Basic concepts of machine learning mathematics

Time:2019-12-10

Derivatives

Definition
Basic concepts of machine learning mathematics

Basic concepts of machine learning mathematics
The geometric meaning reflects the function y = f (x) along the positive direction of X axis at a certain pointRate of change
The rate of change of the physical meaning representation function at this point (instantaneous)

partial derivative

Multiple independent variables are involved. For two independent variablesZ=f(x,y)Is a 3D space. The derivative is a plane, and there is only one tangent of the point on the curve. There are countless for surfaces.
The partial derivative of a multivariable function is its derivative with respect to one of the variables, while keeping the other variables constant.
Basic concepts of machine learning mathematics
The geometric meaning reflects the rate of change of function z = f (x, y) along the positive direction of coordinate axis in a plane with constant variables
The physical meaning of partial derivativeRate of change in the positive direction of the axis

Directional derivative

Definition: the directional derivative of a scalar field at a point along a vector direction, which describes the instantaneous rate of change of the scalar field near the point along the vector direction
The physical meaning of directional derivative indicates that the function follows a certain pointRate of change in a particular direction

Basic concepts of machine learning mathematics

Basic concepts of machine learning mathematics

gradient

Basic concepts of machine learning mathematics
Meaning of gradient: at a certain point in variable space, which direction does the function have the maximum change rate.
The magnitude of the gradient is the directional derivative