机器学习 – 分类与逻辑回归

Classification

To attempt classification, one method is to use linear regression and map all predictions greater than 0.5 as a 1 and all less than 0.5 as a 0. However, this method doesn’t work well because classification is not actually a linear function.

The classification problem is just like the regression problem, except that the values y we now want to predict take on only a small number of discrete values. For now, we will focus on the binary classification problem in which y can take on only two values, 0 and 1. (Most of what we say here will also generalize to the multiple-class case.) For instance, if we are trying to build a spam classifier for email, then x(i) may be some features of a piece of email, and y may be 1 if it is a piece of spam mail, and 0 otherwise. Hence, y∈{0,1}. 0 is also called the negative class, and 1 the positive class, and they are sometimes also denoted by the symbols “-” and “+.” Given x(i), the corresponding y(i) is also called the label for the training example.

Hypothesis Representation

Decision Boundary

In order to get our discrete 0 or 1 classification, we can translate the output of the hypothesis function as follows:

The way our logistic function g behaves is that when its input is greater than or equal to zero, its output is greater than or equal to 0.5:

Remember.

From these statements we can now say:

The decision boundary is the line that separates the area where y = 0 and where y = 1. It is created by our hypothesis function.

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