Reductions Over Axes
A reduction summarizes values.
An axis-specific reduction summarizes along one direction and leaves the other directions.
Matrix reductions
A.shape is (2, 3).
A.sum(axis=0)leaves one value per column.A.sum(axis=1)leaves one value per row.
Reduce by axis
Ready to run.
The removed-axis rule
When a reduction does not keep dimensions, the reduced axis disappears.
For shape (2, 3):
sum(axis=0) -> (3,)
sum(axis=1) -> (2,)
This rule becomes useful when arrays have more dimensions.
Mean over examples
If X.shape is (examples, features), then:
X.mean(axis=0)
computes one mean per feature.
X.mean(axis=1)
computes one mean per example.
Exercise: Feature means
If X.shape is (5, 3) and axis 0 means examples, what is the shape of
X.mean(axis=0)?
Answer it first, then check.
Hint
Remove the axis-0 length from (5, 3).
Solution
The shape is (3,). Reducing over the five examples removes axis 0 and
leaves one mean for each of the three features.