import matplotlib.pyplot as plt
class SVMSoftMargin:
“””
Implementation of a Gentle Margin Assist Vector Machine (SVM).
“””
def __init__(self, alpha: float = 0.001, lambda_: float = 0.01, n_iterations: int = 1000) -> None:
“””
Initializes the SVM mannequin.
Parameters:
alpha (float): Studying charge.
lambda_ (float): Regularization parameter.
n_iterations (int): Variety of coaching iterations.
“””
self.alpha = alpha
self.lambda_ = lambda_
self.n_iterations = n_iterations
self.w = None
self.b = None
def match(self, X: np.ndarray, y: np.ndarray) -> tuple:
“””
Trains the SVM mannequin utilizing gradient descent.
Parameters:
X (np.ndarray): Function matrix.
y (np.ndarray): Goal labels.
Returns:
tuple: Discovered weights and bias.
“””
n_samples, n_features = X.form
self.w = np.zeros(n_features)
self.b = 0
for _ in vary(self.n_iterations):
for i, Xi in enumerate(X):
if y[i] * (np.dot(Xi, self.w) – self.b) >= 1:
self.w -= self.alpha * (2 * self.lambda_ * self.w)
else:
self.w -= self.alpha * (2 * self.lambda_ * self.w – np.dot(Xi, y[i]))
self.b -= self.alpha * y[i]
return self.w, self.b
def predict(self, X: np.ndarray) -> checklist:
“””
Makes predictions on new knowledge.
Parameters:
X (np.ndarray): Function matrix.
Returns:
checklist: Predicted class labels.
“””
predictions = np.dot(X, self.w) – self.b
return [1 if val > 0 else -1 for val in predictions]
def get_hyperplane(x: float, w: np.ndarray, b: float, offset: float) -> float:
“””
Computes the choice boundary hyperplane.
Parameters:
x (float): Function worth.
w (np.ndarray): Weight vector.
b (float): Bias time period.
offset (float): Offset for margin boundary.
Returns:
float: Calculated hyperplane worth.
“””
return (-w[0] * x + b + offset) / w[1]
def plot_svm(X: np.ndarray, y: np.ndarray, w: np.ndarray, b: float, title: str = ‘Plot for Linear SVM’) -> None:
“””
Plots the choice boundary of the SVM mannequin.
Parameters:
X (np.ndarray): Function matrix.
y (np.ndarray): Goal labels.
w (np.ndarray): Weight vector.
b (float): Bias time period.
title (str): Plot title.
“””
fig, ax = plt.subplots()
plt.scatter(X[:, 0], X[:, 1], marker=’o’, c=y)
x0_min, x0_max = np.amin(X[:, 0]), np.amax(X[:, 0])
x1_decision_min, x1_decision_max = get_hyperplane(x0_min, w, b, 0), get_hyperplane(x0_max, w, b, 0)
x1_margin_min, x1_margin_max = get_hyperplane(x0_min, w, b, -1), get_hyperplane(x0_max, w, b, -1)
x1_margin_plus_min, x1_margin_plus_max = get_hyperplane(x0_min, w, b, 1), get_hyperplane(x0_max, w, b, 1)
ax.plot([x0_min, x0_max], [x1_decision_min, x1_decision_max], ‘y–‘)
ax.plot([x0_min, x0_max], [x1_margin_min, x1_margin_max], ‘ok’)
ax.plot([x0_min, x0_max], [x1_margin_plus_min, x1_margin_plus_max], ‘ok’)
ax.set_ylim([np.amin(X[:, 1]) – 3, np.amax(X[:, 1]) + 3])
plt.title(title)
plt.present()
