270:) is particularly important, as it represents the instance preference, meaning how likely a particular instance is to become an exemplar. When it is set to the same value for all inputs, it controls how many classes the algorithm produces. A value close to the minimum possible similarity produces fewer classes, while a value close to or larger than the maximum possible similarity produces many classes. It is typically initialized to the median similarity of all pairs of inputs.
788:
Iterations are performed until either the cluster boundaries remain unchanged over a number of iterations, or some predetermined number (of iterations) is reached. The exemplars are extracted from the final matrices as those whose 'responsibility + availability' for themselves is positive (i.e.
683:
515:
783:
522:
225:
893:
applications. Another recent application was in economics, when the affinity propagation was used to find some temporal patterns in the output multipliers of the US economy between 1997 and 2017.
855:
268:
379:
1146:"Application of multivariate analysis as complementary instrument in studies about structural changes: An example of the multipliers in the US economy"
688:
1197:
49:, affinity propagation does not require the number of clusters to be determined or estimated before running the algorithm. Similar to
1099:
Renchu Guan; Xiaohu Shi; Maurizio
Marchese; Chen Yang; Yanchun Liang (2011). "Text Clustering with Seeds Affinity Propagation".
678:{\displaystyle a(i,k)\gets \min {\left(0,r(k,k)+\sum _{i'\not \in \{i,k\}}\max(0,r(i',k))\right)}\quad {\text{ for }}i\neq k}
149:
921:
914:
878:
903:
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partitioning found Markov clustering to work better for that problem. A semi-supervised variant has been proposed for
53:-medoids, affinity propagation finds "exemplars," members of the input set that are representative of clusters.
932:
886:
981:
792:
866:
1145:
973:
986:
273:
The algorithm proceeds by alternating between two message-passing steps, which update two matrices:
35:
based on the concept of "message passing" between data points. Unlike clustering algorithms such as
1050:"Markov clustering versus affinity propagation for the partitioning of protein interaction graphs"
1173:
1126:
1007:
36:
917:
implementation of affinity propagation is contained in Julia
Statistics's Clustering.jl package.
1165:
1081:
999:
964:
882:
869:
tasks, e.g. clustering of pictures of human faces and identifying regulated transcripts, than
131:. For this example, the negative squared distance of two data points was used i.e. for points
962:
Brendan J. Frey; Delbert Dueck (2007). "Clustering by passing messages between data points".
1157:
1116:
1108:
1071:
1061:
1030:
991:
238:
32:
865:
The inventors of affinity propagation showed it is better for certain computer vision and
369:
77:
be a set of data points, with no assumptions made about their internal structure, and let
977:
1076:
1049:
108:
1191:
1177:
1130:
1011:
925:
510:{\displaystyle r(i,k)\gets s(i,k)-\max _{k'\neq k}{\left\{a(i,k')+s(i,k')\right\}}}
1161:
1144:
Almeida, Lucas
Milanez de Lima; Balanco, Paulo Antonio de Freitas (2020-06-01).
890:
24:
81:
be a function that quantifies the similarity between any two points, such that
1034:
20:
1169:
1066:
995:
43:
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1003:
1112:
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372:
tables. The algorithm then performs the following updates iteratively:
1027:
Non-metric affinity propagation for unsupervised image categorization
368:
Both matrices are initialized to all zeroes, and can be viewed as
357:
as its exemplar, taking into account other points' preference for
778:{\displaystyle a(k,k)\leftarrow \sum _{i'\neq k}\max(0,r(i',k)).}
907:
877:-means was allowed many random restarts and initialized using
935:
implementation is available in the "apcluster" package.
220:{\displaystyle s(i,k)=-\left\|x_{i}-x_{k}\right\|^{2}}
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691:
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382:
241:
152:
1101:
IEEE Transactions on
Knowledge and Data Engineering
849:
777:
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343:that represent how "appropriate" it would be for
734:
616:
547:
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376:First, responsibility updates are sent around:
881:. A study comparing affinity propagation and
8:
611:
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312:, relative to other candidate exemplars for
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1150:Structural Change and Economic Dynamics
1048:James Vlasblom; Shoshana Wodak (2009).
1025:Delbert Dueck; Brendan J. Frey (2007).
945:
7:
850:{\displaystyle (r(i,i)+a(i,i))>0}
1029:. Int'l Conf. on Computer Vision.
906:implementation is included in the
519:Then, availability is updated per
14:
305:is to serve as the exemplar for
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298:that quantify how well-suited
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1:
1162:10.1016/j.strueco.2020.02.006
277:The "responsibility" matrix
1198:Cluster analysis algorithms
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322:The "availability" matrix
1035:10.1109/ICCV.2007.4408853
887:protein interaction graph
16:Algorithm in data mining
1067:10.1186/1471-2105-10-99
996:10.1126/science.1136800
924:version is part of the
910:data mining framework.
851:
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263:{\displaystyle s(i,i)}
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1113:10.1109/tkde.2010.144
867:computational biology
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33:clustering algorithm
29:affinity propagation
978:2007Sci...315..972F
117:is more similar to
1054:BMC Bioinformatics
873:-means, even when
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972:(5814): 972–976.
883:Markov clustering
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987:10.1.1.121.3145
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364:as an exemplar.
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1107:(4): 627–637.
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109:if and only if
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864:
861:Applications
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1156:: 189–207.
1122:11572/89884
891:text mining
283:has values
25:data mining
940:References
31:(AP) is a
21:statistics
1178:216406772
1170:0954-349X
1060:(1): 99.
982:CiteSeerX
727:≠
715:∑
711:←
670:≠
585:∑
545:←
439:≠
423:−
402:←
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175:−
57:Algorithm
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1131:14053903
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897:Software
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915:Julia
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1082:PMID
1000:PMID
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61:Let
23:and
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