Download - Using clustering to learn distance functions for supervised similarity assessment

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w1

Pw2

Pw3

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w1 = w2 = w3 = 1

3

�7UVWKjöj<=@?BA>UVWKM�d%_-UwAD;>=iM�de?D1

PD2

P<U`WKjD3

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cÖ!|}ul¾\n>ryx�z6ÅF��¢<n>rhnOvwsL�O½�pe�t�tn>�:��vÇÊ

n = |O|Ö!|Fuþ\n>ryx�z�x�¾`Â�nO�Dsh�&��v¿sh¼Fn�Å}p�sBpÃ�tn>s

Di

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Ö!|Fuþ\n>ryx�z��O½�|}��shn>rh�L|F�tn0Åπ(Θ, O)

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Ψ(Θ, O) = q(π(Θ, O))����p�½�|qp�sh��xevÁzi|}vF�>sh��x�v'zixer

Θ|}�t��v}º»pÃ�O½�|}��shn>rh��vFº)pe½�º�x�rh��sh¼}u

π

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Θ3

9

D1

0 1 2 3 4 30 1 2 3 1

0 1 2 20 1 3

0 10

D2

0 1 1 1 5 10 1 1 5 1

0 1 5 50 5 1

0 50

D3

0 3 3 2 2 30 3 2 2 3

0 2 2 20 1 3

0 10

D

0 1.67 2 2 3.67 2.330 1.67 1.67 3.33 1.67

0 1.33 3 30 2.33 2.33

0 2.330

� 9<d)CV]\fhd�M0A^j\=i?hAOU`WKM�d»_ÁU`AD;>=�î%é =@?^W<d�îqA^M�CF_¿EK[\ADd�j�[2?B=@W<c59

D =w1D1 + w2D2 + w3D3

w1 + w2 + w3

G�=@;O?hA�P�AD9KdÇU�ùVd�;OU`cFd¿M�SX[2?hA>d�;'UVWKjØU�ùVde;>UVcVd'=@W}ADde;Bæ�_-UwfhCV;>=XAhåÍCV]\fhd�M0A'j\=i?BA>U`W2M�de?)ì±CV;�d�UVMO9UwABA>;D=@]<[\A>d'9KU�ùFd)ADC�]2dÁM�CF_ÁE<[\ADd�jV�Òè:d7CV]\AOU`=@W79

σ1 = 2Pµ1 = 1.3

�σ2 = 2.6

Pµ2 = 1

�σ3 = 2.2

Pµ3 = 3

I � 9KdÐU�ùVde;>UVcVdHj\=@?BA>UVWKM�dËU`WKjÙAD9KdÐU�ùVde;>UVcVd%_ÁU`fhCV;>=�AhåÙd�î<U`_ÁE<S@de?j\=@?BA>UVWKM�dÃè�=XAD9<=@W$A>9<d)M�S@[K?BADd�;�è�=XAD9%;Dd�?BEÒdeM�A:A>C

ΘU`;>d�9

σ = 2.29Pµ = 1.78

I}Rl?D?D[<_Á=@W<cα = 0.2

P�è!d&CV]<A>U`=@W)A>9<d:WKd�èÿè!d�=@cV9}A>?"9{1.14∗0.33333, 1.32∗0.33333, 0.84∗0.33333}

IR�ì ADde;)AD9Kd¿è!d�=@cV9}AO?l92U�ùVd¿]2ded�WØUVj�fh[2?hA>dejÐì±CV;»AD9KdÇM�S@[K?hA>d�;�PÒAD9<dÁì±CFSXS@Cwè�=XWKc�W<deè�CF]\fhdeM�Aj\=@?BA>UVWKM�d»_-UwA>;D=Xî

D=i?�CV]\AOU`=@W<dejV9

D =

0 1.51 1.86 1.95 3.89 2.200 1.51 1.60 3.55 1.51

0 1.26 3.20 3.200 2.60 2.20

0 2.600

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σ = 2.31Pµ = 1.63

I�RT?¿è:d%M�UVWö?BdedVP�AD9Kd�d�î\UV_ÁE<SXd�?

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