Maths 2.4Lesson outlineLesson 4 of 5 in Module 2
Lines, Planes and Hyperplanes
Read `wᵀx + b = 0` as a boundary in any dimension: which side a point is on, and how far away it is.
Video in production.
Learn
In this lesson11 parts
- 01One rule from two measurements
- 02A line as w · x + b = 0
- 03The normal vector and the offset
- 04Three points and their scores
- 05Signed distance
- 06Planes in three dimensions and hyperplanes
- 07Checkpoint: the boundary, its side and its distance
- 08A separating line through the tiny ward
- 09Hard cases and mixed units
- 10Scores, sides and distances in NumPy
- 11Recap, challenge, and next: shapes and distance in d dimensions
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- score
w · x + bfor a pointx|6forP = (4, 3)- normal vector
- a vector perpendicular to a line or plane; here
w|(1, 2) - offset (bias)
b, which moves the line without turning it |−4- half-space
- all the points on one side of a line or plane | the positive side
- signed distance
(w · x + b) / ‖w‖, positive on the sidewpoints to |2.6833- plane
w · x + b = 0in three dimensions |x + 2y + 2z − 6 = 0- hyperplane
- the points where
w · x + b = 0, in any dimension | - linear classifier
- predicts the class from the sign of
w · x + b| the ward line, 14 of 14
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.