Htydjtk

I am implementing multivariate linear regression using numpy, pandas and matplotlib. I am reading data from a file which looks like this:

data.head()



   ldr1  ldr2  servo

0   971   956     -2

1   691   825   -105

2   841   963    -26

3   970   731     44

4   755   939    -69

I proceed to implement gradient descent and computing the cost function. I include reading from file and plotting for completeness.

def read_data(file):

    # read in data using pandas

    data = pd.read_csv(file, sep=" ", header=None)

    data.columns = ["ldr1", "ldr2", "servo"]    # read the data

    print(data.head())

    # print(file_data)

    return data





def plot_data(file_data):

    ldr1 = my_data.iloc[:, 0:1]

    ldr2 = my_data.iloc[:, 1:2]

    servo_correction = my_data.iloc[:, 2:3]



    fig = plt.figure()

    ax = Axes3D(fig)

    ax.scatter(ldr2, ldr1, servo_correction)

    ax.set_zlabel('Delta Servo')

    plt.xlabel("LDR2")

    plt.ylabel("LDR1")

    plt.gca().invert_xaxis()

    plt.show()

    return ldr1, ldr2, servo_correction





# compute cost

def compute_cost(X, y, theta):

    to_be_summed = np.power(((X @ theta.T)-y), 2)

    return np.sum(to_be_summed)/(2 * len(X))





# gradient descent

def gradient_descent(X, y, theta, iters, alpha):

    cost = np.zeros(iters)

    for i in range(iters):

        theta = theta - (alpha / len(X)) * np.sum(X * (X @ theta.T - y), axis=0)

        cost[i] = compute_cost(X, y, theta)

    return theta, cost

I call these functions like so:

my_data = read_data(filename)

ldr1, ldr2, servo = plot_data(my_data)



# we need to normalize the features using mean normalization

my_data = (my_data - my_data.mean())/my_data.std()

# print(my_data.head())



# setting the matrices

X = my_data.iloc[:, 0:2]

ones = np.ones([X.shape[0], 1])

X = np.concatenate((ones, X), axis=1)



y = my_data.iloc[:, 2:3].values  # values converts it from pandas.core.frame.DataFrame to numpy.ndarray

theta = np.zeros([1, 3])



# set hyper parameters

alpha = 0.01

iterations = 1000



# running the gd and cost function

g, cost = gradient_descent(X, y, theta, iterations, alpha)

print("Thetas: ", g)



finalCost = compute_cost(X, y, g)

print("Final Cost: ", finalCost)

I am trying to fit the plane of best fit to this data. Currently my output is:

Thetas:  [[-3.86865143e-17  8.47885685e-01 -5.39083511e-01]]

Final Cost:  0.11972883176814067

This is what I came up with when trying to plot the plane of best fit. I can't seem to get this to work:

def plot_plane(theta, ldr1, ldr2, servo, X, Y):

    z = theta.flat[0] * X + theta.flat[1] * X + theta.flat[2]



    fig = plt.figure()

    ax = Axes3D(fig)

    ax.plot_surface(X, Y, z, rstride=1, cstride=1, alpha=0.2)

    ax.scatter(ldr2, ldr1, servo)

    ax.set_zlabel('Delta Servo')

    plt.xlabel("LDR2")

    plt.ylabel("LDR1")

    plt.gca().invert_xaxis()

    plt.show()



plot_plane(g, ldr1, ldr2, servo, X, y)

Any suggestions on how this can be done?