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!"#$$%&'()*+&,-./0&123452)2-(.6-&
Zornitsa Kozareva!USC/ISI!
Marina del Rey, [email protected]!
www.isi.edu/~kozareva!
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He is seen as a national hero by those who live in Georgia.
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Set of Objects
Feature Representation
Similarity Measure
Element Grouping
Output Interpretation
C"#:?$"'="J$"/"):#DA)'
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• ."_)+DA)0'GC'e':+X''– frequency of term i in document j
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Many low frequency words!
Can we adjust tf?!
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• 4SC0'+)E"$:".'.A%?8"):'P$"j?")%;'
• '."_)+DA)0'4SC'e'9A*Z+3,+^'– ni : number of documents containing term i – N : total number of documents
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• '-,.'&#/':IA'P"#:?$"/'+)%$"8"):".'K;'t]'– subj: John – obj: solution
• !&*,'&#/'A)"'P"#:?$"'– subj-of:find
found
John solution a
to problem
the
subj obj
mod det
pcomp
det
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L['
Set of Objects
Feature Representation
Similarity Measure
Element Grouping
Output Interpretation
<&#:'+/'!+8+9#$+:;a'
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• Hard to define, but we know it when we see it. • Easier to think in terms of the distance between vectors
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`L'
!
d(x, y) = xi " yip
i=1
m
#p
!
x = x1,x2,…,xn( )
!
y = y1,y2,…,yn( )
!
d(x, y) = xi " yi2
i=1
m
#2
!
d(x, y) = xi " yii=1
m
#
Euclidean distance
Manhattan distance
(N#8J9"'
``'
!
42 + 32 = 52Euclidean distance
3
4
!
4 + 3= 7Manhattan distance
reminder buying milk !from home to store!
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:&"'.+/:#)%"'8"#/?$",'
' 'G&"'.+/:#)%"'K":I"")'p#V;'#).'!"98#,'
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' ' ' '2&#)*"'&#+$'J#$:O']'JA+):'
''''''''''''''''''SZp#V;O!"98#^'e'`'
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' ' ''S"%$"#/"'&"+*&:O']'JA+):'
' ' ''G#Q"'?J'/8AQ+)*O']'JA+):'
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`5'
Slide adapted from CMU
29?/:"$+)*'p$A%"//'
• G&"'#%:?#9'%9?/:"$+)*'#9*A$+:&8/'
– @2*5(54?24(K& (KF652/?)O' I&+%&' %$"#:"/' #' &+"$#$%&+%#9'
."%A8JA/+DA)'AP':&"'"9"8"):/'
– I(5..6-2-F& (KF652/?)O' I&+%&' J$A.?%"/' #' /+)*9"'
J#$DDA)+)*'K;'AJD8+q+)*'/A8"'%$+:"$+A)'
`['
Set of Objects
Feature Representation
Similarity Measure
Element Grouping
Output Interpretation
TAVA8B?J'29?/:"$+)*'
B''T"*+)'I+:&'"#%&'"9"8"):'+)'#'/"J#$#:"'%9?/:"$'
B @"$*"'%9?/:"$/'+):A'/?%%"//+E"9;'9#$*"'%9?/:"$'
B ="J"#:'?)D9'A)"'%9?/:"$'+/'9"b'
`6'
Recommended reading: Chapter 14 on Clustering from the book of Manning& Schütze
GAJB.AI)'29?/:"$+)*'
B T"*+)'I+:&'#99'"9"8"):/'+)'#'I&A9"'%9?/:"$'
B S+E+."'%9?/:"$/'+):A'/?%%"//+E"9;'/8#99"$'
%9?/:"$'
B '="J"#:'?)D9'#99'"9"8"):/'#$"'+)'/+)*9":A)'
%9?/:"$/'
`7'
Recommended reading: Chapter 14 on Clustering from the book of Manning& Schütze
29?/:"$'p$AN+8+:;'(/D8#:"'
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`c'
(N#8J9"0'!+)*9"BU+)Q'@":&A.'
'' ' ' ' ''(?%9+."#)'S+/:#)%"'
`Y'
Distance Matrix
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`,'SA'9AAJ'
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!
µk =1ck
xii"Ck
#
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M' ' ' ']'
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M,['' 'M,['
[' ' ' '['
[' ' ' '6'
6' ' ' '6'
6' ' ' '['
[,['' '[,['
5]'
Task: Cluster the following objects into two clusters (k=2)
!
d(x, y) = xi " yii=1
m
#Manhattan distance Use:
Randomly initialize the clusters with the first two objects C1={(0,0)} C2={(0,1)}
Now: 2. Initialize cluster centers. 3a. Calculate the distance between each object and each cluster center, assigning the object to the closest cluster. 3b. Compute new cluster center for each cluster.
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Set of Objects
Feature Representation
Similarity Measure
Element Grouping
Output Interpretation
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