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Local tangent space alignment

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389: 63: 22: 165: 285:-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by 80: 35: 430: 359:
Ma, L.; Crawford, M. M.; Tian, J. W. (2010). "Generalised supervised local tangent space alignment for hyperspectral image classification".
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data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a
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Zhang, Zhenyue; Hongyuan Zha (2004). "Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment".
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to the manifold will become aligned. It begins by computing the
158: 56: 15: 289:, and thus can not be used for classification directly. 404: 87:. Unsourced material may be challenged and removed. 424: 8: 186:. There might be a discussion about this on 50:Learn how and when to remove these messages 431: 417: 331: 224:Learn how and when to remove this message 206:Learn how and when to remove this message 147:Learn how and when to remove this message 310: 7: 385: 383: 320:SIAM Journal on Scientific Computing 85:adding citations to reliable sources 403:. You can help Knowledge (XXG) by 263:is correctly unfolded, all of the 14: 277:of every point. It computes the 31:This article has multiple issues. 387: 281:at every point by computing the 247:, which can efficiently learn a 163: 61: 20: 96:"Local tangent space alignment" 72:needs additional citations for 39:or discuss these issues on the 1: 237:Local tangent space alignment 476: 382: 342:10.1137/s1064827502419154 399:-related article is a 373:10.1049/el.2010.2613 176:confusing or unclear 81:improve this article 450:Dimension reduction 361:Electronics Letters 184:clarify the article 275:-nearest neighbors 243:) is a method for 412: 411: 255:coordinates from 245:manifold learning 234: 233: 226: 216: 215: 208: 157: 156: 149: 131: 54: 467: 460:Statistics stubs 433: 426: 419: 391: 384: 376: 346: 345: 335: 315: 257:high-dimensional 229: 222: 211: 204: 200: 197: 191: 167: 166: 159: 152: 145: 141: 138: 132: 130: 89: 65: 57: 46: 24: 23: 16: 475: 474: 470: 469: 468: 466: 465: 464: 440: 439: 438: 437: 380: 358: 355: 353:Further reading 350: 349: 333:10.1.1.211.9957 317: 316: 312: 307: 295: 253:low-dimensional 251:embedding into 230: 219: 218: 217: 212: 201: 195: 192: 181: 168: 164: 153: 142: 136: 133: 90: 88: 78: 66: 25: 21: 12: 11: 5: 473: 471: 463: 462: 457: 452: 442: 441: 436: 435: 428: 421: 413: 410: 409: 392: 378: 377: 354: 351: 348: 347: 326:(1): 313–338. 309: 308: 306: 303: 302: 301: 294: 291: 232: 231: 214: 213: 196:September 2009 171: 169: 162: 155: 154: 137:September 2009 69: 67: 60: 55: 29: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 472: 461: 458: 456: 453: 451: 448: 447: 445: 434: 429: 427: 422: 420: 415: 414: 408: 406: 402: 398: 393: 390: 386: 381: 374: 370: 366: 362: 357: 356: 352: 343: 339: 334: 329: 325: 321: 314: 311: 304: 300: 297: 296: 292: 290: 288: 284: 280: 279:tangent space 276: 274: 269: 266: 262: 258: 254: 250: 246: 242: 238: 228: 225: 210: 207: 199: 189: 188:the talk page 185: 179: 177: 172:This article 170: 161: 160: 151: 148: 140: 129: 126: 122: 119: 115: 112: 108: 105: 101: 98: –  97: 93: 92:Find sources: 86: 82: 76: 75: 70:This article 68: 64: 59: 58: 53: 51: 44: 43: 38: 37: 32: 27: 18: 17: 405:expanding it 394: 379: 364: 360: 323: 319: 313: 287:data samples 282: 272: 240: 236: 235: 220: 202: 193: 182:Please help 173: 143: 134: 124: 117: 110: 103: 91: 79:Please help 74:verification 71: 47: 40: 34: 33:Please help 30: 268:hyperplanes 444:Categories 397:statistics 367:(7): 497. 305:References 178:to readers 107:newspapers 36:improve it 455:Manifolds 328:CiteSeerX 249:nonlinear 42:talk page 293:See also 261:manifold 265:tangent 174:may be 121:scholar 330:  299:Isomap 123:  116:  109:  102:  94:  395:This 128:JSTOR 114:books 401:stub 241:LTSA 100:news 369:doi 338:doi 83:by 446:: 365:46 363:. 336:. 324:26 322:. 45:. 432:e 425:t 418:v 407:. 375:. 371:: 344:. 340:: 283:d 273:k 239:( 227:) 221:( 209:) 203:( 198:) 194:( 190:. 180:. 150:) 144:( 139:) 135:( 125:· 118:· 111:· 104:· 77:. 52:) 48:(

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improve it
talk page
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verification
improve this article
adding citations to reliable sources
"Local tangent space alignment"
news
newspapers
books
scholar
JSTOR
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confusing or unclear
clarify the article
the talk page
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manifold learning
nonlinear
low-dimensional
high-dimensional
manifold
tangent
hyperplanes
k-nearest neighbors
tangent space
data samples
Isomap

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