A program in python that solves the instructions below, please do not use AI-generated code. I have tried that and gotten nowhere. There are 10 test cases, see below:

1. P (0, 2,+1) (2, 0, -1) (0, 4,+1) (4, 0, -1)
2. L (0, 2,+1) (2, 0, -1) (0, 4, -1) (4, 0, +1) (0, 6, -1) (6, 0, +1)
3. P (2, 0, -1) (5, 2, +1) (0, 4,+1) (4, 0, -1) (6, 1, -1)
4. L (2, 0, -1) (5, 2, +1) (0, 4,+1) (4, 0, -1) (6, 1, -1)
5. P (2, 0, -1) (5, 2, +1) (7, -2, -1) (1, 3,+1) (4, -4, -1) (6, 2, -1)
6. L (2, 0, -1) (5, 2, +1) (7, -2, -1) (1, 3,+1) (4, -4, -1) (6, 2, -1)
7. L (2, 0, -1) (1, -1, -1) (3, -1, -1) (5, 2, +1) (6, 4, +1) (7, 1, +1) (8, 0, -1)
8. P (2, 0, -1) (1, -1, -1) (3, -1, -1) (5, 2, +1) (6, 4, +1) (7, 1, +1) (8, 0, -1)
9. L (2, 0, -1) (1, -1, -1) (3, -1, -1) (5, 2, +1) (6, 4, +1) (7, 1, +1) (8, 0, -1) (-1, -3, -1) (-2, -5, -1) (9, 10, +1)
10. P (2, 0, -1) (1, -1, -1) (3, -1, -1) (5, 2, +1) (6, 4, +1) (7, 1, +1) (8, 0, -1) (-1, -3, -1) (-2, -5, -1) (9, 10, +1)

Description

You are asked to write a program with two functions that apply perceptron or logistic regression techniques to the input and print their outcome.

Perceptron

The first function receives n (<100) triplets of x₁, x₂, y from the user and returns the value for w (weight) that the perceptron algorithm computes to classify the inputs. Here x₁ and x₂ show the input features for each sample, and y shows the class. Consider a binary classification with two possible values for y: -1 and +1. Use the same format for input and output as the example below. Note that before the actual input, another input character P will determine the call for the perceptron function.

Example Input:

P (0, 2,+1) (2, 0, -1) (0, 4,+1) (4, 0, -1) #P indicates perceptron

Example output:

-2.0, 0.0 # referring to w=[-2.0, 0.0]

Use the same procedure for updating w, as discussed in slides (w=w+y*.f). Start from w=[0,0], and update w by a maximum of n*100 times, where n is the number of input samples (100 times iterating over all of the input samples).

Logistic regression

The second function receives a similar input as described above with the only difference in the first input character (L instead of P). The desired task will still be binary classification. The output, in this case, will be printing the probability values that logistic regression computes for each input belonging to the positive class. Set alpha (learning rate) equal to 0.1.

Example Input:

L (0, 2,+1) (2, 0, -1) (0, 4, -1) (4, 0, +1) (0, 6, -1) (6, 0, +1) #L indicates Logistic Reg.

Example output:

0.29 0.71 0.14 0.86 0.06 0.94

For logistic regression, use the basic procedure introduced in class (w=w+*g(w)). Start from w=[0,0], and update w by a maximum of n*100 times, where n is the number of input samples (100 times iterating over all of the input samples). Note that when g(z)=sigmoid(z), we will have g'(z)=g(z)(1-g(z)). This is also shown on the Common Activation Functions slide. It is not necessarily needed here, but for this case, you can further simplify this calculation (see here, note the end of the doc).

Some Other Examples

Input:

L (0, 2,+1) (2, 0, -1) (0, 4,+1) (4, 0, -1)

Output:

0.98 0.02 1.0 0.0

Input:

L (0, 2,+1) (2, 0, -1) (0, 4, -1) (4, 0, +1) (0, 6, -1) (6, 0, +1)

Output:

0.29 0.71 0.14 0.86 0.06 0.94

Input:

P (0, 2,+1) (2, 0, -1) (0, 4, -1) (4, 0, +1) (0, 6, -1) (6, 0, +1)

Output:

0.0, -2.0

Input:

P (0, 2,+1) (2, 0, -1) (0, 4,+1) (4, 0, -1)

Output:

-2.0, 0.0

Input:

L (8, 12,+1) (2, 4, -1) (0, 5, -1) (2, 9, +1) (4, 7, -1) (5, 3, +1)

Output:

0.92 0.64 0.46 0.6 0.76 0.84

Input:

L (8, 12,+1) (-3, 6, -1) (0, 18, -1) (11, 15, +1) (9, 7, -1) (10, 8, +1)

Output:

1.0 0.0 0.01 1.0 1.0 1.0

Input:

L (8, 2,+1) (-3, 6, -1) (0, 18, -1) (11, 1, +1) (9, 7, -1) (10, 2, +1)

Output:

0.99 0.0 0.0 1.0 0.01 1.0

Input:

L (6, 2,+1) (7, 6, -1) (10, 18, -1) (11, 1, +1) (9, 7, -1) (10, 2, +1)

Output:

0.97 0.01 0.0 1.0 0.01 1.0

Input:

L (16, 2,+1) (7, 6, -1) (8, 5, -1) (11, 1, +1) (9, 7, -1) (10, 2, +1)

Output:

1.0 0.0 0.01 1.0 0.0 0.99

Input:

P (1, -2,+1) (-2, 3, -1) (2, 9,+1) (4, 8, -1)

Output:

-8.0, -6.0

Input:

P (3, -12,+1) (3, 11, -1) (5, 19,+1) (4, 12, -1) (5, 20, +1) (3, 2, -1)

Output:

6.0, 1.0

Input:

P (2, 10,+1) (-3, 2, -1) (3, 9,+1) (14, 1, -1) (15, 0, +1) (7, 6, -1) (5, 12, +1) (4, 22, -1)

Output:

-2.0, -10.0