Linear classifier and nonlinear classifier

*********************** the difference between linear and nonlinear ********************************

1. Linear linear, the relation between the quantity and the quantity in proportion and in the straight line, can be understood mathematically as the function of the first order derivative as the constant;
Nonlinear non-linear refers to the relationship between non-proportional and not linear, and the first derivative is not constant.


2. Linear can be considered as a 1-time curve, such as Y=ax+b, which is a straight line
Non-linear can be thought to be more than 2 times of the curve, such as Y=ax^2+bx+c, (x^2 is x 2 times), that is not a straight line can


3. The relationship between the two variables is a function--the image is a straight line, so the relationship between the two variables is a "linear relationship";
If it is not a function relationship--the image is not a straight line, it is a nonlinear relationship


4. "Linear" and "nonlinear" are commonly used to distinguish the dependence of the function y = f (x) on the argument x. A linear function is a function, and its image is a straight line. Other functions are nonlinear functions whose images are not straight lines.
Linear, which refers to the relationship between quantity and quantity in proportional, straight line, represents rule and smooth motion in space and time, while nonlinearity refers to the relation of non-proportional, not linear, which represents irregular motion and mutation.
For example, the normal resistor is a linear element, the voltage U at both ends of the resistor R, and the current flow I, is a linear relationship, that is, R=u/i,r is a destiny. The forward characteristic of a diode is a typical nonlinear relationship, and the voltage u at both ends of the diode is not a fixed ratio to the current I flow, i.e. the forward resistance value of the diode, which is different from the different operating points (U, i).


5. Mathematically, a linear relationship is defined as a y=ax+b between an independent variable x and the dependent variable yo, (a, B is a constant), that is, a linear relationship between X and Y.
Can not be expressed as y=ax+b, (b is constant), that is, non-linear relationship, the nonlinear relationship may be two times, three times such a function relationship, it may be no relationship.

****************************** linear classifier and nonlinear classifier *****************************************

Linear classifier: The model is a linear function of the parameters, the classification plane is (super) plane;
Nonlinear classifier: The model interface can be a combination of a curved surface or a super plane.
Typical linear classifiers are perceptron, LDA, Logistic regression, SVM (linear core);
A typical nonlinear classifier has naive Bayes (which has the article that this essence is linear, http://dataunion.org/12344.html), KNN, decision Tree, SVM (nonlinear kernel)