O'Reilly logo

Machine Learning with Spark - Second Edition by Nick Pentreath, Manpreet Singh Ghotra, Rajdeep Dua

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Hyperplanes

Vectors of field type real numbers are difficult to visualize if n is not 1,2, or 3. Familiar objects like lines and planes make sense for any value of n. Line L along the direction defined by a vector v, through a point P labeled by a vector u, can be written as follows:

L = {u + tv | t ∈ R}

Given two non-zero vectors, u and v, they determine a plane if both the vectors are not in the same line, and one of the vectors is a scalar multiple of the other. The addition of two vectors is accomplished by laying the vectors head to tail in a sequence to create a triangle. If u and v lie in a plane, then their sum lies in the plane of u and v. The plane represented by two vectors u and v can be mathematically shown as follows:

{P ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required