# Daily Archives: September 19, 2020

## liner equation, non-linear equation

Single layer machine learning is actually linear equation. Linear equation is at most multi-variant polynomial equation, which at most include multiplication and adding.

Deep learning uses multi layers. The multi layers is considered to be non-linear equation.  Non-linear equation may include sin, cos, square etc on variances.

Both linear and non-linear equation fits curvature. However, non-linear is more flexible. Below are the equations for linear and non-linear ones.

Linear equations:

$Y =\beta _{0} + \beta _{1}X_{1} + \beta _{2}X_{2} + \cdots + \beta _{k}X_{k}$

$Y =\beta _{0} + \beta _{1}X_{1} + \beta _{2}X_{1}^2$

Non-linear equations:

$\theta_{1} * X^\theta2$

$\theta_{1} + (\theta_{2}-\theta_{1}) * exp (-\theta_{3} * X ^\theta4)$

$\theta_{1} * cos(X + \theta_{4}) + \theta_{2} * cos (2 * X + \theta_{4}) + \theta_{3}$

reference