Statistics and Data Analysis for Microarrays Using R and Bioconductor, 2nd Edition

Cluster analysis 575

d

SE

(x, y) =

s

1

R

2

1

(x

1

− y

1

)

2

+ ··· +

1

R

2

n

(x

n

− y

n

)

2

=

v

u

u

t

n

X

i=1

1

R

2

i

(x

i

− y

i

)

2

(18.21)

where R

i

is the range of the da ta along dimension i.

18.2.8 Mahalanobis distance

The standardiz ed Euclidean distance used the idea of weighting each dimen-

sion by a quantity inversely proportional to the amount of variability along

that dimension. This is equivalent to distorting the space by shrinking it a long

the axes of large variance and expanding it along the axes of low variance. This

can be g e ne ralized. One might want to distort the space in an arbitrary way,

not necessarily along the axes. This is achieved by the Mahalano bis distance.

The