714:
412:
107:
407:{\displaystyle d(A,B)=\sum _{i=1}^{n}\left(\sum _{j=1}^{n}{\frac {|p_{ij}|}{\max _{k}|p_{ik}|}}-1\right)+\sum _{j=1}^{n}\left(\sum _{i=1}^{n}{\frac {|p_{ij}|}{\max _{k}|p_{kj}|}}-1\right),P=A^{-1}B}
99:
448:
755:
496:
476:
554:
515:
Póczos, Barnabás; Takács, Bálint; Lőrincz, András (2005). Gama, João; Camacho, Rui; Brazdil, Pavel B.; Jorge, Alípio Mário; Torgo, Luís (eds.).
538:
748:
40:
652:
774:
741:
57:
779:
558:
48:
580:
36:
455:
32:
44:
690:
605:
534:
725:
420:
633:
595:
524:
451:
516:
43:
algorithms and for comparing solutions. It is named after
Japanese information theorist
721:
579:
Sobhani, Elaheh; Comon, Pierre; Jutten, Christian; Babaie-Zadeh, Massoud (2022-06-01).
481:
461:
768:
678:
600:
713:
458:. The Amari distance is invariant to permutation and scaling of the columns of
637:
694:
624:
609:
626:
The
Elements of Statistical Learning: Data Mining, Inference, and Prediction
523:. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer: 698–706.
555:"R Graphical Manual – Compute the 'Amari' distance between two matrices"
529:
632:. Springer Series in Statistics (2nd ed.). Springer New York.
623:
Hastie, Trevor; Friedman, Jerome; Tibshirani, Robert (2009).
651:
Amari, Shun-ichi; Cichocki, Andrzej; Yang, Howard (1995).
450:
is a scale and permutation matrix, i.e. the product of a
47:
and was originally introduced as a performance index for
729:
653:"A New Learning Algorithm for Blind Signal Separation"
581:"CorrIndex: A permutation invariant performance index"
484:
464:
423:
110:
60:
490:
470:
442:
406:
93:
16:Similarity measure between two invertible matrices
660:Advances in Neural Information Processing Systems
333:
208:
94:{\displaystyle A,B\in \mathbb {R} ^{n\times n}}
517:"Independent Subspace Analysis on Innovations"
417:It is non-negative and cancels if and only if
749:
677:Bach, Francis R.; Jordan, Michael I. (2002).
8:
756:
742:
599:
528:
483:
463:
428:
422:
392:
360:
351:
342:
336:
325:
316:
307:
304:
298:
287:
272:
261:
235:
226:
217:
211:
200:
191:
182:
179:
173:
162:
147:
136:
109:
79:
75:
74:
59:
39:, useful for checking for convergence in
679:"Kernel Independent Component Analysis"
507:
7:
710:
708:
683:Journal of Machine Learning Research
728:. You can help Knowledge (XXG) by
14:
712:
361:
343:
326:
308:
236:
218:
201:
183:
126:
114:
41:independent component analysis
1:
601:10.1016/j.sigpro.2022.108457
54:For two invertible matrices
521:Machine Learning: ECML 2005
796:
707:
638:10.1007/978-0-387-84858-7
443:{\displaystyle A^{-1}B}
49:blind source separation
724:-related article is a
492:
472:
444:
408:
303:
277:
178:
152:
95:
493:
473:
445:
409:
283:
257:
158:
132:
96:
775:Linear algebra stubs
482:
462:
421:
108:
101:, it is defined as:
58:
530:10.1007/11564096_71
37:invertible matrices
488:
468:
456:permutation matrix
440:
404:
341:
216:
91:
33:similarity measure
780:Signal estimation
737:
736:
588:Signal Processing
540:978-3-540-31692-3
491:{\displaystyle B}
471:{\displaystyle A}
366:
332:
241:
207:
787:
758:
751:
744:
716:
709:
699:
698:
674:
668:
667:
657:
648:
642:
641:
631:
620:
614:
613:
603:
585:
576:
570:
569:
567:
566:
557:. Archived from
551:
545:
544:
532:
512:
497:
495:
494:
489:
477:
475:
474:
469:
449:
447:
446:
441:
436:
435:
413:
411:
410:
405:
400:
399:
378:
374:
367:
365:
364:
359:
358:
346:
340:
330:
329:
324:
323:
311:
305:
302:
297:
276:
271:
253:
249:
242:
240:
239:
234:
233:
221:
215:
205:
204:
199:
198:
186:
180:
177:
172:
151:
146:
100:
98:
97:
92:
90:
89:
78:
23:, also known as
795:
794:
790:
789:
788:
786:
785:
784:
765:
764:
763:
762:
705:
703:
702:
676:
675:
671:
655:
650:
649:
645:
629:
622:
621:
617:
583:
578:
577:
573:
564:
562:
553:
552:
548:
541:
514:
513:
509:
504:
480:
479:
460:
459:
452:diagonal matrix
424:
419:
418:
388:
347:
331:
312:
306:
282:
278:
222:
206:
187:
181:
157:
153:
106:
105:
73:
56:
55:
45:Shun'ichi Amari
17:
12:
11:
5:
793:
791:
783:
782:
777:
767:
766:
761:
760:
753:
746:
738:
735:
734:
722:linear algebra
717:
701:
700:
669:
643:
615:
571:
546:
539:
506:
505:
503:
500:
487:
467:
439:
434:
431:
427:
415:
414:
403:
398:
395:
391:
387:
384:
381:
377:
373:
370:
363:
357:
354:
350:
345:
339:
335:
328:
322:
319:
315:
310:
301:
296:
293:
290:
286:
281:
275:
270:
267:
264:
260:
256:
252:
248:
245:
238:
232:
229:
225:
220:
214:
210:
203:
197:
194:
190:
185:
176:
171:
168:
165:
161:
156:
150:
145:
142:
139:
135:
131:
128:
125:
122:
119:
116:
113:
88:
85:
82:
77:
72:
69:
66:
63:
21:Amari distance
15:
13:
10:
9:
6:
4:
3:
2:
792:
781:
778:
776:
773:
772:
770:
759:
754:
752:
747:
745:
740:
739:
733:
731:
727:
723:
718:
715:
711:
706:
696:
692:
689:(Jul): 1–48.
688:
684:
680:
673:
670:
665:
661:
654:
647:
644:
639:
635:
628:
627:
619:
616:
611:
607:
602:
597:
593:
589:
582:
575:
572:
561:on 2015-01-09
560:
556:
550:
547:
542:
536:
531:
526:
522:
518:
511:
508:
501:
499:
485:
465:
457:
453:
437:
432:
429:
425:
401:
396:
393:
389:
385:
382:
379:
375:
371:
368:
355:
352:
348:
337:
320:
317:
313:
299:
294:
291:
288:
284:
279:
273:
268:
265:
262:
258:
254:
250:
246:
243:
230:
227:
223:
212:
195:
192:
188:
174:
169:
166:
163:
159:
154:
148:
143:
140:
137:
133:
129:
123:
120:
117:
111:
104:
103:
102:
86:
83:
80:
70:
67:
64:
61:
52:
50:
46:
42:
38:
34:
30:
26:
22:
730:expanding it
719:
704:
686:
682:
672:
666:. MIT Press.
663:
659:
646:
625:
618:
591:
587:
574:
563:. Retrieved
559:the original
549:
520:
510:
416:
53:
35:between two
29:Amari metric
28:
24:
20:
18:
25:Amari index
769:Categories
594:: 108457.
565:2019-05-16
502:References
695:1533-7928
610:0165-1684
430:−
394:−
369:−
285:∑
259:∑
244:−
160:∑
134:∑
84:×
71:∈
693:
608:
537:
454:and a
720:This
656:(PDF)
630:(PDF)
584:(PDF)
31:is a
726:stub
691:ISSN
606:ISSN
535:ISBN
478:and
27:and
19:The
634:doi
596:doi
592:195
525:doi
334:max
209:max
771::
685:.
681:.
662:.
658:.
604:.
590:.
586:.
533:.
519:.
498:.
51:.
757:e
750:t
743:v
732:.
697:.
687:3
664:8
640:.
636::
612:.
598::
568:.
543:.
527::
486:B
466:A
438:B
433:1
426:A
402:B
397:1
390:A
386:=
383:P
380:,
376:)
372:1
362:|
356:j
353:k
349:p
344:|
338:k
327:|
321:j
318:i
314:p
309:|
300:n
295:1
292:=
289:i
280:(
274:n
269:1
266:=
263:j
255:+
251:)
247:1
237:|
231:k
228:i
224:p
219:|
213:k
202:|
196:j
193:i
189:p
184:|
175:n
170:1
167:=
164:j
155:(
149:n
144:1
141:=
138:i
130:=
127:)
124:B
121:,
118:A
115:(
112:d
87:n
81:n
76:R
68:B
65:,
62:A
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
