Wine Chemistry and Biochemistry

700 P.J. Mart ́ın-Alvarez ́

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0

20

40

60

80

100

120

Linkage Distance

Fig. 13.5Dendrogram for the 16 wines according to their volatile compounds content

X 1 X 2 ... Xp

Observ.

W 1

1

2

...

n 1

⎛

⎜

⎜

⎝

x 1 , 1 x 1 , 2 ... x 1 ,p

x 2 , 1 x 2 , 2 ... x 2 ,p

... ... ... ...

xn 1 , 1 xn 1 , 2 ... xn 1 ,p

⎞

⎟

⎟

⎠

X 1 X 2 ... Xp

Observ.

W 2

1

2

...

n 1

⎛

⎜

⎜

⎝

x 1 , 1 x 1 , 2 ... x 1 ,p

x 2 , 1 x 2 , 2 ... x 2 ,p

... ... ... ...

xn 2 , 1 xn 2 , 2 ... xn 2 ,p

⎞

⎟

⎟

⎠

...

X 1 X 2 ... Xp

Observ.

Wk

1

2

...

nk

⎛

⎜

⎜

⎝

x 1 , 1 x 1 , 2 ... x 1 ,p

x 2 , 1 x 2 , 2 ... x 2 ,p

... ... ... ...

xnk, 1 xnk, 2 ... xnk,p

⎞

⎟

⎟

⎠

The main objective of these techniques is to obtain, from the information of

n=

∑

ni, genuine observations (training set),classification rulesthat can be used

to differentiate thekgroups and to use these rules to assign new samples (test set)
into one ofkgroups. The most frequently used supervised classification methods