ml►a-algorithm

ml-a02-multiple_linear_regression

Multiple Linear Regression

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import numpy as np
from numpy import genfromtxt
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
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data = genfromtxt(r"Delivery.csv", delimiter=",")
print(data)
[[100.    4.    9.3]
 [ 50.    3.    4.8]
 [100.    4.    8.9]
 [100.    2.    6.5]
 [ 50.    2.    4.2]
 [ 80.    2.    6.2]
 [ 75.    3.    7.4]
 [ 65.    4.    6. ]
 [ 90.    3.    7.6]
 [ 90.    2.    6.1]]

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# all data until the last column
x_data = data[:, :-1]
# label: the last column
y_data = data[:, -1]
print(x_data)
print(y_data)
[[100.   4.]
 [ 50.   3.]
 [100.   4.]
 [100.   2.]
 [ 50.   2.]
 [ 80.   2.]
 [ 75.   3.]
 [ 65.   4.]
 [ 90.   3.]
 [ 90.   2.]]
[9.3 4.8 8.9 6.5 4.2 6.2 7.4 6.  7.6 6.1]

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def compute_error(theta0, theta1, theta2, x_data, y_data):
    totalError = 0
    for i in range(0, len(x_data)):
        totalError += (y_data[i] - (theta1 * x_data[i, 0] + theta2 * x_data[i, 1] + theta0))**2
    return totalError / float(len(x_data))

def gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs):
    # total data number
    m = float(len(x_data))
    for i in range(epochs):
        theta0_grad = 0
        theta1_grad = 0
        theta2_grad = 0
        for j in range(0, len(x_data)):
            theta0_grad += (1/m) * ((theta1 * x_data[j, 0] + theta2 * x_data[j, 1] + theta0) - y_data[j])
            theta1_grad += (1/m) * x_data[j, 0] * ((theta1 * x_data[j, 0] + theta2 * x_data[j, 1] + theta0) - y_data[j])
            theta2_grad += (1/m) * x_data[j, 1] * ((theta1 * x_data[j, 0] + theta2 * x_data[j, 1] + theta0) - y_data[j])
        theta0 = theta0 - (lr * theta0_grad)
        theta1 = theta1 - (lr * theta1_grad)
        theta2 = theta2 - (lr * theta2_grad)
    return theta0, theta1, theta2
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lr = 0.0001
theta0 = 0
theta1 = 0
theta2 = 0
epochs = 1000
print("starting theta0={0}, theta1={1}, theta2={2}, error={3}"
      .format( theta0,theta1,theta2,compute_error(theta0, theta1, theta2, x_data, y_data)))
print("Running...")
theta0, theta1, theta2 = gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs)
print("After {0} iterations theta0={1}, theta1={2}, theta2={3}, error={4}"
      .format( epochs, theta0,theta1,theta2,compute_error(theta0, theta1, theta2, x_data, y_data)))    
      
starting theta0=0, theta1=0, theta2=0, error=47.279999999999994
Running...
After 1000 iterations theta0=0.006971416196678632, theta1=0.08021042690771771, theta2=0.07611036240566814, error=0.7731271432218118

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ax = plt.figure().add_subplot(111, projection="3d")
# c='r' => red color, marker='o' => use o to print the figure, s=100 => the marker size is 100
ax.scatter(x_data[:, 0], x_data[:, 1], y_data, c='r', marker="o", s=100)

x0 = x_data[:, 0]
x1 = x_data[:, 1]
x0, x1 = np.meshgrid(x0, x1)
z = theta0 + theta1 * x0 + theta1 * x1
ax.plot_surface(x0, x1, z)

ax.set_xlabel('Miles')
ax.set_ylabel('Num of Deliveries')
ax.set_zlabel('Time')
plt.show()

PS:
Delivery.csv

Sklearn

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import numpy as np
from numpy import genfromtxt
import matplotlib.pyplot as plt
from sklearn import linear_model
from mpl_toolkits.mplot3d import Axes3D
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data = genfromtxt(r"Delivery.csv", delimiter=",")
print(data)
[[100.    4.    9.3]
 [ 50.    3.    4.8]
 [100.    4.    8.9]
 [100.    2.    6.5]
 [ 50.    2.    4.2]
 [ 80.    2.    6.2]
 [ 75.    3.    7.4]
 [ 65.    4.    6. ]
 [ 90.    3.    7.6]
 [ 90.    2.    6.1]]

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# all data until the last column
x_data = data[:, :-1]
# label: the last column
y_data = data[:, -1]
print(x_data)
print(y_data)
[[100.   4.]
 [ 50.   3.]
 [100.   4.]
 [100.   2.]
 [ 50.   2.]
 [ 80.   2.]
 [ 75.   3.]
 [ 65.   4.]
 [ 90.   3.]
 [ 90.   2.]]
[9.3 4.8 8.9 6.5 4.2 6.2 7.4 6.  7.6 6.1]

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model = linear_model.LinearRegression()
model.fit(x_data, y_data)
LinearRegression()
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print("coefficients:", model.coef_)
print("intercept:", model.intercept_)

x_test = [[102,4]]
predict = model.predict(x_test)
print("predict:", predict)
coefficients: [0.0611346  0.92342537]
intercept: -0.868701466781709
predict: [9.06072908]

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ax = plt.figure().add_subplot(111, projection="3d")
ax.scatter(x_data[:,0], x_data[:,1], y_data, c='r', marker='o', s=100)
x0 = x_data[:,0]
x1 = x_data[:,1]
x0,x1 = np.meshgrid(x0,x1)

z = model.intercept_ + x0*model.coef_[0] + x1*model.coef_[1]

ax.plot_surface(x0, x1, z)
ax.set_xlabel('Miles')
ax.set_ylabel('Num of Deliveries')
ax.set_zlabel('Time')

plt.show()