neural networks

Prediction Functions
Remember: a prediction function is the
function that predicts what the output should be,
given the input
Last time we looked at linear functions, which
are commonly used as prediction functions.
Linear Classification
A linear function divides the coordinate
space into two parts.
• Every point is either on one side of the line (or
plane or hyperplane) or the other.
• Unless it is exactly on the line… we’ll come back to
this case in a minute.
• This means it can only separate two classes.
• Classification with two classes is called binary
classification.
• Conventionally, one class is called the positive
class and the other is the negative class.
• We’ll discuss classification with >2 classes later on.
Classi?er, an illustration

A classi?er partitions the observation space X into class-labelled regions X
,
i = 1, . . . , |Y |.

Classi?cation determines to which region X
an observed feature vector x
belongs.

Borders between regions are called
decision boundaries.