SPSS® 12.0 Command Syntax Reference

230 CLUSTER
CHEBYCHEV Chebychev distance metric. The distance between two items is the maximum
absolute difference between the values for the items.
BLOCK City-block or Manhattan distance. The distance between two items is the
sum of the absolute differences between the values for the items.
MINKOWSKI(p) Distance in an absolute Minkowski power metric. The distance between two
items is the pth root of the sum of the absolute differences to the pth power
between the values for the items. Appropriate selection of the integer parameter
p yields Euclidean and many other distance metrics.
POWER(p,r) Distance in an absolute power metric. The distance between two items is the
rth root of the sum of the absolute differences to the pth power between the
values for the items. Appropriate selection of the integer parameters p and r
yields Euclidean, squared Euclidean, Minkowski, city-block, and many
other distance metrics.
Measures for Frequency Count Data
CHEBYCHEV( x, y)
= maxi xi – yi BLOCK( xy , ) = Σixi– yi MINKOWSKI( xy , ) = ( Σixi– y p
i )
POWER( xy , ) = ( Σixi– y p
i )
For frequency count data, use any one of the following keywords on MEASURE:
CHISQ Based on the chi-square test of equality for two sets of frequencies. The
magnitude of this dissimilarity measure depends on the total frequencies of
the two cases or variables whose dissimilarity is computed. Expected values
are from the model of independence of cases or variables x and y.
CHISQ( x, y)
=
PH2 Phi-square between sets of frequencies. This is the CHISQ measure
normalized by the square root of the combined frequency. Therefore, its
value does not depend on the total frequencies of the two cases or variables
whose dissimilarity is computed.
PH2( x, y)
=
1 r /
1 p /
Σi( xi – Ex ( i)
) 2
----------------------------------
( )
Σi yi Ey ( – ( i)
) 2
+ ----------------------------------
( )
Ex i
Ey i
Σi( xi – Ex ( i)
) 2
----------------------------------
Ex ( i)
Σi yi Ey ( – ( i)
) 2
+ ----------------------------------
Ey ( i)
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