def get_training_examples():
X1 = np.array([[10, 10], [8, 6], [8, 10], [8, 8], [12, 6], [9, 5], [11, 8],
[11, 5]])
X2 = np.array([[10, 13], [6, 5], [6, 9], [9, 2], [14, 8], [12, 11],
[10, 13], [13, 4]])
y1 = np.ones(len(X1))
y2 = np.ones(len(X2)) * -1
return get_dataset(X1, y1, X2, y2)
def get_training_examples():
X1 = np.array([[10, 10], [6, 6], [6, 11], [3, 15], [12, 6], [9, 5],
[16, 3], [11, 5]])
X2 = np.array([[3, 6], [6, 3], [2, 9], [9, 2], [18, 1], [1, 18], [1, 13],
[13, 1]])
y1 = np.ones(len(X1))
y2 = np.ones(len(X2)) * -1
return get_dataset(X1, y1, X2, y2)
from succinctly.algorithms.smo_algorithm import SmoAlgorithm
def linear_kernel(x1, x2):
return np.dot(x1, x2)
def compute_w(multipliers, X, y):
return np.sum(multipliers[i] * y[i] * X[i] for i in range(len(y)))
if __name__ == '__main__':
seed(5) # to have reproducible results
X_data, y_data = get_dataset(linearly_separable.get_training_examples)
smo = SmoAlgorithm(X_data,
y_data,
C=10,
tol=0.001,
kernel=linear_kernel,
use_linear_optim=True)
smo.main_routine()
w = compute_w(smo.alphas, X_data, y_data)
print('w = {}'.format(w))
# -smo.b because Platt uses the convention w.x-b=0
import numpy as np
from succinctly.datasets import get_dataset, linearly_separable as ls
import cvxopt.solvers
def compute_w(multipliers, X, y):
return sum(multipliers[i] * y[i] * X[i] for i in range(len(y)))
def compute_b(w, X, y):
return np.sum([y[i] - np.dot(w, X[i]) for i in range(len(X))]) / len(X)
if __name__ == '__main__':
X, y = get_dataset(ls.get_training_examples)
m = X.shape[0]
# Gram matrix - The matrix of all possible inner products of X.
K = np.array([np.dot(X[i], X[j]) for j in range(m)
for i in range(m)]).reshape((m, m))
P = cvxopt.matrix(np.outer(y, y) * K)
q = cvxopt.matrix(-1 * np.ones(m))
# Equality constraints
A = cvxopt.matrix(y, (1, m))
b = cvxopt.matrix(0.0)
# Inequality constraints
G = cvxopt.matrix(np.diag(-1 * np.ones(m)))
h = cvxopt.matrix(np.zeros(m))
