Bdtjtk

I'm currently using the 'Sigmoid' function, which the 'cost' function uses in order to determine, where the line should be within the scatter plot diagram. However, upon output, the x and y arrays are outputted onto the scatter plot with the correct keys, but the line is absent from the diagram.

The code that determines the theta is as follows:

def loadTrgDf():

    train, test = proc.getTrainingData()



    # x derives from spouses and siblings

    x = train.iloc[:, 2:4]



    # y derives from the actual output

    y = train.iloc[:, 1]



    # Split and zeros

    initial_theta = np.zeros(x.shape[1])



    # Calculate the threta

    theta = opt.fmin_cg(cost, initial_theta, cost_gradient, (x, y))



    print(" ")

    print(theta)



    # Store for readability

    sibSpTheta = theta[0]

    parchTheta = theta[1]

The findings are then plotted into a scatter graph here:

    # Plot findings

    fig, ax = plt.subplots()



    for index, row in train.iterrows():

        if row['Survived'] == 1:

            ax.scatter(row['SibSp'], row['Parch'], marker="+", c='green')

        else:

            ax.scatter(row['SibSp'], row['Parch'], marker="x", c='red', linewidth=1)



    plt.title("Survival Rate", fontsize=16)

    plt.xlabel("Spouses", fontsize=14)

    plt.ylabel("Siblings", fontsize=14)



    plt.legend(["survived", "not survived"])



    plt.show()



    x_axis = np.array([x.min(), x.max()])

    y_axis = (-1 / 1) * (sibSpTheta * x_axis + parchTheta)

    ax.plot(x_axis, y_axis, linewidth=2)

    fig

The code below is used by the opt.fmin_cg function:

def sigmoid(z):

    return 1 / (1 + np.exp(-z))



def cost(theta, x, y):

    predictions = sigmoid(x @ theta)

    predictions[predictions == 1] = 0.5 # log(1)=0 causes division error during optimization

    error = -y * np.log(predictions) - (1 - y) * np.log(1 - predictions)

    return sum(error) / len(y);



def cost_gradient(theta, x, y):

    predictions = sigmoid(x @ theta);

    return x.transpose() @ (predictions - y) / len(y)

Values:

   PassengerId  Survived  SibSp  Parch

77            78         0      0      0

748          749         0      1      0

444          445         1      0      0

361          362         0      1      0

576          577         1      0      0

27            28         0      3      2

232          233         0      0      0

424          425         0      1      1

785          786         0      0      0

...          ...        ...    ...    ...

x contains the IV's SibSp and Parch

y contains the DV survived

This is the unexpected output:

This is the expected output:

EDIT:
The line appeared! However, it's inaccurate.

The issue is not with the plotting, but with the regression concept.

y_axis = (-1 / 1) * (sibSpTheta * x_axis + parchTheta)

This derives from the calculation that looks like this:

weights * features = weight0 + weight1 * feature1 + weight2 * feature2 + ...

You need to create a weight which corresponds to no feature value so this line becomes something that looks like this:

freeWeight = theta[0]

sibSpTheta = theta[1]

parchTheta = theta[2]



y_axis = (-1 / freeWeight) * (sibSpTheta * x_axis + parchTheta)

This can be done by creating an extra column which corresponds to no feature but has a dummy value when you splice your data frame. This process is called scaling.

Moving onto the x and + markers. You need to loop the x data frame. Not the full train data frame.