def _setup_svm(self, examples, classes, C):
kernel = kernel_by_name(self.kernel, gamma=self.gamma, p=self.p)
n = len(examples)
e = np.matrix(np.ones((n, 1)))
# Kernel and Hessian
if kernel is None:
K = None
H = None
else:
K = _smart_kernel(kernel, examples)
D = spdiag(classes)
H = D * K * D
# Term for -sum of alphas
f = -e
# Sum(y_i * alpha_i) = 0
A = classes.T.astype(float)
b = np.matrix([0.0])
# 0 <= alpha_i <= C
lb = np.matrix(np.zeros((n, 1)))
if type(C) == float:
ub = C * e
else:
# Allow for C to be an array
ub = C
return K, H, f, A, b, lb, ub
def predict(self, bags):
"""
@param bags : a sequence of n bags; each bag is an m-by-k array-like
object containing m instances with k features
@return : an array of length n containing real-valued label predictions
(threshold at zero to produce binary predictions)
"""
if self._sv_bags is None or len(self._sv_bags) == 0:
return np.zeros(len(bags))
else:
kernel = kernel_by_name(self.kernel, p=self.p, gamma=self.gamma)
K = kernel(map(np.asmatrix, bags), self._sv_bags)
return np.array(self._b + K * spdiag(self._sv_y) * self._sv_alphas).reshape((-1,))
def predict(self, bags):
"""
@param bags : a sequence of n bags; each bag is an m-by-k array-like
object containing m instances with k features
@return : an array of length n containing real-valued label predictions
(threshold at zero to produce binary predictions)
"""
if self._sv_bags is None or len(self._sv_bags) == 0:
return np.zeros(len(bags))
else:
kernel = kernel_by_name(self.kernel, p=self.p, gamma=self.gamma)
K = kernel(list(map(np.asmatrix, bags)), self._sv_bags)
return np.array(self._b + K * spdiag(self._sv_y) * self._sv_alphas).reshape((-1,))
def predict(self, X):
"""
@param X : an n-by-m array-like object containing n examples with m
features
@return : an array of length n containing real-valued label predictions
(threshold at zero to produce binary predictions)
"""
if self._sv_X is None or len(self._sv_X) == 0:
return np.zeros(len(X))
else:
kernel = kernel_by_name(self.kernel, p=self.p, gamma=self.gamma)
K = kernel(np.asmatrix(X), self._sv_X)
return np.array(self._b + K * spdiag(self._sv_y) * self._sv_alphas).reshape((-1,))
def predict(self, bags):
"""
@param bags : a sequence of n bags; each bag is an m-by-k array-like
object containing m instances with k features
@return : an array of length n containing real-valued label predictions
(threshold at zero to produce binary predictions)
"""
if self._b is None:
return np.zeros(len(bags))
else:
bags = [np.asmatrix(bag) for bag in bags]
k = kernel_by_name(self.kernel, p=self.p, gamma=self.gamma)
D = spdiag(self._y)
return np.array([np.max(self._b + self._alphas.T * D * self._V *
k(self._X, bag))
for bag in bags])
def fit(self, bags, y):
"""
@param bags : a sequence of n bags; each bag is an m-by-k array-like
object containing m instances with k features
@param y : an array-like object of length n containing -1/+1 labels
"""
def transform(mx):
"""
Transform into np.matrix if array/list
ignore scipy.sparse matrix
"""
if issparse(mx):
return mx.todense()
return np.asmatrix(mx)
self._bags = [transform(bag) for bag in bags]
y = np.asmatrix(y).reshape((-1, 1))
bs = BagSplitter(self._bags, y)
best_obj = float('inf')
best_svm = None
for rr in range(self.restarts + 1):
if rr == 0:
if self.verbose:
print('Non-random start...')
pos_bag_avgs = np.vstack(
[np.average(bag, axis=0) for bag in bs.pos_bags])
else:
if self.verbose:
print('Random restart %d of %d...' % (rr, self.restarts))
pos_bag_avgs = np.vstack(
[rand_convex(len(bag)) * bag for bag in bs.pos_bags])
intial_instances = np.vstack([bs.neg_instances, pos_bag_avgs])
classes = np.vstack([-np.ones((bs.L_n, 1)), np.ones((bs.X_p, 1))])
# Setup SVM and QP
if self.scale_C:
C = self.C / float(len(intial_instances))
else:
C = self.C
setup = self._setup_svm(intial_instances, classes, C)
K = setup[0]
qp = IterativeQP(*setup[1:])
# Fix Gx <= h
neg_cons = spzeros(bs.X_n, bs.L_n)
for b, (l, u) in enumerate(slices(bs.neg_groups)):
neg_cons[b, l:u] = 1.0
pos_cons = speye(bs.X_p)
bot_left = spzeros(bs.X_p, bs.L_n)
top_right = spzeros(bs.X_n, bs.X_p)
half_cons = sparse([[neg_cons, bot_left], [top_right, pos_cons]])
qp.G = sparse([-speye(bs.X_p + bs.L_n), half_cons])
qp.h = cvxmat(
np.vstack([
np.zeros((bs.X_p + bs.L_n, 1)), C * np.ones(
(bs.X_p + bs.X_n, 1))
]))
# Precompute kernel for all positive instances
kernel = kernel_by_name(self.kernel, gamma=self.gamma, p=self.p)
K_all = kernel(bs.instances, bs.instances)
neg_selectors = np.array(range(bs.L_n))
class MISVMCCCP(CCCP):
def bailout(cself, svm, selectors, instances, K):
return svm
def iterate(cself, svm, selectors, instances, K):
cself.mention('Training SVM...')
alphas, obj = qp.solve(cself.verbose)
# Construct SVM from solution
svm = SVM(kernel=self.kernel,
gamma=self.gamma,
p=self.p,
verbose=self.verbose,
sv_cutoff=self.sv_cutoff)
svm._X = instances
svm._y = classes
svm._alphas = alphas
svm._objective = obj
svm._compute_separator(K)
svm._K = K
cself.mention('Recomputing classes...')
p_confs = svm.predict(bs.pos_instances)
pos_selectors = bs.L_n + np.array([
l + np.argmax(p_confs[l:u])
for l, u in slices(bs.pos_groups)
])
new_selectors = np.hstack([neg_selectors, pos_selectors])
if selectors is None:
sel_diff = len(new_selectors)
else:
sel_diff = np.nonzero(new_selectors -
selectors)[0].size
cself.mention('Selector differences: %d' % sel_diff)
if sel_diff == 0:
return None, svm
elif sel_diff > 5:
# Clear results to avoid a
# bad starting point in
# the next iteration
qp.clear_results()
cself.mention('Updating QP...')
indices = (new_selectors, )
K = K_all[indices].T[indices].T
D = spdiag(classes)
qp.update_H(D * K * D)
return {
'svm': svm,
'selectors': new_selectors,
'instances': bs.instances[indices],
'K': K
}, None
cccp = MISVMCCCP(verbose=self.verbose,
svm=None,
selectors=None,
instances=intial_instances,
K=K,
max_iters=self.max_iters)
svm = cccp.solve()
if svm is not None:
obj = float(svm._objective)
if obj < best_obj:
best_svm = svm
best_obj = obj
if best_svm is not None:
self._X = best_svm._X
self._y = best_svm._y
self._alphas = best_svm._alphas
self._objective = best_svm._objective
self._compute_separator(best_svm._K)
def fit(self, bags, y):
"""
@param bags : a sequence of n bags; each bag is an m-by-k array-like
object containing m instances with k features
@param y : an array-like object of length n containing -1/+1 labels
"""
self._bags = list(map(np.asmatrix, bags))
bs = BagSplitter(self._bags, np.asmatrix(y).reshape((-1, 1)))
self._X = np.vstack([
bs.pos_instances, bs.pos_instances, bs.pos_instances,
bs.neg_instances
])
self._y = np.vstack([
np.matrix(np.ones((bs.X_p + bs.L_p, 1))),
-np.matrix(np.ones((bs.L_p + bs.L_n, 1)))
])
if self.scale_C:
C = self.C / float(len(self._bags))
else:
C = self.C
# Setup SVM and adjust constraints
_, _, f, A, b, lb, ub = self._setup_svm(self._y, self._y, C)
ub[:bs.X_p] *= (float(bs.L_n) / float(bs.X_p))
ub[bs.X_p:bs.X_p + 2 * bs.L_p] *= (float(bs.L_n) / float(bs.L_p))
K = kernel_by_name(self.kernel, gamma=self.gamma, p=self.p)(self._X,
self._X)
D = spdiag(self._y)
ub0 = np.matrix(ub)
ub0[bs.X_p:bs.X_p + 2 * bs.L_p] *= 0.5
def get_V(pos_classifications):
eye_n = bs.L_n + 2 * bs.L_p
top = np.zeros((bs.X_p, bs.L_p))
for row, (i, j) in enumerate(slices(bs.pos_groups)):
top[row, i:j] = _grad_softmin(-pos_classifications[i:j],
self.alpha).flat
return sp.bmat([[sp.coo_matrix(top), None],
[None, sp.eye(eye_n, eye_n)]])
V0 = get_V(np.matrix(np.zeros((bs.L_p, 1))))
qp = IterativeQP(D * V0 * K * V0.T * D, f, A, b, lb, ub0)
best_obj = float('inf')
best_svm = None
for rr in range(self.restarts + 1):
if rr == 0:
if self.verbose:
print('Non-random start...')
# Train on instances
alphas, obj = qp.solve(self.verbose)
else:
if self.verbose:
print('Random restart %d of %d...' % (rr, self.restarts))
alphas = np.matrix([uniform(0.0, 1.0)
for i in range(len(lb))]).T
obj = Objective(0.0, 0.0)
svm = MICA(kernel=self.kernel,
gamma=self.gamma,
p=self.p,
verbose=self.verbose,
sv_cutoff=self.sv_cutoff)
svm._X = self._X
svm._y = self._y
svm._V = V0
svm._alphas = alphas
svm._objective = obj
svm._compute_separator(K)
svm._K = K
class missCCCP(CCCP):
def bailout(cself, svm, obj_val):
return svm
def iterate(cself, svm, obj_val):
cself.mention('Linearizing constraints...')
classifications = svm._predictions[bs.X_p:bs.X_p + bs.L_p]
V = get_V(classifications)
cself.mention('Computing slacks...')
# Difference is [1 - y_i*(w*phi(x_i) + b)]
pos_differences = 1.0 - classifications
neg_differences = 1.0 + classifications
# Slacks are positive differences only
pos_slacks = np.multiply(pos_differences > 0,
pos_differences)
neg_slacks = np.multiply(neg_differences > 0,
neg_differences)
all_slacks = np.hstack([pos_slacks, neg_slacks])
cself.mention('Linearizing...')
# Compute gradient across pairs
slack_grads = np.vstack([
_grad_softmin(pair, self.alpha) for pair in all_slacks
])
# Stack results into one column
slack_grads = np.vstack([
np.ones((bs.X_p, 1)), slack_grads[:, 0],
slack_grads[:, 1],
np.ones((bs.L_n, 1))
])
# Update QP
qp.update_H(D * V * K * V.T * D)
qp.update_ub(np.multiply(ub, slack_grads))
# Re-solve
cself.mention('Solving QP...')
alphas, obj = qp.solve(self.verbose)
new_svm = MICA(kernel=self.kernel,
gamma=self.gamma,
p=self.p,
verbose=self.verbose,
sv_cutoff=self.sv_cutoff)
new_svm._X = self._X
new_svm._y = self._y
new_svm._V = V
new_svm._alphas = alphas
new_svm._objective = obj
new_svm._compute_separator(K)
new_svm._K = K
if cself.check_tolerance(obj_val, obj):
return None, new_svm
return {'svm': new_svm, 'obj_val': obj}, None
cccp = missCCCP(verbose=self.verbose,
svm=svm,
obj_val=None,
max_iters=self.max_iters)
svm = cccp.solve()
if svm is not None:
obj = float(svm._objective)
if obj < best_obj:
best_svm = svm
best_obj = obj
if best_svm is not None:
self._V = best_svm._V
self._alphas = best_svm._alphas
self._objective = best_svm._objective
self._compute_separator(best_svm._K)
self._bag_predictions = self.predict(self._bags)
def fit(self, bags, y):
"""
@param bags : a sequence of n bags; each bag is an m-by-k array-like
object containing m instances with k features
@param y : an array-like object of length n containing -1/+1 labels
"""
self._bags = map(np.asmatrix, bags)
bs = BagSplitter(self._bags,
np.asmatrix(y).reshape((-1, 1)))
self._X = np.vstack([bs.pos_instances,
bs.pos_instances,
bs.pos_instances,
bs.neg_instances])
self._y = np.vstack([np.matrix(np.ones((bs.X_p + bs.L_p, 1))),
-np.matrix(np.ones((bs.L_p + bs.L_n, 1)))])
if self.scale_C:
C = self.C / float(len(self._bags))
else:
C = self.C
# Setup SVM and adjust constraints
_, _, f, A, b, lb, ub = self._setup_svm(self._y, self._y, C)
ub[:bs.X_p] *= (float(bs.L_n) / float(bs.X_p))
ub[bs.X_p: bs.X_p + 2 * bs.L_p] *= (float(bs.L_n) / float(bs.L_p))
K = kernel_by_name(self.kernel, gamma=self.gamma, p=self.p)(self._X, self._X)
D = spdiag(self._y)
ub0 = np.matrix(ub)
ub0[bs.X_p: bs.X_p + 2 * bs.L_p] *= 0.5
def get_V(pos_classifications):
eye_n = bs.L_n + 2 * bs.L_p
top = np.zeros((bs.X_p, bs.L_p))
for row, (i, j) in enumerate(slices(bs.pos_groups)):
top[row, i:j] = _grad_softmin(-pos_classifications[i:j], self.alpha).flat
return sp.bmat([[sp.coo_matrix(top), None],
[None, sp.eye(eye_n, eye_n)]])
V0 = get_V(np.matrix(np.zeros((bs.L_p, 1))))
qp = IterativeQP(D * V0 * K * V0.T * D, f, A, b, lb, ub0)
best_obj = float('inf')
best_svm = None
for rr in range(self.restarts + 1):
if rr == 0:
if self.verbose:
print('Non-random start...')
# Train on instances
alphas, obj = qp.solve(self.verbose)
else:
if self.verbose:
print('Random restart %d of %d...' % (rr, self.restarts))
alphas = np.matrix([uniform(0.0, 1.0) for i in range(len(lb))]).T
obj = Objective(0.0, 0.0)
svm = MICA(kernel=self.kernel, gamma=self.gamma, p=self.p,
verbose=self.verbose, sv_cutoff=self.sv_cutoff)
svm._X = self._X
svm._y = self._y
svm._V = V0
svm._alphas = alphas
svm._objective = obj
svm._compute_separator(K)
svm._K = K
class missCCCP(CCCP):
def bailout(cself, svm, obj_val):
return svm
def iterate(cself, svm, obj_val):
cself.mention('Linearizing constraints...')
classifications = svm._predictions[bs.X_p: bs.X_p + bs.L_p]
V = get_V(classifications)
cself.mention('Computing slacks...')
# Difference is [1 - y_i*(w*phi(x_i) + b)]
pos_differences = 1.0 - classifications
neg_differences = 1.0 + classifications
# Slacks are positive differences only
pos_slacks = np.multiply(pos_differences > 0, pos_differences)
neg_slacks = np.multiply(neg_differences > 0, neg_differences)
all_slacks = np.hstack([pos_slacks, neg_slacks])
cself.mention('Linearizing...')
# Compute gradient across pairs
slack_grads = np.vstack([_grad_softmin(pair, self.alpha)
for pair in all_slacks])
# Stack results into one column
slack_grads = np.vstack([np.ones((bs.X_p, 1)),
slack_grads[:, 0],
slack_grads[:, 1],
np.ones((bs.L_n, 1))])
# Update QP
qp.update_H(D * V * K * V.T * D)
qp.update_ub(np.multiply(ub, slack_grads))
# Re-solve
cself.mention('Solving QP...')
alphas, obj = qp.solve(self.verbose)
new_svm = MICA(kernel=self.kernel, gamma=self.gamma, p=self.p,
verbose=self.verbose, sv_cutoff=self.sv_cutoff)
new_svm._X = self._X
new_svm._y = self._y
new_svm._V = V
new_svm._alphas = alphas
new_svm._objective = obj
new_svm._compute_separator(K)
new_svm._K = K
if cself.check_tolerance(obj_val, obj):
return None, new_svm
return {'svm': new_svm, 'obj_val': obj}, None
cccp = missCCCP(verbose=self.verbose, svm=svm, obj_val=None,
max_iters=self.max_iters)
svm = cccp.solve()
if svm is not None:
obj = float(svm._objective)
if obj < best_obj:
best_svm = svm
best_obj = obj
if best_svm is not None:
self._V = best_svm._V
self._alphas = best_svm._alphas
self._objective = best_svm._objective
self._compute_separator(best_svm._K)
self._bag_predictions = self.predict(self._bags)
def fit(self, bags, y):
"""
@param bags : a sequence of n bags; each bag is an m-by-k array-like
object containing m instances with k features
@param y : an array-like object of length n containing -1/+1 labels
"""
self._bags = map(np.asmatrix, bags)
bs = BagSplitter(self._bags,
np.asmatrix(y).reshape((-1, 1)))
self._X = bs.instances
Ln = bs.L_n
Lp = bs.L_p
Xp = bs.X_p
m = Ln + Xp
if self.scale_C:
C = self.C / float(len(self._bags))
else:
C = self.C
K = kernel_by_name(self.kernel, gamma=self.gamma, p=self.p)(self._X, self._X)
new_classes = np.matrix(np.vstack([-np.ones((Ln, 1)),
np.ones((Xp, 1))]))
self._y = new_classes
D = spdiag(new_classes)
setup = list(self._setup_svm(new_classes, new_classes, C))[1:]
setup[0] = np.matrix([0])
qp = IterativeQP(*setup)
c = cvxmat(np.hstack([np.zeros(Lp + 1),
np.ones(Xp + Ln)]))
b = cvxmat(np.ones((Xp, 1)))
A = spz(Xp, Lp + 1 + Xp + Ln)
for row, (i, j) in enumerate(slices(bs.pos_groups)):
A[row, i:j] = 1.0
bottom_left = sparse(t([[-spI(Lp), spz(Lp)],
[spz(m, Lp), spz(m)]]))
bottom_right = sparse([spz(Lp, m), -spI(m)])
inst_cons = sparse(t([[spz(Xp, Lp), -spo(Xp)],
[spz(Ln, Lp), spo(Ln)]]))
G = sparse(t([[inst_cons, -spI(m)],
[bottom_left, bottom_right]]))
h = cvxmat(np.vstack([-np.ones((Xp, 1)),
np.zeros((Ln + Lp + m, 1))]))
def to_V(upsilon):
bot = np.zeros((Xp, Lp))
for row, (i, j) in enumerate(slices(bs.pos_groups)):
bot[row, i:j] = upsilon.flat[i:j]
return sp.bmat([[sp.eye(Ln, Ln), None],
[None, sp.coo_matrix(bot)]])
class MICACCCP(CCCP):
def bailout(cself, alphas, upsilon, svm):
return svm
def iterate(cself, alphas, upsilon, svm):
V = to_V(upsilon)
cself.mention('Update QP...')
qp.update_H(D * V * K * V.T * D)
cself.mention('Solve QP...')
alphas, obj = qp.solve(self.verbose)
svm = MICA(kernel=self.kernel, gamma=self.gamma, p=self.p,
verbose=self.verbose, sv_cutoff=self.sv_cutoff)
svm._X = self._X
svm._y = self._y
svm._V = V
svm._alphas = alphas
svm._objective = obj
svm._compute_separator(K)
svm._K = K
cself.mention('Update LP...')
for row, (i, j) in enumerate(slices(bs.pos_groups)):
G[row, i:j] = cvxmat(-svm._dotprods[Ln + i: Ln + j].T)
h[Xp: Xp + Ln] = cvxmat(-(1 + svm._dotprods[:Ln]))
cself.mention('Solve LP...')
sol, _ = linprog(c, G, h, A, b, verbose=self.verbose)
new_upsilon = sol[:Lp]
if cself.check_tolerance(np.linalg.norm(upsilon - new_upsilon)):
return None, svm
return {'alphas': alphas, 'upsilon': new_upsilon, 'svm': svm}, None
best_obj = float('inf')
best_svm = None
for rr in range(self.restarts + 1):
if rr == 0:
if self.verbose:
print('Non-random start...')
upsilon0 = np.matrix(np.vstack([np.ones((size, 1)) / float(size)
for size in bs.pos_groups]))
else:
if self.verbose:
print('Random restart %d of %d...' % (rr, self.restarts))
upsilon0 = np.matrix(np.vstack([rand_convex(size).T
for size in bs.pos_groups]))
cccp = MICACCCP(verbose=self.verbose, alphas=None, upsilon=upsilon0,
svm=None, max_iters=self.max_iters)
svm = cccp.solve()
if svm is not None:
obj = float(svm._objective)
if obj < best_obj:
best_svm = svm
best_obj = obj
if best_svm is not None:
self._V = best_svm._V
self._alphas = best_svm._alphas
self._objective = best_svm._objective
self._compute_separator(best_svm._K)
self._bag_predictions = self.predict(self._bags)