page 267:
Appendix A. Experimental setup or N
Page 270 and 271:
B.1. Clustering indeterminacies in
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
Page 286 and 287:
C.1. Configuration of a random hier
Page 288 and 289:
C.2. Estimation of the computationa
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
Page 326 and 327:
C.4. Computationally optimal RHCA,
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
Page 354 and 355:
Page 356 and 357:
Page 358 and 359:
Page 360 and 361:
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
D.1. Experiments on consensus-based
Page 372 and 373:
Page 374 and 375:
Page 376 and 377:
Page 378 and 379:
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
D.2. Experiments on selection-based
Page 386 and 387:
Page 388 and 389:
Page 390 and 391:
Page 392 and 393:
Page 394 and 395:
Page 396 and 397:
E.1. CAL500 data set φ (NMI) 1 0.8
Page 398 and 399:
E.1. CAL500 data set φ (NMI) CSPA
Page 400 and 401:
E.2. InternetAds data set φ (NMI)
Page 402 and 403:
E.3. Corel data set φ (NMI) 1 0.8
Page 404 and 405:
Page 406 and 407:
Page 408 and 409:
Page 410 and 411:
F.1. Iris data set φ (NMI) 1 0.8 0
Page 412 and 413:
F.3. Glass data set CSPA EAC HGPA M
Page 414 and 415:
F.5. WDBC data set φ (NMI) 1 0.8 0
Page 416 and 417:
F.7. MFeat data set φ (NMI) 1 0.8
Page 418 and 419:
F.9. Segmentation data set φ (NMI)
Page 420 and 421:
F.10. BBC data set φ (NMI) 1 0.8 0
Page 422 and 423:
F.11. PenDigits data set φ (NMI) 1
show all

TESI DOCTORAL - La Salle

Create successful ePaper yourself

Delete template?

Save as template?