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![Page 1: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/1.jpg)
Similarity Evaluation Techniques for Filtering Problems
??Vagan TerziyanVagan TerziyanUniversity of JyvaskylaUniversity of Jyvaskyla
![Page 2: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/2.jpg)
Evaluating Distance between Various Domain Objects and Concepts - one of the basic abilities of an intelligent agent
Are these two the same?
… No !The difference is
equal to 0.234
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Contents
Goal Basic Concepts External Similarity Evaluation An Example Internal Similarity Evaluation Conclusions
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Reference
Puuronen S., Terziyan V., A Similarity Evaluation A Similarity Evaluation Technique for Data Mining with an Ensemble of Technique for Data Mining with an Ensemble of ClassifiersClassifiers, In: A.M. Tjoa, R.R. Wagner and A. Al-Zobaidie (Eds.), Proc. of the 11th Intern. Workshop on Database and Expert Systems Applications, IEEE CS Press, Los Alamitos, California, 2000, pp. 1155-1159. http://dlib.computer.org/conferen/dexa/0680/pdf/06801155.pdf
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Goal
The goal of this research is to develop simple similarity evaluation technique to be used for social filtering
Result of social filtering here here is prediction of a customer’s evaluation of certain product based on known opinions about this product from other customers
![Page 6: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/6.jpg)
Basic Concepts:Virtual Training Environment (VTE)
VTE is a quadruple:
<D,C,S,P>• D is the set of goods D1, D2,..., Dn in the VTE;
• C is the set of evaluation marks C1, C2,..., Cm , that are used to rank the products;
• S is the set of customers S1, S2,..., Sr , who select evaluation marks to rank the products;
• P is the set of semantic predicates that define relationships between D, C, S
![Page 7: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/7.jpg)
Basic Concepts:Semantic Predicate P
. te D to evalualect C to se
refuseselect or does not ,if S
;aluate D to ev
o select C refuses t,if S
;D product aluate the to ev
ark C selects mstomer S,if the cu
),S,CP(D
ij
k
i
jk
i
jk
kji
0
1
1
![Page 8: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/8.jpg)
Problem 1:Deriving External Similarity Values
DC
S
DiCj
Sk
SDk,i
DCi,j
SCk,j
![Page 9: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/9.jpg)
External Similarity Values
External Similarity Values (ESV): binary relations DC, SC, and SD between the elements of (sub)sets of D and C; S and C; and S and D.
ESV are based on total support among all the customers for voting for the appropriate connection (or refusal to vote)
DC
S
DiCj
Sk
SDk,i
DCi,j
SCk,j
![Page 10: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/10.jpg)
Problem 2:Deriving Internal Similarity Values
D C
S
Di’
SSk’,k’’
DDi’,i’’ CCj’,j’’
Di’’
Cj’
Cj’’
Sk’
Sk’’
![Page 11: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/11.jpg)
Internal Similarity Values
Internal Similarity Values (ISV): binary relations between two subsets of D, two subsets of C and two subsets of S.
ISV are based on total support among all the customers for voting for the appropriate connection (or refusal to vote)
D C
S
Di’
SSk’,k’’
DDi’,i’’ CCj’,j’’
Di’’
Cj’
Cj’’
Sk’
Sk’’
![Page 12: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/12.jpg)
Why we Need Similarity Values (or Distance Measure) ? Distance between products is used to advertise the
customers a new product based on evaluation of already known similar products
distance between evaluations is necessary to estimate evaluation error when necessary, e.g. in the case of adaptive filtering technologies used
distance between customers is useful to evaluate weights of all customers when necessary, e.g. to be able to integrate their opinions by weighted voting.
![Page 13: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/13.jpg)
Deriving External Relation DC:How well evaluation fits the product
DC CD P D C S D D C Ci j j i i j k i jk
r
, , ( , , ), ,
DC
S
DiCj
Sk2
DCi,j=3
Sk1
Sk3
Customers
Products Evaluation marks
![Page 14: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/14.jpg)
Deriving External Relation SC:Measures customer’s competence in the use of evaluation marks
The value of the relation (Sk,Cj) in a way represents the total support that the customer Sk obtains selecting (refusing to select) the mark Cj to evaluate all the products.
SC CS DC P D C S S S C Ck j j k i j i j ki
n
k j, , , ( , , ), ,
![Page 15: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/15.jpg)
Example of SC Relation
DC
SSk
Cj
D2
SCk,j=4
D1
D4
D3
CDj1 = -3
CDj2 = 6
CDj3 = 0
CDj4 = 1
Customers
Products Evaluation marks
![Page 16: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/16.jpg)
Deriving External Relation SD:Measures customer’s competence in the products
The value of the relation (Sk,Di) represents the total support that the agent Sk receives selecting (or refusing to select) all the solutions to solve the problem Di.
SD DS DC P D C S S S D Dk i i k i j i j kj
m
k i, , , ( , , ), ,
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Example of SD Relation
DC
SSk
Di
C1
SDk,i=2
C2
CD1i = -3
CD2i = 5
ProductsEvaluation marks
Customers
![Page 18: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/18.jpg)
Normalizing External Relations to the Interval [0,1]
min(value)-max(value)
)valuemin( value=value valuegnormalizin
-
DC CDDC r
ri j j ii j
, ,,
2
SC CSSC n r
n rk j j kk j
, ,, ( )
( )
2
2 1
SD DSSD m r
m rk i i kk i
, ,, ( )
( )
2
2 1
n is the number of products
m is the number of evaluation marks
r is the number of customers
![Page 19: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/19.jpg)
Competence of a customer
Di
Conceptual pattern of goods’ features
Conceptual pattern of evaluation marks definitions
GoodsEvaluation
marks
Cj
Customer
Competence in the goods
Competence in the evaluation marks
![Page 20: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/20.jpg)
Customer’s Evaluation:competence quality in Products
Q Sn
SDDk k i
i
n( ) , 1
![Page 21: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/21.jpg)
Customer’s Evaluation:competence quality in evaluation marks use
Q Sm
SCCk k j
j
m( ) , 1
![Page 22: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/22.jpg)
Quality Balance Theorem
Q S Q SDk
Ck( ) ( )
The evaluation of a customer’s competence (ranking, weighting, quality evaluation) does not depend on the competence area “virtual world of products” or “conceptual world of evaluation marks” because both competence values are always equal.
![Page 23: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/23.jpg)
Proof
Q Sn
SDn
SD m r
m rD
k k ii
nk i
i
n( )
( )
( ),,
1 1 2
2 1
1
2
2 1n
DC P D C S m r
m r
i j i j kj
m
i
n( ( , , )) ( )
( )
,
1
2
2 1m
DC P D C S n r
n r
i j i j ki
n
j
m( ( , , )) ( )
( )
,
...
...
1 2
2 1
1
m
SC n r
n r mSC Q S
k j
j
m
k jj
mC
k,
,
( )
( )( )
![Page 24: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/24.jpg)
An Example
Let us suppose that four customers have to evaluate three products from virtual shop using five different evaluation marks available.
The customers should define their selection of appropriate mark for every product.
The final goal is to obtain a cooperative evaluation result of all the customers concerning the quality of products.
![Page 25: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/25.jpg)
C set (evaluation marks) in the Example
Evaluation marks Notation
Nicely designed C1
Expensive C2
Easy to use C3
Reliable C4
Safe C5
![Page 26: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/26.jpg)
S (customers) Set in the Example
Customers IDs Notation
Fox S1
Wolf S2
Cat S3
Hare S4
![Page 27: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/27.jpg)
D (products) Set in the Example
D2 - Nokia Communicator 9110
D1 - Ultra Cast Spinning Reel
D3 - iGrafx Process Management
Software
![Page 28: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/28.jpg)
Evaluations Made for the Good “Reel”
D1
P(D,C,S) C1 C2 C3 C4 C5
S1 1 -1 -1 0 -1
S2 0+ -1** 0 ++ 1* -1***
S3 0 0 -1 1 0
S4 1 -1 0 0 1Customer Wolf prefers to select mark Reliable* to evaluate “Reel” and it refuses to select Expensive** or Safe***. Wolf does not use or refuse to use the Nicely designed+ or Easy to use++ marks for evaluation.
![Page 29: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/29.jpg)
Evaluations Made for the Good “Communicator”
D2
P C1 C2 C3 C4 C5
S1 -1 0 -1 0 1
S2 1 -1 -1 0 0
S3 1 -1 0 1 1
S4 -1 0 0 1 0
![Page 30: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/30.jpg)
Evaluations Made for the Good “Software”
D3
P C1 C2 C3 C4 C5
S1 1 0 1 -1 0
S2 0 1 0 -1 1
S3 -1 -1 1 -1 1
S4 -1 -1 1 -1 1
![Page 31: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/31.jpg)
Example: Calculating Value DC3,4
D3
P C1 C2 C3 C4 C5
S1 1 0 1 -1 0
S2 0 1 0 -1 1
S3 -1 -1 1 -1 1
S4 -1 -1 1 -1 1
r
kjikjiijji CCDDSCDPCDDC ,),,,(,,
4)1()1()1()1(),,(4
434,3 k
kSCDPDC
![Page 32: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/32.jpg)
Resulting DC relation
DC C1 C2 C3 C4 C5
D1 2 -3 -2 2 -1
D2 0 -2 -2 2 2
D3 -1 -1 3 -4 3
![Page 33: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/33.jpg)
Normalized and “Thresholded” DC relation
[DC] C1 C2 C3 C4 C5
D1 0.75 0.125 0.25 0.75 0.375D2 0.5 0.25 0.25 0.75 0.75D3 0.375 0.375 0.875 0 0.875
[DC] 0.75 C1 C2 C3 C4 C5
D1 1 -1 -1 1 0
D2 0 -1 -1 1 1
D3 0 0 1 -1 1
0 10.50.25 0.75
0 1-1
![Page 34: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/34.jpg)
Result of Cooperative Goods Evaluation Based on DC Relation
D2 is reliable, safe, not expensive,
but not easy to use
D1 is nicely designed, reliable, not
expensive, but not easy to use
D3 is easy to use, safe, but not
reliable
![Page 35: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/35.jpg)
An Example: Calculating Value SD1,1
D1
P C1 C2 C3 C4 C5
S1 1 -1 -1 0 -1S2 0 -1 0 1 -1
S3 0 0 -1 1 0
S4 1 -1 0 0 1
DC C1 C2 C3 C4 C5
D1 2 -3 -2 2 -1
D2 0 -2 -2 2 2
D3 -1 -1 3 -4 3
8)1()1(02)1()2()1()3(12),,(5
11,11,1 j
jj SCDPDCSD
m
jikkjijikiik DDSSSCDPDCDSSD ,),,,(,,,
![Page 36: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/36.jpg)
An Example: Calculating Value SC4,4
n
ijkkjijikjjk CCSSSCDPDCCSSC ,),,,(,,,
DC C1 C2 C3 C4C5
D1 2 -3 -2 2 -1
D2 0 -2 -2 2 2
D3 -1 -1 3 -4 3
P C1 C2 C3 C4C5
D1
S41 -1 0 0 1
D2
S4-1 0 0 1 0
D3
S4-1 -1 1 -1 1
6)1()4(1202),,(3
444,4,4 i
ii SCDPDCSC
![Page 37: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/37.jpg)
Resulting SD and SC relations
SD D1 D2 D3
S1 8 4 6
S2 6 4 6
S3 4 6 12
S4 4 2 12
SC C1 C2 C3 C4 C5
S1 1 3 7 4 3
S2 0 4 2 6 4
S3 1 3 5 8 5
S4 3 4 3 6 2
![Page 38: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/38.jpg)
… or similar to “Software” .
Fox’s evaluations should be rejected ifthey concern goods similar to “Communicator”
Evaluations obtained from thecustomer Fox should be accepted if heevaluates goods similar to “Reels” ...
Normalized and “Thresholded” SD relation
[SD] 0.75 D1 D2 D3
S1 1 -1 1
S2 1 -1 1
S3 -1 1 1
S4 -1 -1 1
FoxWolfCatHare
![Page 39: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/39.jpg)
Only evaluation from the customerCat can be accepted if it concernsgoods similar to “Communicator”
Normalized and “Thresholded” SD relation
[SD] 0.75 D1 D2 D3
S1 1 -1 1
S2 1 -1 1
S3 -1 1 1
S4 -1 -1 1
FoxWolfCatHare
All four customers are expectedto give an acceptable evaluations
concerning “Software” related goods
![Page 40: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/40.jpg)
… or reliability of a good .
Evaluation obtained from the customer Fox should be accepted if it concern usability (easy to use) of a good...
Fox’s evaluations should be rejected
if they concern design of goods
Normalized and “Thresholded” SC relation
[SC]0.75 C1 C2 C3 C4 C5
S1 -1 0 1 1 0
S2 -1 1 -1 1 1
S3 -1 0 1 1 1
S4 0 1 0 1 -1
FoxWolfCatHare
Nicely designed Expensive
Easy to use Reliable Safe
![Page 41: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/41.jpg)
Problem 2:Deriving Internal Similarity Values
D C
S
Di’
SSk’,k’’
DDi’,i’’ CCj’,j’’
Di’’
Cj’
Cj’’
Sk’
Sk’’
![Page 42: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/42.jpg)
Internal Similarity Values
Internal Similarity Values (ISV): binary relations between two subsets of D, two subsets of C and two subsets of S.
ISV are based on total support among all the customers for voting for the appropriate connection (or refusal to vote)
D C
S
Di’
SSk’,k’’
DDi’,i’’ CCj’,j’’
Di’’
Cj’
Cj’’
Sk’
Sk’’
![Page 43: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/43.jpg)
Deriving Internal Similarity Values
Set A Set I
A’
A”
A’I
IA”
A’A”I
A’
A”
a)
Set A
Set I
A’
A”
A’I
JA”
A’A”IJ
A’
A”
b)
Set J
IJ
Via one intermediate set Via two intermediate sets
![Page 44: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/44.jpg)
Internal Similarity for Customers:Goods-based Similarity
D C
SS’S’’D
S’’
S’DS’’
S’D
S S S S S S S D DSD' '' ' '' ' '',
Goods
Customers
![Page 45: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/45.jpg)
Internal Similarity for Customers:Evaluation marks-Based Similarity
D C
SS’S’’C
S’’
S’
CS’’
S’C
S S S S S S S C CSC' '' ' '' ' '',
Evaluation marks
Customers
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Internal Similarity for Customers:Evaluation marks-Goods-Based Similarity
D C
SS’S’’CD
S’’
S’DS’’S’C
CD
S S S S S S S C CD DSCD' '' ' '' ' '',
Customers
Evaluation marks
Goods
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Internal Similarity for Evaluation Marks
DC
S
C’C’’S
C’’
C’
C’S
SC’’
DC
S
C’C’’D
C’’
C’C’D
DC’’
DC
S
C’C’’DS
C’’
C’C’D
SC’’DS
Customers-based similarity Goods-based similarity
Goods-customers-based similarity
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Internal Similarity for Goods
Customers-based similarity Evaluation marks-based similarity
Evaluation marks-customers-based similarity
DC
S
D’D’’S
D’’
D’
D’S
SD’’
DC
S
D’D’’C
D’’
D’ D’C
CD’’
DC
S
D’D’’CS
D’’
D’ D’C
SD’’CS
![Page 49: Similarity Evaluation Techniques for Filtering Problems ? Vagan Terziyan University of Jyvaskyla vagan@it.jyu.fi.](https://reader036.fdocuments.in/reader036/viewer/2022062511/5517cbe0550346892b8b4d2c/html5/thumbnails/49.jpg)
Normalized and “Thresholded” DDC relation
[CD] 0.75 D1 D2 D3
C1 1 0 0
C2 -1 -1 0
C3 -1 -1 1
C4 1 1 -1
C5 0 1 1
[DC] 0.75 C1 C2 C3 C4 C5
D1 1 -1 -1 1 0
D2 0 -1 -1 1 1
D3 0 0 1 -1 1
[DD] 0.75 D1 D2 D3
D1 1 1 -1
D2 1 1 0
D3 -1 0 1
similar
neutral
different
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Conclusion
Discussion was given to methods of deriving the total support of each binary similarity relation. This can be used, for example, to derive the most supported goods evaluation and to rank the customers according to their competence
We also discussed relations between elements taken from the same set: goods, evaluation marks, or customers. This can be used, for example, to divide customers into groups of similar competence relatively to the goods evaluation environment