## Logistic regression

- Linear regression problems one how to determine whether the tumor is malignant?

- linear regression robust enough, if there is noise, immediately, "surrender"

### Logistic regression - Classification

### Sigmoid function (compression function)

We will fit out the value of the linear regression compressed with a compression function, the compression is completed -

0.5 with a probability to make the decision boundary, the sample can be divided into two categories, i.e. positive samples

• sigmoid function, the determined value of the positive and negative z g (z) is greater than the last 0.5 or less than 0.5;

I.e. z is greater than 0, g (z) is greater than 0.5, when z is less than 0, g (z) is less than 0.5

• When the z expression is classified corresponding to a boundary, exactly corresponding to different sides of the boundary z negative classification,

It makes the classification boundary sides respectively g (z)> 0.5, and g (z) <0.5, so depending on the magnitude relation g (z) and 0.5,

Classification can be achieved

### Logistic regression loss function

- the problem of quadratic loss function

**Loss function**

In this way, we obtain a convex function.

### Gradient descent method to solve