function interval and geometric interval and (difference between perceptron and support vector machine)

Introduction

The function interval and geometry interval are explained in the support vector machine, and we mainly explain the difference between the function interval and the geometrical interval in this blog post. This post mainly explains the simple review knowledge, the big guy does not spray. function interval vs. geometric interval

On a two-dimensional plane, the distance from a point distance over a plane can be expressed as the degree of certainty of categorical prediction, and the farther away the distance is, the more confident the classification is correct. |w∗x+b| | W∗x + B | |w*x+b| represents the point x x x distance from the ultra-planar distance, while (w∗x+b) ∗y (w∗x + b) ∗y (w*x+b) *y denotes the correctness of the classification and the degree of certainty, for a given training data set T and Hyper-plane (w,b), defines the hyper-plane about the sample The function interval for point (Xi,yi) (x i, y i) (x_i,y_i) is
Ri=yi (w∗xi+b) R i = y I (w∗x i + B) r_i =y_i (w*x_i+b)

The function interval can indicate the correctness and accuracy of the classification, but in the process of selecting the Super plane, only the function interval is not enough, if we will w,b W, b w,b are enlarged twice times. The function interval becomes twice times the original, but the superelevation plane does not change. It is therefore necessary to add a certain constraint, such as normalization, to the direction amount W w w w| | =1 | | W | | = 1 | | w| | = 1. This becomes the geometric interval.
The geometry interval is in the form
Ri=yi (w| | w| | ∗xi+b| | w| |) R i = y I (w | | w | |∗x i + b | |