Today I Learned

Some of the things I've learned every day since Oct 10, 2016

Category Archives: machine learning

88: Dummy Variables

In statistics, a dummy variable is an independent variable which only takes on the values 0 or 1. This is used as an indicator variable, categorizing the object in question and adjusting its model accordingly: if the value is 1, the weight of the dummy variable will be factored in, but not if the value is 0.

Advertisements

74: Linearly Separable Values (Euclidean)

2 sets X_1, X_2 of points in n-dimensional Euclidean space E^n are linearly separable if and only if there exists a non-zero vector \mathbf{w} \in E^n and a number k such that

\mathbf{w} \cdot \mathbf{x} < k

holds for every \mathbf{x} \in X_1, and does not hold for every \mathbf{x'} \in X_2. Intuitively, this means that two sets of points in an n-dimensional Euclidean space are linearly separable if there is an (n-1)-dimensional plane that when inserted into the same space separates the two sets.

(This concept could probably be extended to spaces which share certain properties with E^n, such as having a partial order, closure, etc., but E^n gives the simplest example.)