computes the vector whose i^th entry is k(SVM_X[i],x)
'''
def k(y):
#return np.dot(x,y) # returns the identity kernel
#return (1+np.dot(x,y)) # returns the linear basis kernel
gamma = 2
sqr_diff = np.linalg.norm(x-y)**2
sqr_diff *= -1.0*gamma
return np.exp(sqr_diff)
return np.apply_along_axis(k, 1, SVM_X ).reshape(-1,1)
# Carry out training, primal and/or dual
a, SVM_alpha, SVM_X, SVM_Y, support = p2.dual_SVM(X, Y, C, K)
def get_prediction_constants():
ay = SVM_alpha*SVM_Y
# get gram matrix for only support X values
SVM_K = K[support]
SVM_K = SVM_K.T[support]
SVM_K = SVM_K.T
# compute bias
bias = np.nansum([SVM_Y[i] - np.dot(ay.T, SVM_K[i]) for i in range(len(SVM_Y))]) / len(SVM_Y)
return ay, bias
# Define the predictSVM(x) function, which uses trained parameters
# Define the predict_gaussianSVM(x) function, which uses trained parameters, alpha
def wrapper_linear(name, C):
print '======Training======'
# load data from csv files
train = loadtxt('data/data' + name + '_train.csv')
# use deep copy here to make cvxopt happy
X = train[:, 0:2].copy()
Y = train[:, 2:3].copy()
# Define parameters
K = p2.linear_gram(X)
def column_kernel(SVM_X, x):
'''
Given an array of X values and a new x to predict,
computes the vector whose i^th entry is k(SVM_X[i],x)
'''
def k(y):
#return np.dot(x,y) # returns the identity kernel
return (1 + np.dot(x, y)) # returns the linear basis kernel
return np.apply_along_axis(k, 1, SVM_X).reshape(-1, 1)
# Carry out training, primal and/or dual
a, SVM_alpha, SVM_X, SVM_Y, support = p2.dual_SVM(X, Y, C, K)
def get_prediction_constants():
ay = SVM_alpha * SVM_Y
# get gram matrix for only support X values
SVM_K = K[support]
SVM_K = SVM_K.T[support]
SVM_K = SVM_K.T
# compute bias
bias = np.nansum(
[SVM_Y[i] - np.dot(ay.T, SVM_K[i])
for i in range(len(SVM_Y))]) / len(SVM_Y)
return ay, bias
# Define the predictSVM(x) function, which uses trained parameters
# Define the predict_gaussianSVM(x) function, which uses trained parameters, alpha
ay, bias = get_prediction_constants()
def predictSVM(x):
'''
The predicted value is given by h(x) = sign( sum_{support vectors} alpha_i y_i k(x_i,x) )
'''
debug = False
x = x.reshape(1, -1)
if debug: print 'Classify x: ', x
# predict new Y output
kernel = column_kernel(SVM_X, x)
y = np.dot(ay.T, kernel)
if debug:
print 'New y ', y
return y + bias
def classification_error(X_train, Y_train):
''' Computes the error of the classifier on some training set'''
n, d = X_train.shape
incorrect = 0.0
for i in range(n):
if predictSVM(X_train[i]) * Y_train[i] < 0:
incorrect += 1
return incorrect / n
train_err = classification_error(X, Y)
# plot training results
plotDecisionBoundary(X,
Y,
predictSVM, [-1, 0, 1],
title='SVM Train on dataset ' + str(name) +
' with C = ' + str(C))
pl.savefig('prob2linear_kernelSVMtrain_' + str(name) + '_with C=' +
str(C) + '.png')
print '======Validation======'
# load data from csv files
validate = loadtxt('data/data' + name + '_validate.csv')
X = validate[:, 0:2]
Y = validate[:, 2:3]
validation_err = classification_error(X, Y)
# plot validation results
plotDecisionBoundary(X,
Y,
predictSVM, [-1, 0, 1],
title='SVM Validate on dataset ' + str(name) +
' with C = ' + str(C))
pl.savefig('prob2linear_kernelSVMvalidate_' + str(name) + '_with C=' +
str(C) + '.png')
f = open(
'errors for linear kernel dataset ' + str(name) + ' with C = ' +
str(C) + '.txt', 'w')
f.write('Train err: ')
f.write(str(train_err))
f.write('\n')
f.write('Validate err: ')
f.write(str(validation_err))
f.write('\n')
f.write('Number of SVMs: ')
f.write(str(len(SVM_Y)))
f.close()
print 'Done plotting...'
