CS109A Introduction to Data Science
Advanced Section 9: Support Vector Machine Demo¶
Harvard University
Fall 2018
Instructors: Pavlos Protopapas and Kevin Rader
In [1]:
## RUN THIS CELL TO GET THE RIGHT FORMATTING
import requests
from IPython.core.display import HTML
styles = requests.get("https://raw.githubusercontent.com/Harvard-IACS/2018-CS109A/master/content/styles/cs109.css").text
HTML(styles)
Out[1]:
In [9]:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.svm import SVC
In [5]:
%matplotlib notebook
import ipywidgets as widgets
from ipywidgets import interact
W,b slider¶
In [6]:
fig,ax = plt.subplots(1,1)
delta=.1
x_grid, y_grid = np.meshgrid(np.arange(-4, 4, delta), np.arange(-4, 4, delta))
def contour_plot(w1=1,w2=1,b=0,alpha=1):
plt.cla()
model_grid = w1*x_grid+w2*y_grid+b
# contour
cs = ax.contour(x_grid, y_grid, model_grid, [-10,-5,-1,0,1,5,10])
plt.clabel(cs);
plt.show()
contour_plot()
def update(w1, w2, b, alpha):
plt.cla()
model_grid = alpha*w1*x_grid+alpha*w2*y_grid+b
# contour
cs = ax.contour(x_grid, y_grid, model_grid, [-2,-1,0,1,2])
plt.clabel(cs);
fig.show()
interact(update, w1=widgets.FloatSlider(min=-10.0,max=10.0,value=1.0),
w2=widgets.FloatSlider(min=-10.0,max=10.0,value=1.0),
b=widgets.FloatSlider(min=-10.0,max=10.0,value=0),
alpha=widgets.FloatSlider(min=0,max=10.0,value=1.0));
C slider¶
In [11]:
%matplotlib notebook
x_train = np.array([
[1,1],
[2,1],
[3,3],
[4,1],
[2,2],
# [2.5,2], #really good non-seperable example
[2.5,1.5], #really good seperable example
])
y_train = np.array([0,0,1,1,1,0])
fig, ax = plt.subplots(1,1)
# grid
delta=.1
x_grid, y_grid = np.meshgrid(np.arange(0, 4, delta), np.arange(0, 4, delta))
grid_dataset = np.hstack([x_grid.reshape(-1,1),y_grid.reshape(-1,1)])
def contour(cur_c):
plt.cla()
fitted_model = SVC(kernel='linear', C=cur_c).fit(x_train,y_train)
out = fitted_model.decision_function(grid_dataset)
# points
ax.scatter(x_train[:,0],x_train[:,1], c=y_train);
# contour
model_grid = out.reshape(x_grid.shape)
cs = ax.contour(x_grid, y_grid, model_grid, [-1,0,1])
plt.clabel(cs);
fig.show()
contour(1)
def update(cur_c,kernel_toggle=False):
if kernel_toggle:
cur_kernel = 'rbf'
else:
cur_kernel = 'linear'
plt.cla()
fitted_model = SVC(kernel=cur_kernel, C=cur_c).fit(x_train,y_train)
out = fitted_model.decision_function(grid_dataset)
# points
ax.scatter(x_train[:,0],x_train[:,1], c=y_train);
# contour
model_grid = out.reshape(x_grid.shape)
cs = ax.contour(x_grid, y_grid, model_grid, [-1,0,1])
plt.clabel(cs);
fig.show()
interact(update, cur_c=widgets.FloatSlider(min=.001,max=50,value=1, step=.1),
kernel_toggle = widgets.ToggleButton(value=False, description="RBF"));
Gamma slider¶
In [12]:
x_train = np.array([
[1,1],
[2,1],
[3,3],
[4,1],
[2,2],
[2.5,2], #really good non-seperable example
# [2.5,1.5], #really good seperable example
])
y_train = np.array([0,0,1,1,1,0])
fig, ax = plt.subplots(1,1)
# grid
delta=.01
x_grid, y_grid = np.meshgrid(np.arange(0, 4, delta), np.arange(0, 4, delta))
grid_dataset = np.hstack([x_grid.reshape(-1,1),y_grid.reshape(-1,1)])
def contour(cur_c):
plt.cla()
fitted_model = SVC(kernel='linear', C=cur_c).fit(x_train,y_train)
out = fitted_model.decision_function(grid_dataset)
# points
ax.scatter(x_train[:,0],x_train[:,1], c=y_train);
# contour
model_grid = out.reshape(x_grid.shape)
cs = ax.contour(x_grid, y_grid, model_grid, [-1,0,1])
plt.clabel(cs);
fig.show()
contour(1)
def update(cur_c,gamma=0):
cur_kernel = 'rbf'
plt.cla()
fitted_model = SVC(kernel=cur_kernel, C=cur_c, gamma=gamma).fit(x_train,y_train)
out = fitted_model.decision_function(grid_dataset)
# points
ax.scatter(x_train[:,0],x_train[:,1], c=y_train);
# contour
model_grid = out.reshape(x_grid.shape)
cs = ax.contour(x_grid, y_grid, model_grid)
plt.clabel(cs);
fig.show()
interact(update, cur_c=widgets.FloatSlider(min=.001,max=50,value=1, step=.1),
gamma=widgets.FloatSlider(min=.001,max=50,value=1, step=.1));
