Hessian

Hessian

Derivative가 일계도 미분 값이라면, Hessian은 이계도 미분.
“For any $y=f(x)$, expressed as a multiplier $\alpha$ to a tiny increment$\Delta x$ to obtain the increments $\Delta y$ to the output”

\begin{bmatrix} \frac{\partial^2 f}{\partial {x_1}^2} & \frac{\partial y}{\partial x_1 \partial {x_2}} & \cdots & \frac{\partial^2 f}{\partial {x_1} \partial {x_n}} & \\ \frac{\partial^2 f}{\partial {x_2} \partial {x_1}} & \frac{\partial y}{\partial {x_2}^2} & \cdots & \frac{\partial^2 f}{\partial {x_2} \partial {x_n}} & \\ \cdots & \cdots & \cdots & \cdots \\ \frac{\partial^2 f}{\partial {x_n} \partial {x_1}} & \frac{\partial y}{\partial {x_n} \partial {x_2}} & \cdots & \frac{\partial^2 f}{\partial {x_n}^2} & \\ \end{bmatrix} \end{equation}$$