def svm_classify(newdata, SVM):
"""SVM classifier.
Args:
newdata (ndarray): Input test set (of unseen data).\n
SVM (dictinary): The trained SVM from 'svm_train'.
Yields:
prediction (ndarray): The list of predictions .
Example:
Calculate the distance matrix to itself.
>>> K = kernel(X, X)
"""
# Unpack the SVM dictionary
sv = SVM['support_vector']
alpha_hat = SVM['alpha_hat']
scale = SVM['scale']
bias = SVM['bias']
shift = SVM['shift']
sigma = SVM['sigma']
# Shift and scale the support vectors
for c in range(len(sv[0])):
sv[:, c] = scale[c] * (sv[:, c] + shift[c])
# Shift and scale the data
for c in range(len(newdata[0])):
newdata[:, c] = scale[c] * (newdata[:, c] + shift[c])
# Get the RBF kernel
G = np.asmatrix(kernel_svm_rbf(sv.T, newdata.T, sigma)).T
# Classify new data
f = np.dot(G, alpha_hat.T) + bias
# Class prediction is determined by the sign of the dot product above
prediction = np.sign(f)
prediction = np.array(prediction)
return (prediction)
def svm_classify(newdata, SVM):
"""SVM classifier.
Args:
newdata (ndarray): Input test set (of unseen data).\n
SVM (dictinary): The trained SVM from 'svm_train'.
Yields:
prediction (ndarray): The list of predictions .
Example:
Calculate the distance matrix to itself.
>>> K = kernel(X, X)
"""
# Unpack the SVM dictionary
sv = SVM['support_vector']
alpha_hat = SVM['alpha_hat']
scale = SVM['scale']
bias = SVM['bias']
shift = SVM['shift']
sigma = SVM['sigma']
# Shift and scale the support vectors
for c in range(len(sv[0])):
sv[:, c] = scale[c] * (sv[:, c] + shift[c])
# Shift and scale the data
for c in range(len(newdata[0])):
newdata[:, c] = scale[c] * (newdata[:, c] + shift[c])
# Get the RBF kernel
G = np.asmatrix(kernel_svm_rbf(sv.T, newdata.T, sigma)).T
# Classify new data
f = np.dot(G, alpha_hat.T) + bias
# Class prediction is determined by the sign of the dot product above
prediction = np.sign(f)
prediction = np.array(prediction)
return(prediction)
def svm_train(X, y, sigma, C):
"""SVM training for a 2 label classification problem. Label -1 and 1 are
used to distinguise between the two classes.
Args:
X (ndarray): Input training data set.\n
y (ndarray): Label for the training set.\n
sigma (float): The variance of the RBF kernel.\n
C (float): Upper bound optimization value.
Yields:
SVM (dict): A container of the trained values (support vectors etc.).
Example:
Train the synthetic SVM data set
>>> SVM = svm_train(Train, target, 1, 1000)
"""
# Scale data set (other scaling can be used instead)
shift = np.mean(X, axis=0)
stdiv = np.std(X, axis=0)
scale = 1/stdiv
# Apply scaling
for c in range(len(X[0])):
X[:, c] = scale[c] * (X[:, c] + shift[c])
# Generate kernel
kernel = kernel_svm_rbf(X.T, X.T, sigma)
# Make kernel symmetric
kernel = (kernel + kernel.T)/2 # + np.diag(1 / (np.ones((len(y),1)) * C))
# Formulate as QP as the problem min: 1/2*x'*H*x + f'*x
# Construct H: Represents the Hessian matrix
H = y.dot(y.T) * kernel
# Make H symmetric
# H = (H+H.T)/2
# Construct f: Represents the linear term
f = -np.ones(len(X))
# Construct Aeq: Represents the linear coefficients in Aeq*x = beq
Aeq = y.T
# Construct beq: Represents the constant vector in Aeq*x = beq
beq = 0
# Construct lb: Represents the lower bounds elementwise in lb
lb = np.zeros(len(y))
# Construct ub: Represents the upper bounds elemetwise in ub
ub = C*np.ones(len(y))
# QP solver
res = qp_optimizer(H, f, Aeq, beq, lb, ub)
# The support vectors are non-zero of res.x
reference = np.sqrt(np.spacing(1))
support_vector_index = find(res.x > reference)
support_vector = X[support_vector_index, :]
# Hat
alpha_hat = y[support_vector_index].T * res.x[support_vector_index]
# Find the bias (several possibilities)
max_pos = np.argmax(res.x)
bias = y[max_pos] - np.sum(alpha_hat * kernel[support_vector_index, max_pos])
# Rescale data
for c in range(len(support_vector[0])):
support_vector[:, c] = (support_vector[:, c]/scale[c]) - shift[c]
# Construct a dictonary of the trained values
SVM = {}
SVM['support_vector'] = support_vector
SVM['support_vector_index'] = support_vector_index
SVM['sigma'] = sigma
SVM['C'] = C
SVM['alpha_hat'] = alpha_hat
SVM['shift'] = shift
SVM['scale'] = scale
SVM['bias'] = bias
return(SVM)
