The following table gives some training data to be used in the classification of
flower types. Petal length and width are given for two different flowers. Plot this
information on a graph (utilizing the same scale for the *petal length* and
*petal width* axes) and then answer the questions below.

------------------------------------
| Petal Length | Petal Width | Class |
|--------------+-------------+-------|
| 4 | 3 | 1 |
|--------------+-------------+-------|
| 4.5 | 4 | 1 |
|--------------+-------------+-------|
| 3 | 4 | 1 |
|--------------+-------------+-------|
| 6 | 1 | 2 |
|--------------+-------------+-------|
| 7 | 1.5 | 2 |
|--------------+-------------+-------|
| 6.5 | 2 | 2 |
------------------------------------

**a)** Calculate the mean, or prototype, vectors
for the two flower types described above. **b)** Determine the decision
functions
for each class. **c)** Determine the equation of the boundary (*i.e.*
) and plot the decision surface
on your graph. **d)** Notice that substitution of a pattern from class
into your answer from the previous section yields a positive valued
, while a pattern belonging to the
class
yields a negative value. How would you use this information to determine a new pattern's
class membership?