Today I Learned

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

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.

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.)