This problem does not require the use of data mining software and focuses on knowledge of concepts and basic calculations.

Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table.

Characteristic Cluster $1$ Cluster $2$ Cluster $3$

Alcohol $0\mathrm{.}8190\mathrm{.}1640\mathrm{.}937$

Malic Acid $0\mathrm{.}3290\mathrm{.}8690\mathrm{.}368$

Ash $0\mathrm{.}2480\mathrm{.}1860\mathrm{.}393$

Alkalinity $0\mathrm{.}6770\mathrm{.}5230\mathrm{.}249$

Magnesium $0\mathrm{.}6430\mathrm{.}0750\mathrm{.}573$

Phenols $0\mathrm{.}8250\mathrm{.}9770\mathrm{.}034$

Flavonoids $0\mathrm{.}8961\mathrm{.}2120\mathrm{.}083$

Nonflavonoids $0\mathrm{.}5950\mathrm{.}7240\mathrm{.}009$

Proanthocyanidins $0\mathrm{.}6190\mathrm{.}7780\mathrm{.}010$

Color Intensity $0\mathrm{.}1350\mathrm{.}9390\mathrm{.}881$

Hue $0\mathrm{.}4971\mathrm{.}1620\mathrm{.}437$

Dilution $0\mathrm{.}7441\mathrm{.}2890\mathrm{.}295$

Proline $1\mathrm{.}1170\mathrm{.}4060\mathrm{.}776$

Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should he place this new wine? Justify your choice with appropriate calculations.

Characteristic

Alcohol $0\mathrm{.}937$

Malic Acid $0\mathrm{.}394$

Ash $0\mathrm{.}135$

Alkalinity $0\mathrm{.}686$

Magnesium $1\mathrm{.}156$

Phenols $1\mathrm{.}18$

Flavonoids $0\mathrm{.}087$

Nonflavonoids $0\mathrm{.}462$

Proanthocyanidins $0\mathrm{.}143$

Color Intensity $0\mathrm{.}711$

Hue $0\mathrm{.}797$

Dilution $0\mathrm{.}339$

Proline $0\mathrm{.}096$

Calculate the following Euclidean distances. $($Round your answers to three decimal places.$)$

$$ Euclidean distance from new wine and Cluster $1$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ Euclidean distance from new wine and Cluster $2$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$$ Euclidean distance from new wine and Cluster $3$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

In which cluster of wines should he place this new wine? Select $($Cluster $1,$ Cluster $2$ or Cluster $3)$