def _mario_helper(bands, s, poly_order, opts, callback):
# Build the polynomial basis over the bands.
P = hermvander(bands, poly_order - 1)
f = P.sum(axis=0)
if HAS_CVXOPT:
solvers.options['show_progress'] = opts['disp']
solvers.options['maxiters'] = opts['maxiter']
solvers.options['abstol'] = opts['tol']
solvers.options['reltol'] = opts['tol']
solvers.options['feastol'] = 1e-100 # For some reason this helps.
try:
res = solvers.lp(cvx_matrix(f), cvx_matrix(-P), cvx_matrix(-s))
except ValueError as e:
# This can be thrown when poly_order is too large for the data size.
res = {'status': e.message, 'x': None}
return res, P
res = linprog(f,
A_ub=-P,
b_ub=-s,
bounds=(-np.inf, np.inf),
options=opts,
callback=callback)
res = {'status': res.message, 'x': res.x if res.success else None}
return res, P
def cvxopt_solver(G, h, A, b, c, n):
# cvxopt doesn't allow redundant constraints in the linear program Ax = b,
# so we need to do some preprocessing to find and remove any linearly
# dependent rows in the augmented matrix [A | b].
#
# First we do Gaussian elimination to put the augmented matrix into row
# echelon (reduced row echelon form is not necessary). Since b comes as a
# numpy array (that is, a row vector), we need to convert it to a numpy
# matrix before transposing it (that is, to a column vector).
b = np.mat(b).T
A_b = np.hstack((A, b))
A_b, permutation = to_row_echelon(np.hstack((A, b)))
# Next, we apply the inverse of the permutation applied to compute the row
# echelon form.
P = dictionary_to_permutation(permutation)
A_b = P.I * A_b
# Trim any rows that are all zeros. The call to np.any returns an array of
# Booleans that correspond to whether a row in A_b is all zeros. Indexing
# A_b by an array of Booleans acts as a selector. We need to use np.asarray
# in order for indexing to work, since it expects a row vector instead of a
# column vector.
A_b = A_b[np.any(np.asarray(A_b) != 0, axis=1)]
# Split the augmented matrix back into a matrix and a vector.
A, b = A_b[:, :-1], A_b[:, -1]
# Apply the linear programming solver; cvxopt requires that these are all
# of a special type of cvx-specific matrix.
G, h, A, b, c = (cvx_matrix(M) for M in (G, h, A, b, c))
solution = cvx_solvers.lp(c, G, h, A, b)
if solution['status'] == 'optimal':
return True, solution['x']
# TODO status could be 'unknown' here, but we're currently ignoring that
return False, None
def cvxopt_solver(G, h, A, b, c, n):
# cvxopt doesn't allow redundant constraints in the linear program Ax = b,
# so we need to do some preprocessing to find and remove any linearly
# dependent rows in the augmented matrix [A | b].
#
# First we do Gaussian elimination to put the augmented matrix into row
# echelon (reduced row echelon form is not necessary). Since b comes as a
# numpy array (that is, a row vector), we need to convert it to a numpy
# matrix before transposing it (that is, to a column vector).
b = np.mat(b).T
A_b = np.hstack((A, b))
A_b, permutation = to_row_echelon(np.hstack((A, b)))
# Next, we apply the inverse of the permutation applied to compute the row
# echelon form.
P = dictionary_to_permutation(permutation)
A_b = P.I * A_b
# Trim any rows that are all zeros. The call to np.any returns an array of
# Booleans that correspond to whether a row in A_b is all zeros. Indexing
# A_b by an array of Booleans acts as a selector. We need to use np.asarray
# in order for indexing to work, since it expects a row vector instead of a
# column vector.
A_b = A_b[np.any(np.asarray(A_b) != 0, axis=1)]
# Split the augmented matrix back into a matrix and a vector.
A, b = A_b[:, :-1], A_b[:, -1]
# Apply the linear programming solver; cvxopt requires that these are all
# of a special type of cvx-specific matrix.
G, h, A, b, c = (cvx_matrix(M) for M in (G, h, A, b, c))
solution = cvx_solvers.lp(c, G, h, A, b)
if solution['status'] == 'optimal':
return True, solution['x']
# TODO status could be 'unknown' here, but we're currently ignoring that
return False, None
def _mario_helper(bands, s, poly_order, opts, callback):
# Build the polynomial basis over the bands.
P = hermvander(bands, poly_order-1)
f = P.sum(axis=0)
if HAS_CVXOPT:
solvers.options['show_progress'] = opts['disp']
solvers.options['maxiters'] = opts['maxiter']
solvers.options['abstol'] = opts['tol']
solvers.options['reltol'] = opts['tol']
solvers.options['feastol'] = 1e-100 # For some reason this helps.
try:
res = solvers.lp(cvx_matrix(f), cvx_matrix(-P), cvx_matrix(-s))
except ValueError as e:
# This can be thrown when poly_order is too large for the data size.
res = {'status': e.message, 'x': None}
return res, P
res = linprog(f, A_ub=-P, b_ub=-s, bounds=(-np.inf,np.inf), options=opts,
callback=callback)
res = {'status': res.message, 'x': res.x if res.success else None}
return res, P
def binary_part_b(train, test):
train = train.loc[(train[784] == 2) | (train[784] == 3)]
train = train.reset_index(drop=True)
train_X = train.iloc[:, 0:784]
train_Y = train.iloc[:, 784]
train_X = (train_X.as_matrix()) / 255
train_Y = train_Y.as_matrix()
train_Y[train_Y == 2] = -1
train_Y[train_Y == 3] = 1
test = test.loc[(test[784] == 2) | (test[784] == 3)]
test = test.reset_index(drop=True)
test_X = test.iloc[:, 0:784]
test_Y = test.iloc[:, 784]
test_X = (test_X.as_matrix()) / 255
test_Y = test_Y.as_matrix()
test_Y[test_Y == 2] = -1
test_Y[test_Y == 3] = 1
R = pdist(train_X, 'sqeuclidean')
K = np.exp(-0.05 * sqf(R))
x = train_Y[:, None]
y = np.transpose(train_Y[:, None])
K = x @ y * K
pts = train_X.shape[0]
p = cvx_matrix(K)
q = cvx_matrix(-1 * np.ones((pts, 1)))
m = np.diag(-1 * np.ones(pts))
n = np.identity(pts)
G = cvx_matrix(np.vstack((m, n)))
h = cvx_matrix(np.hstack((np.zeros(pts), np.ones(pts))))
A = cvx_matrix(train_Y.reshape(1, -1).astype(np.double))
b = cvx_matrix(np.zeros(1))
result = solvers.qp(p, q, G, h, A, b)
x_val = np.array(result['x']).flatten()
val = .0001
y_val = np.arange(len(x_val))[x_val > val]
alpha = x_val[x_val > val]
xi = train_X[x_val > val]
yi = train_Y[x_val > val]
b = 0
for i in range(len(yi)):
b += yi[i]
temp = K[y_val[i], x_val > val]
b -= np.sum(alpha * temp * yi)
b /= len(yi)
pts = test_X.shape[0]
pred_y = np.zeros(pts)
for i in range(pts):
val = 0
for j in range(len(alpha)):
temp = test_X[i] - xi[j]
temp = np.exp((temp.dot(temp)) * 0.05 * -1)
val += alpha[j] * yi[j] * temp
pred_y[i] = val
pred_y += b
pred_y[pred_y >= 0] = 1
pred_y[pred_y < 0] = -1
accuracy = (np.sum(pred_y == test_Y)) / pts * 100
print(accuracy)
def binary_part_a(train, test):
train = train.loc[(train[784] == 2) | (train[784] == 3)]
train = train.reset_index(drop=True)
train_X = train.iloc[:, 0:784]
train_Y = train.iloc[:, 784]
train_X = (train_X.as_matrix()) / 255
train_Y = train_Y.as_matrix()
train_Y[train_Y == 2] = -1
train_Y[train_Y == 3] = 1
test = test.loc[(test[784] == 2) | (test[784] == 3)]
test = test.reset_index(drop=True)
test_X = test.iloc[:, 0:784]
test_Y = test.iloc[:, 784]
test_X = (test_X.as_matrix()) / 255
test_Y = test_Y.as_matrix()
test_Y[test_Y == 2] = -1
test_Y[test_Y == 3] = 1
H = train_Y[:, None] * train_X
K = H @ np.transpose(H)
pts = train_X.shape[0]
f = train_X.shape[1]
P = cvx_matrix(K)
q = -1 * cvx_matrix(np.ones((pts, 1)))
m = np.diag(-1 * np.ones(pts))
n = np.identity(pts)
G = cvx_matrix(np.vstack((m, n)))
h = cvx_matrix(np.hstack((np.zeros(pts), np.ones(pts))))
A = cvx_matrix(train_Y.reshape(1, -1).astype(np.double))
b = cvx_matrix(np.zeros(1))
result = solvers.qp(P, q, G, h, A, b)
x_val = np.array(result['x'])
w = np.sum(x_val * train_Y[:, None] * train_X, axis=0)
b = (train_Y[(x_val > 0.0001).reshape(-1)] -
(train_X[(x_val > 0.0001).reshape(-1)].dot(w)))[0]
pts = test_Y.shape[0]
pred_y = test_X.dot(w) + b
pred_y[pred_y < 0] = -1
pred_y[pred_y >= 0] = 1
accuracy = np.sum(pred_y == test_Y) / pts * 100
print(accuracy)
def multi_part_a(train, test):
k = list(itertools.combinations([i for i in range(5)], 2))
#k=[(0,1),(7,9)]
total_classes = len(k)
final_pred = []
list3 = []
for i in range(total_classes):
train_X, train_Y = train_data_format(train, k[i][0], k[i][1])
test_X, test_Y = test_data_format(test, k[i][0], k[i][1])
R = pdist(train_X, 'sqeuclidean')
K = np.exp(-0.05 * sqf(R))
x = train_Y[:, None]
y = np.transpose(train_Y[:, None])
K = x @ y * K
pts = train_X.shape[0]
p = cvx_matrix(K)
q = cvx_matrix(-1 * np.ones((pts, 1)))
m = np.diag(-1 * np.ones(pts))
n = np.identity(pts)
G = cvx_matrix(np.vstack((m, n)))
h = cvx_matrix(np.hstack((np.zeros(pts), np.ones(pts))))
A = cvx_matrix(train_Y.reshape(1, -1).astype(np.double))
b = cvx_matrix(np.zeros(1))
result = solvers.qp(p, q, G, h, A, b)
x_val = np.array(result['x']).flatten()
#print(x_val)
val = .0001
y_val = np.arange(len(x_val))[x_val > val]
alpha = x_val[x_val > val]
#print(alpha)
xi = train_X[x_val > val]
#print(xi)
yi = train_Y[x_val > val]
#print(yi)
b = 0
for ii in range(len(yi)):
b += yi[ii]
temp = K[y_val[ii], x_val > val]
b -= np.sum(alpha * temp * yi)
b /= len(yi)
pts = test_X.shape[0]
pred_y = np.zeros(pts)
for iii in range(pts):
val = 0
for j in range(len(alpha)):
temp = test_X[iii] - xi[j]
temp = np.exp((temp.dot(temp)) * 0.05 * -1)
val += alpha[j] * yi[j] * temp
pred_y[iii] = val
pred_y += b
pred_y[pred_y >= 0] = 1
pred_y[pred_y < 0] = -1
accuracy = (np.sum(pred_y == test_Y)) / pts * 100
print(accuracy)
pred_y[pred_y < 0] = k[i][0]
pred_y[pred_y > 0] = k[i][1]
final_pred.append(pred_y)
list2 = []
for j in final_pred[i]:
if j == 1:
list2.append(k[i][1])
else:
list2.append(k[i][0])
list3.append(list2)
print('value of i is:' + str(i))
list4 = np.transpose(np.array(list3))
final_predcition = []
for it in range(list4.shape[0]):
val = max(set(list(list4[i])), key=list(list4[i]).count)
final_predcition.append(val)
final_predcition = np.array(final_predcition)
accuracy = (np.sum(final_predcition == test_Y)) / pts * 100
print(accuracy)
return final_predcition
def fit(self, X, Y):
n_samples = X.shape[0]
# n_features = X.shape[1]
K = np.zeros((n_samples, n_samples))
if self.kernel is 'linear':
for i in range(n_samples):
for j in range(n_samples):
K[i, j] = linear(X[i], X[j])
elif self.kernel is 'poly':
for i in range(n_samples):
for j in range(n_samples):
K[i, j] = polynomial(X[i], X[j], self.p)
elif self.kernel is 'rbf':
for i in range(n_samples):
for j in range(n_samples):
K[i, j] = gaussian(X[i], X[j], self.gamma)
else:
raise Exception('Invalid kernel')
#Declaring parameters for CVX solvers
P = cvx_matrix(np.outer(Y, Y) * K)
q = cvx_matrix(-np.ones((n_samples, 1)))
Y = Y.astype('double')
A = cvx_matrix(Y.reshape((1, -1)))
b = cvx_matrix(0.0)
if self.C is None:
G = cvx_matrix(-np.identity(n_samples))
h = cvx_matrix(np.zeros((n_samples, 1)))
else:
t1 = -np.identity(n_samples)
t2 = np.identity(n_samples)
G = cvx_matrix(np.vstack((t1, t2)))
t1 = np.zeros((n_samples, 1))
t2 = np.ones((n_samples, 1)) * self.C
h = cvx_matrix(np.vstack((t1, t2)))
answer = cvx_solvers.qp(P, q, G, h, A, b)
lag_mul = np.ravel(answer['x'])
support_vectors = lag_mul > 1e-5
indexes = np.arange(len(lag_mul))
lag_indexes = indexes[support_vectors]
self.lag_mul = lag_mul[support_vectors]
self.sv_x = X[support_vectors]
self.support_vectors_ = self.sv_x.astype()
# for i in range(self.sv_x.shape[0]):
# self.support_vectors_.append(float(self.sv_x[i]))
print(self.support_vectors_)
self.sv_y = Y[support_vectors]
# print(self.sv_x,self.sv_y)
print('No. of support vectors = ' + str(len(self.lag_mul)))
#intercept
self.b = 0
for i in range(len(self.lag_mul)):
# print(K[lag_indexes[i],lag_indexes].shape)
self.b = self.sv_y[i] - np.sum(
self.lag_mul * self.sv_y * K[lag_indexes[i], lag_indexes])
# print(self.b)
self.b = self.b / len(self.lag_mul)
