def plotcontour(traceJ, timegap, eta, imagename, converged):
plt.ion()
pltfig = plt.figure()
#create a mesh using numpy
T0, T1 = np.mgrid[0:2:50j, -1:1:50j]
mesh = np.c_[T0.flatten(), T1.flatten()]
reshapevalue = T0.shape
Jvalue = (np.array([J(point) for point in mesh]).reshape(reshapevalue))
plt.xlabel(r'$\theta 0$')
plt.ylabel(r'$\theta 1$')
plt.contour(T0, T1, Jvalue, cmap=cm.RdBu_r)
plt.title("Contour Plot (eta = " + str(eta) + ")")
plt.show()
i = 0
for value in traceJ:
i += 1
plt.plot([value[0]], [value[1]], color='b', marker='x', markersize=2)
if (timegap > 0.0):
plt.pause(timegap)
if (not converged and i > 99):
break
save_plots(plt, imagename)
plt.close()
def plotlinearboundary(mu, sigma, show=True):
sigma_inverse = la.pinv(sigma)
# parameters of line equation : Ax = B
tempmu = np.transpose(mu[0] - mu[1])
A = 2 * tempmu @ sigma_inverse
B = np.transpose(mu[0]) @ sigma_inverse @ mu[0] - np.transpose(
mu[1]) @ sigma_inverse @ mu[1] - 2 * np.log(len(canada) / len(alaska))
# plot data points
plt.scatter(alaska[:, 0], alaska[:, 1], marker='o', color='b')
plt.scatter(canada[:, 0], canada[:, 1], marker='x', color='r')
classalaska = plotpatches.Patch(color='b', label="Alaska")
classcanada = plotpatches.Patch(color='r', label="Canada")
# plotting line
x0 = x[:, 0]
x1 = x[:, 1]
x1 = (B - A[0] * x0) / (A[1])
if (show):
line, = plt.plot(x0, x1, color="g", label="Decision Boundary")
plt.legend(handles=[classalaska, classcanada, line])
plt.xlabel(r'Feature 0 ($X_0)$')
plt.ylabel(r'Feature 1 ($X_1)$')
plt.title("Linear decision boundary")
save_plots(plt, "ques4_part(c).png")
plt.show()
return x0, x1
def plotmesh(traceJ, timegap):
plt.ion()
pltfig = plt.figure()
#create a mesh using numpy
T0, T1 = np.mgrid[0:2:50j, -1:1:50j]
xt = T0.flatten()
yt = T1.flatten()
mesh = np.c_[xt, yt]
#meshplot = pltfig.add_subplot(111, projection = '3d')
meshplot = pltfig.gca(projection='3d')
#compute Jvalues for the grid according to our mesh points
Jvalue = (np.array([J(point) for point in mesh]).reshape(50, 50))
meshplot.set_xlabel(r'$\theta 0$', labelpad=15)
meshplot.set_ylabel(r'$\theta 1$', labelpad=15)
meshplot.set_zlabel(r'$J(\theta)$', labelpad=15)
meshplot.plot_surface(T0, T1, Jvalue, cmap=cm.RdBu_r)
plt.show()
for value in traceJ:
meshplot.plot([value[0]], [value[1]], [value[2]],
color='b',
marker='x',
markersize=2)
if (timegap > 0.0):
plt.pause(timegap)
save_plots(plt, "ques_1c.png")
plt.close()
def plotting(theta):
def colorslist():
colors = []
for cls in y:
if cls:
colors.append("r")
else:
colors.append("b")
return colors
color = colorslist()
plt.scatter(x[:, 1], x[:, 2], c=color)
# finding x2 value using line equation --> x2 = (-theta0 -theta1 x1) / theta2 for each x
yy = []
for xi in x:
value = (-theta[0] - theta[1] * xi[1]) / theta[2]
yy.append(value)
cls0 = plotpatches.Patch(color='blue', label='Class 0')
cls1 = plotpatches.Patch(color='red', label='Class 1')
line, = plt.plot(x[:, 1], yy, 'g', label="Decision Boundary")
plt.xlabel(r'Feature 0 ($X_0)$')
plt.ylabel(r'Feature 1 ($X_1)$')
plt.legend(handles=[cls0, cls1, line])
save_plots(plt, "ques3_b.png")
plt.show()
def weightedregression(tau, imagename):
#generating points for plot
maxx = np.amax(x[:, 1])
minx = np.amin(x[:, 1])
pointsforplot = np.linspace(minx, maxx)
result = np.array([])
for point in pointsforplot:
w = np.exp(-1 * ((point - x[:, 1])**2 / (2 * tau**2)))
W = np.diag(w)
transposex = np.transpose(x)
inversematrix = la.inv(transposex @ W @ x)
theta = inversematrix @ transposex @ W @ y
result = np.append(result, [theta @ np.array([1, point])])
# plot of the result obtained from weighted regression
line, = plt.plot(pointsforplot,
result,
'b',
label="Hypothesis for " + r'$\tau = ' + str(tau))
data, = plt.plot(x[:, 1], y, 'rx', label="Data")
plt.xlabel("input x")
plt.ylabel("output y")
plt.legend(handles=[data, line])
plt.title("for value tau = " + str(tau))
save_plots(plt, imagename)
plt.show()
def plotdata():
plt.scatter(alaska[:, 0], alaska[:, 1], marker='o', color='b')
plt.scatter(canada[:, 0], canada[:, 1], marker='x', color='r')
classalaska = plotpatches.Patch(color='b', label="Alaska")
classcanada = plotpatches.Patch(color='r', label="Canada")
plt.title("Plot of training data")
#plt.legend(handles=[classalaska, classcanada])
plt.legend(handles=[classalaska, classcanada])
save_plots(plt, "ques4_part(b).png")
plt.show()
def plotdata(theta):
data, = plt.plot(x[:, 1], y, 'rx', label="Data")
hy = list(map(lambda y: theta @ y, x))
plt.xlabel("Acidity of Wine (Normalised) ")
plt.ylabel("Density Of Wine ")
line, = plt.plot(x[:, 1], hy, "b", label="Hypothesis")
plt.legend(handles=[data, line])
save_plots(plt, "ques_1b.png")
plt.show()
def plotquadgda(mu, sigma, line0, line1):
print("Part E")
# plot data points
plt.scatter(alaska[:, 0], alaska[:, 1], marker='o', color='b')
plt.scatter(canada[:, 0], canada[:, 1], marker='x', color='r')
classalaska = plotpatches.Patch(color='b', label="Alaska")
classcanada = plotpatches.Patch(color='r', label="Canada")
# plotting line
line, = plt.plot(line0, line1, color="g", label="Linear Decision Boundary")
sigma_inverse0 = la.pinv(sigma[0])
sigma_det0 = la.det(sigma[0])
sigma_inverse1 = la.pinv(sigma[1])
sigma_det1 = la.det(sigma[1])
# computing parameters of equation x'Ax + BX + C = 0
A = sigma_inverse0 - sigma_inverse1
mu_transpose0 = np.transpose(mu[0])
mu_transpose1 = np.transpose(mu[1])
B = -2 * (mu_transpose0 @ sigma_inverse0 - mu_transpose1 @ sigma_inverse1)
C = (mu_transpose0 @ sigma_inverse0 @ mu[0] -
mu_transpose1 @ sigma_inverse1 @ mu[1] - 2 * np.log(
(len(canada) / len(alaska)) * (sigma_det0 / sigma_det1)))
#create a mesh using numpy
T0, T1 = np.mgrid[-5:5:50j, -7.5:7.5:50j]
xt = T0.flatten()
yt = T1.flatten()
mesh = np.c_[xt, yt]
# quadratic boundary
quadboundary = np.array([])
for point in mesh:
value = np.transpose(point) @ A @ point + B @ point + C
quadboundary = np.append(quadboundary, [value])
quadboundary = quadboundary.reshape(T0.shape)
plt.contour(T0, T1, quadboundary, [0], colors="y")
quadlabel = lines.Line2D(color='yellow',
label="quadratic decision boundary",
xdata=[],
ydata=[])
plt.title("Quadratic Gaussian Discriminant analysis")
plt.xlabel("Input Feature(x1)")
plt.ylabel("Input Feature(x2)")
plt.legend(handles=[classalaska, classcanada, line, quadlabel])
save_plots(plt, "ques4_part(e).png")
plt.show()
def unweightedregression():
# computing theta using normal equation
transposex = np.transpose(x)
inversematrix = la.inv(transposex @ x)
theta = inversematrix @ transposex @ y
print("theta parameters : ", theta, "\n")
hy = list(map(lambda y: theta @ y, x))
line, = plt.plot(x[:, 1], hy, "b", label="Hypothesis")
data, = plt.plot(x[:, 1], y, 'rx', label="Data")
plt.legend(handles=[data, line])
plt.xlabel("input x")
plt.ylabel("output y")
save_plots(plt, "ques_2a.png")
plt.show()
