def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
self.mapp = None
self.root = KNode()
self.realData = data
self.root.n_box = None
self.root.n_budget = Params.maxHeight
def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
# ## initialize the root
self.root = KNode()
self.root.n_data = data
self.root.n_box = np.array([Params.LOW, Params.HIGH])
self.root.n_budget = Params.maxHeight
def buildIndex(self):
""" Function to build the tree structure, fanout = 4 by default for spatial (2D) data """
budget_c = self.getCountBudget()
self.root.n_count = self.getCount(self.root, budget_c[0]) # ## add noisy count to root
stack = deque()
stack.append(self.root)
nleaf = 0 # ## leaf counter
max_depth = -1
# ## main loop
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # ## curr is a leaf node
if curr.n_depth < Params.maxHeight: # ## if a node ends up earlier than maxHeight, it should be able to use the remaining count budget
remainingEps = sum(budget_c[curr.n_depth + 1:])
curr.n_count = self.getCount(curr, remainingEps)
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # ## curr needs to split
curr.n_budget -= 1 # ## some budget will be used regardless the split is successful or not
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(), KNode() # create sub-nodes
nw_coord, ne_coord, nw_node.n_data, ne_node.n_data, sw_node.n_data, se_node.n_data = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
# ## update bounding box, depth, count, budget for the four subnodes
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw], [x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se], [curr.n_box[1, 0], curr.n_box[1, 1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]], [x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]], [curr.n_box[1, 0], y_se]])
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
# if (sub_node.n_depth == Params.maxHeight and sub_node.n_data is not None):
# print len(sub_node.n_data[0])
sub_node.n_count = self.getCount(sub_node, budget_c[sub_node.n_depth])
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
curr.n_data = None # ## do not need the data points coordinates now
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
# ## initialize the root
self.root = KNode()
self.root.n_data = data
self.root.n_box = np.array([Params.LOW, Params.HIGH])
self.root.n_budget = Params.maxHeight
def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
self.mapp = None
self.root = KNode()
self.realData = data
self.root.n_box = None
self.root.n_budget = Params.maxHeight
def buildIndex(self):
stack = deque()
stack.append(self.root)
nleaf = 0 # leaf counter
max_depth = -1
self.root.n_count = np.sum(self.mapp)
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # curr is a leaf node
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # curr needs to split
curr.n_budget -= 1
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(), KNode() # create sub-nodes
nw_coord, ne_coord, count_tmp = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw], [x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se], [curr.n_box[1, 0], curr.n_box[1, 1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]], [x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]], [curr.n_box[1, 0], y_se]])
c_t = 0
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
sub_node.n_count = count_tmp[c_t]
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
c_t += 1
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
def buildIndex(self):
""" Function to build the tree structure, fanout = 4 by default for spatial (2D) data """
budget_c = self.getCountBudget()
self.root.n_count = self.getCount(
self.root, budget_c[0]) # ## add noisy count to root
stack = deque()
stack.append(self.root)
nleaf = 0 # ## leaf counter
max_depth = -1
# ## main loop
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # ## curr is a leaf node
if curr.n_depth < Params.maxHeight: # ## if a node ends up earlier than maxHeight, it should be able to use the remaining count budget
remainingEps = sum(budget_c[curr.n_depth + 1:])
curr.n_count = self.getCount(curr, remainingEps)
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # ## curr needs to split
curr.n_budget -= 1 # ## some budget will be used regardless the split is successful or not
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(
), KNode() # create sub-nodes
nw_coord, ne_coord, nw_node.n_data, ne_node.n_data, sw_node.n_data, se_node.n_data = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
# ## update bounding box, depth, count, budget for the four subnodes
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw],
[x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se],
[curr.n_box[1, 0], curr.n_box[1,
1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]],
[x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]],
[curr.n_box[1, 0], y_se]])
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
# if (sub_node.n_depth == Params.maxHeight and sub_node.n_data is not None):
# print len(sub_node.n_data[0])
sub_node.n_count = self.getCount(
sub_node, budget_c[sub_node.n_depth])
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
curr.n_data = None # ## do not need the data points coordinates now
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
def buildIndex(self):
stack = deque()
stack.append(self.root)
nleaf = 0 # leaf counter
max_depth = -1
self.root.n_count = np.sum(self.mapp)
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # curr is a leaf node
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # curr needs to split
curr.n_budget -= 1
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(
), KNode() # create sub-nodes
nw_coord, ne_coord, count_tmp = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw],
[x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se],
[curr.n_box[1, 0], curr.n_box[1,
1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]],
[x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]],
[curr.n_box[1, 0], y_se]])
c_t = 0
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
sub_node.n_count = count_tmp[c_t]
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
c_t += 1
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
class Kd_cell(Kd_pure):
""" Kd tree based on syntatic data generation and a grid structure. See
Y. Xiao, L. Xiong, and C. Yuan, Differentially private data release
through multidimensional partitioning, in SDM Workshop, VLDB, 2010
"""
def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
self.mapp = None
self.root = KNode()
self.realData = data
self.root.n_box = None
self.root.n_budget = Params.maxHeight
def getCountBudget(self):
count_eps = self.param.Eps * 0.5
H = Params.maxHeight
if self.param.geoBudget == 'none':
return [count_eps / (H + 1) for _ in range(H + 1)]
elif self.param.geoBudget == 'aggressive':
unit = count_eps / (2**(H + 1) - 1)
return [unit * 2**i for i in range(H + 1)]
elif self.param.geoBudget == 'quadratic':
unit = count_eps * (np.sqrt(2) - 1) / (2**(0.5 * (H + 1)) - 1)
return [unit * 2**(0.5 * i) for i in range(H + 1)]
elif self.param.geoBudget == 'optimal':
unit = count_eps * ((2**(1.0 / 3)) - 1) / (2**((1.0 / 3) *
(H + 1)) - 1)
return [unit * 2**((1.0 / 3) * i) for i in range(H + 1)]
elif self.param.geoBudget == 'quartic':
unit = count_eps * ((2**(1.0 / 4)) - 1) / (2**((1.0 / 4) *
(H + 1)) - 1)
return [unit * 2**((1.0 / 4) * i) for i in range(H + 1)]
else:
logging.error('No such geoBudget scheme')
sys.exit(1)
def synthetic_gen(self):
"""Apply a grid structure on the domain and perturb the count using half
of the available privacy budget """
logging.debug('generating synthetic map...')
data = self.realData
unit = Params.unitGrid
x_min = np.floor(Params.LOW[0] / unit) * unit
x_max = np.ceil(Params.HIGH[0] / unit) * unit
y_min = np.floor(Params.LOW[1] / unit) * unit
y_max = np.ceil(Params.HIGH[1] / unit) * unit
x_CELL = int(np.rint((x_max - x_min) / unit))
y_CELL = int(np.rint((y_max - y_min) / unit))
self.root.n_box = np.array([[x_min, y_min], [x_max, y_max]])
self.mapp = np.zeros(
(x_CELL, y_CELL)) - 1 # ## initialize every cell with -1
for i in range(Params.NDATA): # ## populate the map
point = data[:, i]
cell_x = int(np.floor((point[0] - x_min) / unit))
cell_y = int(np.floor((point[1] - y_min) / unit))
if self.mapp[cell_x, cell_y] != -1:
self.mapp[cell_x, cell_y] += 1
else:
self.mapp[cell_x, cell_y] = 1
for i in range(x_CELL): # ## perturb the counts
for j in range(y_CELL):
if self.mapp[i, j] != -1:
self.mapp[i, j] += np.rint(
self.differ.getNoise(1, 0.5 * self.param.Eps))
else:
self.mapp[i, j] = np.rint(
self.differ.getNoise(1, 0.5 * self.param.Eps))
# if noisy count is negative, ignore the noise and generate no points
if self.mapp[i, j] < 0:
self.mapp[i, j] = 0
def cell_setLeaf(self, curr):
""" Throw away the counts based on the syntatic data """
curr.n_count = 0
return
def testLeaf(self, curr):
if (curr.n_count <= self.param.minPartSize) or (
curr.n_depth == Params.maxHeight) or (self.uniform_test(
curr, self.param.cellDistance)):
return True
return False
def uniform_test(self, curr, distance):
""" One of the stopping conditions: cell is uniform according to some threshold 'distance') """
unit = Params.unitGrid
x_min = int(np.rint((curr.n_box[0, 0] - self.root.n_box[0, 0]) / unit))
x_max = int(np.rint((curr.n_box[1, 0] - self.root.n_box[0, 0]) / unit))
y_min = int(np.rint((curr.n_box[0, 1] - self.root.n_box[0, 1]) / unit))
y_max = int(np.rint((curr.n_box[1, 1] - self.root.n_box[0, 1]) / unit))
data = self.mapp[x_min:x_max, y_min:y_max]
total = np.sum(data)
avg = total / ((x_max - x_min) * (y_max - y_min))
dist = np.sum(np.abs(data - avg))
if dist > distance:
return False
else:
return True
def buildIndex(self):
stack = deque()
stack.append(self.root)
nleaf = 0 # leaf counter
max_depth = -1
self.root.n_count = np.sum(self.mapp)
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # curr is a leaf node
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # curr needs to split
curr.n_budget -= 1
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(
), KNode() # create sub-nodes
nw_coord, ne_coord, count_tmp = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw],
[x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se],
[curr.n_box[1, 0], curr.n_box[1,
1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]],
[x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]],
[curr.n_box[1, 0], y_se]])
c_t = 0
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
sub_node.n_count = count_tmp[c_t]
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
c_t += 1
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
def getCoordinates(self, curr):
dim_1 = curr.n_depth % Params.NDIM # primary split dimension
UNIT = Params.unitGrid
x_min = int(np.rint((curr.n_box[0, 0] - self.root.n_box[0, 0]) / UNIT))
x_max = int(np.rint((curr.n_box[1, 0] - self.root.n_box[0, 0]) / UNIT))
y_min = int(np.rint((curr.n_box[0, 1] - self.root.n_box[0, 1]) / UNIT))
y_max = int(np.rint((curr.n_box[1, 1] - self.root.n_box[0, 1]) / UNIT))
total = np.sum(self.mapp[x_min:x_max, y_min:y_max])
if dim_1 == 0:
for i in range(x_max - x_min):
if np.sum(self.mapp[x_min:x_min + i + 1,
y_min:y_max]) >= total / 2:
break
split_prm = (x_min + i + 1) * UNIT + self.root.n_box[0, 0]
half_1 = np.sum(self.mapp[x_min:x_min + i + 1, y_min:y_max])
half_2 = np.sum(self.mapp[x_min + i + 1:x_max, y_min:y_max])
for j in range(y_max - y_min):
if np.sum(self.mapp[x_min:x_min + i + 1,
y_min:y_min + j + 1]) >= half_1 / 2:
break
split_sec1 = self.root.n_box[0, 1] + (y_min + j + 1) * UNIT
n_sw = np.sum(self.mapp[x_min:x_min + i + 1, y_min:y_min + j + 1])
n_nw = np.sum(self.mapp[x_min:x_min + i + 1, y_min + j + 1:y_max])
for k in range(y_max - y_min):
if np.sum(self.mapp[x_min + i + 1:x_max,
y_min:y_min + k + 1]) >= half_2 / 2:
break
split_sec2 = self.root.n_box[0, 1] + (y_min + k + 1) * UNIT
n_se = np.sum(self.mapp[x_min + i + 1:x_max, y_min:y_min + k + 1])
n_ne = np.sum(self.mapp[x_min + i + 1:x_max, y_min + k + 1:y_max])
return (split_prm, split_sec1), (split_prm,
split_sec2), (n_nw, n_ne, n_sw,
n_se)
else:
for i in range(y_max - y_min):
if np.sum(self.mapp[x_min:x_max,
y_min:y_min + i + 1]) >= total / 2:
break
split_prm = self.root.n_box[0, 1] + (y_min + i + 1) * UNIT
half_1 = np.sum(self.mapp[x_min:x_max, y_min:y_min + i + 1])
half_2 = np.sum(self.mapp[x_min:x_max, y_min + i + 1:y_max])
for j in range(x_max - x_min):
if np.sum(self.mapp[x_min:x_min + j + 1,
y_min:y_min + i + 1]) >= half_1 / 2:
break
split_sec1 = (x_min + j + 1) * UNIT + self.root.n_box[0, 0]
n_sw = np.sum(self.mapp[x_min:x_min + j + 1, y_min:y_min + i + 1])
n_se = np.sum(self.mapp[x_min + j + 1:x_max, y_min:y_min + i + 1])
for k in range(x_max - x_min):
if np.sum(self.mapp[x_min:x_min + k + 1,
y_min + i + 1:y_max]) >= half_2 / 2:
break
split_sec2 = (x_min + k + 1) * UNIT + self.root.n_box[0, 0]
n_nw = np.sum(self.mapp[x_min:x_min + k + 1, y_min + i + 1:y_max])
n_ne = np.sum(self.mapp[x_min + k + 1:x_max, y_min + i + 1:y_max])
return (split_sec2, split_prm), (split_sec1,
split_prm), (n_nw, n_ne, n_sw,
n_se)
def populate_synthetic_tree(self):
""" Populate real data to the synthetic tree """
logging.debug('populating synthetic tree...')
a_data = self.realData
ndata = a_data.shape[1]
for i in range(ndata):
ptx = a_data[0, i]
pty = a_data[1, i]
leaf = self.root.find_subnode(ptx, pty)
leaf.n_count += 1
# traverse the tree and update leaf counts
stack = deque()
stack.append(self.root)
while len(stack) > 0:
cur_node = stack.popleft()
if cur_node.n_isLeaf is True: # leaf
cur_node.n_count += self.differ.getNoise(
1, 0.5 * self.param.Eps)
else:
stack.append(cur_node.nw)
stack.append(cur_node.ne)
stack.append(cur_node.sw)
stack.append(cur_node.se)
class KTree(object):
"""Generic tree template"""
def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
# ## initialize the root
self.root = KNode()
self.root.n_data = data
self.root.n_box = np.array([Params.LOW, Params.HIGH])
self.root.n_budget = Params.maxHeight
def getSplitBudget(self):
"""return a list of h budget values for split"""
raise NotImplementedError
def getCountBudget(self):
"""return a list of (h+1) budget values for noisy count"""
raise NotImplementedError
def getNoisyMedian(self, array, left, right, epsilon):
"""return the split value of an array"""
raise NotImplementedError
def getCoordinates(self, curr):
"""
return the coordinate of lower-right point of the NW sub-node
and the upper-left point of the SW sub-node and the data points
in the four subnodes, i.e.
return (x_nw,y_nw),(x_se,y_se), nw_data, ne_data, sw_data, se_data
"""
raise NotImplementedError
def getSplit(self, array, left, right, epsilon):
"""
return the split point given an array, may be data-independent or
true median or noisy median, depending on the type of the tree
"""
raise NotImplementedError
def getCount(self, curr, epsilon):
""" return true count or noisy count of a node, depending on epsilon"""
if curr.n_data is None:
count = 0
else:
count = curr.n_data.shape[1]
if epsilon < 10 ** (-6):
return count
else:
return count + self.differ.getNoise(1, epsilon)
def testLeaf(self, curr):
""" test whether a node should be a leaf node """
if (curr.n_depth == Params.maxHeight) or \
(curr.n_budget <= 0) or \
(curr.n_data is None or curr.n_data.shape[1] == 0) or \
(curr.n_count <= self.param.minPartSize):
return True
return False
def cell_setLeaf(self, curr):
""" will be overrided in kd_cell """
return
def buildIndex(self):
""" Function to build the tree structure, fanout = 4 by default for spatial (2D) data """
budget_c = self.getCountBudget()
self.root.n_count = self.getCount(self.root, budget_c[0]) # ## add noisy count to root
stack = deque()
stack.append(self.root)
nleaf = 0 # ## leaf counter
max_depth = -1
# ## main loop
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # ## curr is a leaf node
if curr.n_depth < Params.maxHeight: # ## if a node ends up earlier than maxHeight, it should be able to use the remaining count budget
remainingEps = sum(budget_c[curr.n_depth + 1:])
curr.n_count = self.getCount(curr, remainingEps)
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # ## curr needs to split
curr.n_budget -= 1 # ## some budget will be used regardless the split is successful or not
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(), KNode() # create sub-nodes
nw_coord, ne_coord, nw_node.n_data, ne_node.n_data, sw_node.n_data, se_node.n_data = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
# ## update bounding box, depth, count, budget for the four subnodes
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw], [x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se], [curr.n_box[1, 0], curr.n_box[1, 1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]], [x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]], [curr.n_box[1, 0], y_se]])
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
# if (sub_node.n_depth == Params.maxHeight and sub_node.n_data is not None):
# print len(sub_node.n_data[0])
sub_node.n_count = self.getCount(sub_node, budget_c[sub_node.n_depth])
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
curr.n_data = None # ## do not need the data points coordinates now
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
def rect_intersect(self, hrect, query):
"""
checks if the hyper-rectangle intersects with the
hyper-rectangle defined by the query in every dimension
"""
bool_m1 = query[0, :] >= hrect[1, :]
bool_m2 = query[1, :] <= hrect[0, :]
bool_m = np.logical_or(bool_m1, bool_m2)
if np.any(bool_m):
return False
else:
return True
def rangeCount(self, query):
"""
Query answering function. Find the number of data points within a query rectangle.
"""
stack = deque()
stack.append(self.root)
count = 0.0
# ## Below are three variables recording the number of 1) whole leaf 2) partial leaf 3) whole internal node,
# ## respectively, which contribute to the query answer. For debug purpose only.
l_whole, l_part, i_whole = 0, 0, 0
while len(stack) > 0:
curr = stack.popleft()
_box = curr.n_box
if curr.n_isLeaf is True:
frac = 1
if self.rect_intersect(_box, query):
for i in range(_box.shape[1]):
if _box[1, i] == _box[0, i] or Params.WorstCase == True:
frac *= 1
else:
frac *= (min(query[1, i], _box[1, i]) - max(query[0, i], _box[0, i])) / (
_box[1, i] - _box[0, i])
count += curr.n_count * frac
if 1.0 - frac < 10 ** (-6):
l_whole += 1
else:
l_part += 1
else: # ## if not leaf
bool_matrix = np.zeros((2, query.shape[1]))
bool_matrix[0, :] = query[0, :] <= _box[0, :]
bool_matrix[1, :] = query[1, :] >= _box[1, :]
if np.all(bool_matrix) and self.param.useLeafOnly is False: # ## if query range contains node range
count += curr.n_count
i_whole += 1
else:
if self.rect_intersect(curr.nw.n_box, query):
stack.append(curr.nw)
if self.rect_intersect(curr.ne.n_box, query):
stack.append(curr.ne)
if self.rect_intersect(curr.sw.n_box, query):
stack.append(curr.sw)
if self.rect_intersect(curr.se.n_box, query):
stack.append(curr.se)
return float(count) # , i_whole, l_whole, l_part
def adjustConsistency(self):
"""
Post processing for uniform noise across levels. Due to
Michael Hay, Vibhor Rastogi, Gerome Miklau, Dan Suciu,
Boosting the Accuracy of Differentially-Private Histograms Through Consistency,
VLDB 2010
"""
logging.debug('adjusting consistency...')
# ## upward pass
self.root.get_z()
# ## downward pass
queue = deque()
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
adjust = (curr.n_count - curr.nw.n_count - curr.ne.n_count - curr.sw.n_count - curr.se.n_count) / 4.0
for subnode in [curr.nw, curr.ne, curr.sw, curr.se]:
subnode.n_count += adjust
queue.append(subnode)
def postProcessing(self):
"""
Post processing for general noise distribution across levels. Due to
G. Cormode, M. Procopiuc, E. Shen, D. Srivastava and T. Yu,
Differentially Private Spatial Decompositions, ICDE 2012.
"""
logging.debug("post-processing...")
budget = self.getCountBudget() # ## count budget for h+1 levels
H = Params.maxHeight
# ## Phase 1 (top-down)
queue = deque()
self.root.n_count *= budget[self.root.n_depth] ** 2
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
for subnode in [curr.nw, curr.ne, curr.sw, curr.se]:
subnode.n_count = curr.n_count + subnode.n_count * (budget[subnode.n_depth] ** 2)
queue.append(subnode)
# ## Phase 2 (bottom-up)
self.root.update_count()
# ## Phase 3 (top-down)
queue = deque()
E_root = 0
for i in range(H + 1):
E_root += 4 ** i * budget[H - i] * budget[H - i]
self.root.n_count /= E_root
self.root.n_F = 0
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
h = H - curr.n_depth - 1 # ## height of curr's children
E_h = 0
for i in range(h + 1):
E_h += 4 ** i * budget[H - i] * budget[H - i]
for subnode in [curr.nw, curr.ne, curr.sw, curr.se]:
subnode.n_F = curr.n_F + curr.n_count * (budget[curr.n_depth] ** 2)
subnode.n_count = (subnode.n_count - 4 ** h * subnode.n_F) / E_h
queue.append(subnode)
def pruning(self):
"""
If the tree is grown without the stopping condition of minLeafSize, prune it here after post processing
"""
logging.debug("pruning...")
queue = deque()
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
if curr.n_count <= self.param.minPartSize:
curr.n_isLeaf = True
else:
queue.append(curr.nw)
queue.append(curr.ne)
queue.append(curr.sw)
queue.append(curr.se)
def buildIndex(self):
budget_c = self.getCountBudget()
logging.debug('encoding coordinates...')
RES = self.param.Res # order of Hilbert curve
ndata = self.realData.shape[1]
hidx = np.zeros(ndata)
for i in range(ndata):
hx, hy = self.get_Hcoord(self.realData[0, i], self.realData[1, i],
RES)
hidx[i] = self.h_encode(hx, hy, RES)
hidx = np.sort(hidx)
logging.debug('building index...')
self.root.n_data = hidx
self.root.n_box = (0, 2**(2 * RES) - 1)
self.root.n_count = self.getCount(self.root, budget_c[0])
stack = deque()
stack.append(self.root)
tree = [self.root]
leaf_li = [] # storage of all leaves
nleaf = 0 # leaf counter
max_depth = -1
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # curr is a leaf node
if curr.n_depth < Params.maxHeight:
remainingEps = sum(budget_c[curr.n_depth + 1:])
curr.n_count = self.getCount(curr, remainingEps)
nleaf += 1
curr.n_isLeaf = True
leaf_li.append(curr)
else: # curr needs to split
curr.n_budget -= 1
tmp = self.getCoordinates(curr)
if tmp is False: # if split fails
stack.append(curr)
continue
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(
), KNode() # create sub-nodes
split_prm, split_sec1, split_sec2, nw_node.n_data, ne_node.n_data, sw_node.n_data, se_node.n_data = tmp
nw_node.n_box = (curr.n_box[0], split_sec1)
ne_node.n_box = (split_sec1, split_prm)
sw_node.n_box = (split_prm, split_sec2)
se_node.n_box = (split_sec2, curr.n_box[1])
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
sub_node.n_count = self.getCount(
sub_node, budget_c[sub_node.n_depth])
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
tree.append(sub_node)
curr.n_data = None
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
# # convert hilbert values in leaf nodes to real coordinates and update bounding box
logging.debug('decoding and updating bounding box...')
for leaf in leaf_li:
bbox = np.array([[1000.0, 1000.0], [-1000.0, -1000.0]],
dtype='float64')
for hvalue in leaf.n_data:
hx, hy = self.h_decode(int(hvalue), RES)
x, y = self.get_Rcoord(hx, hy, RES)
bbox[0, 0] = x if x < bbox[0, 0] else bbox[0, 0]
bbox[1, 0] = x if x > bbox[1, 0] else bbox[1, 0]
bbox[0, 1] = y if y < bbox[0, 1] else bbox[0, 1]
bbox[1, 1] = y if y > bbox[1, 1] else bbox[1, 1]
leaf.n_box = bbox
# # update bounding box bottom-up
tree = sorted(tree, cmp=self.cmp_node)
logging.debug('updating box for each node in the tree...')
for node in tree:
if node.n_data is None:
node.n_box = np.zeros((2, 2))
node.n_box[0,
0] = min(node.ne.n_box[0, 0], node.nw.n_box[0, 0],
node.se.n_box[0, 0], node.sw.n_box[0, 0])
node.n_box[0,
1] = min(node.ne.n_box[0, 1], node.nw.n_box[0, 1],
node.se.n_box[0, 1], node.sw.n_box[0, 1])
node.n_box[1,
0] = max(node.ne.n_box[1, 0], node.nw.n_box[1, 0],
node.se.n_box[1, 0], node.sw.n_box[1, 0])
node.n_box[1,
1] = max(node.ne.n_box[1, 1], node.nw.n_box[1, 1],
node.se.n_box[1, 1], node.sw.n_box[1, 1])
class KTree(object):
"""Generic tree template"""
def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
# ## initialize the root
self.root = KNode()
self.root.n_data = data
self.root.n_box = np.array([Params.LOW, Params.HIGH])
self.root.n_budget = Params.maxHeight
def getSplitBudget(self):
"""return a list of h budget values for split"""
raise NotImplementedError
def getCountBudget(self):
"""return a list of (h+1) budget values for noisy count"""
raise NotImplementedError
def getNoisyMedian(self, array, left, right, epsilon):
"""return the split value of an array"""
raise NotImplementedError
def getCoordinates(self, curr):
"""
return the coordinate of lower-right point of the NW sub-node
and the upper-left point of the SW sub-node and the data points
in the four subnodes, i.e.
return (x_nw,y_nw),(x_se,y_se), nw_data, ne_data, sw_data, se_data
"""
raise NotImplementedError
def getSplit(self, array, left, right, epsilon):
"""
return the split point given an array, may be data-independent or
true median or noisy median, depending on the type of the tree
"""
raise NotImplementedError
def getCount(self, curr, epsilon):
""" return true count or noisy count of a node, depending on epsilon"""
if curr.n_data is None:
count = 0
else:
count = curr.n_data.shape[1]
if epsilon < 10 ** (-6):
return count
else:
return count + self.differ.getNoise(1, epsilon)
def testLeaf(self, curr):
""" test whether a node should be a leaf node """
if (curr.n_depth == Params.maxHeight) or \
(curr.n_budget <= 0) or \
(curr.n_data is None or curr.n_data.shape[1] == 0) or \
(curr.n_count <= self.param.minPartSize):
return True
return False
def cell_setLeaf(self, curr):
""" will be overrided in kd_cell """
return
def buildIndex(self):
""" Function to build the tree structure, fanout = 4 by default for spatial (2D) data """
budget_c = self.getCountBudget()
self.root.n_count = self.getCount(self.root, budget_c[0]) # ## add noisy count to root
stack = deque()
stack.append(self.root)
nleaf = 0 # ## leaf counter
max_depth = -1
# ## main loop
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # ## curr is a leaf node
if curr.n_depth < Params.maxHeight: # ## if a node ends up earlier than maxHeight, it should be able to use the remaining count budget
remainingEps = sum(budget_c[curr.n_depth + 1:])
curr.n_count = self.getCount(curr, remainingEps)
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # ## curr needs to split
curr.n_budget -= 1 # ## some budget will be used regardless the split is successful or not
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(), KNode() # create sub-nodes
nw_coord, ne_coord, nw_node.n_data, ne_node.n_data, sw_node.n_data, se_node.n_data = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
# ## update bounding box, depth, count, budget for the four subnodes
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw], [x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se], [curr.n_box[1, 0], curr.n_box[1, 1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]], [x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]], [curr.n_box[1, 0], y_se]])
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
# if (sub_node.n_depth == Params.maxHeight and sub_node.n_data is not None):
# print len(sub_node.n_data[0])
sub_node.n_count = self.getCount(sub_node, budget_c[sub_node.n_depth])
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
curr.n_data = None # ## do not need the data points coordinates now
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
def rect_intersect(self, hrect, query):
"""
checks if the hyper-rectangle intersects with the
hyper-rectangle defined by the query in every dimension
"""
bool_m1 = query[0, :] >= hrect[1, :]
bool_m2 = query[1, :] <= hrect[0, :]
bool_m = np.logical_or(bool_m1, bool_m2)
if np.any(bool_m):
return False
else:
return True
def rangeCount(self, query):
"""
Query answering function. Find the number of data points within a query rectangle.
"""
stack = deque()
stack.append(self.root)
count = 0.0
# ## Below are three variables recording the number of 1) whole leaf 2) partial leaf 3) whole internal node,
# ## respectively, which contribute to the query answer. For debug purpose only.
l_whole, l_part, i_whole = 0, 0, 0
while len(stack) > 0:
curr = stack.popleft()
_box = curr.n_box
if curr.n_isLeaf is True:
frac = 1
if self.rect_intersect(_box, query):
for i in range(_box.shape[1]):
if _box[1, i] == _box[0, i] or Params.WorstCase == True:
frac *= 1
else:
frac *= (min(query[1, i], _box[1, i]) - max(query[0, i], _box[0, i])) / (
_box[1, i] - _box[0, i])
count += curr.n_count * frac
if 1.0 - frac < 10 ** (-6):
l_whole += 1
else:
l_part += 1
else: # ## if not leaf
bool_matrix = np.zeros((2, query.shape[1]))
bool_matrix[0, :] = query[0, :] <= _box[0, :]
bool_matrix[1, :] = query[1, :] >= _box[1, :]
if np.all(bool_matrix) and self.param.useLeafOnly is False: # ## if query range contains node range
count += curr.n_count
i_whole += 1
else:
if self.rect_intersect(curr.nw.n_box, query):
stack.append(curr.nw)
if self.rect_intersect(curr.ne.n_box, query):
stack.append(curr.ne)
if self.rect_intersect(curr.sw.n_box, query):
stack.append(curr.sw)
if self.rect_intersect(curr.se.n_box, query):
stack.append(curr.se)
return float(count) # , i_whole, l_whole, l_part
def adjustConsistency(self):
"""
Post processing for uniform noise across levels. Due to
Michael Hay, Vibhor Rastogi, Gerome Miklau, Dan Suciu,
Boosting the Accuracy of Differentially-Private Histograms Through Consistency,
VLDB 2010
"""
logging.debug('adjusting consistency...')
# ## upward pass
self.root.get_z()
# ## downward pass
queue = deque()
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
adjust = (curr.n_count - curr.nw.n_count - curr.ne.n_count - curr.sw.n_count - curr.se.n_count) / 4.0
for subnode in [curr.nw, curr.ne, curr.sw, curr.se]:
subnode.n_count += adjust
queue.append(subnode)
def postProcessing(self):
"""
Post processing for general noise distribution across levels. Due to
G. Cormode, M. Procopiuc, E. Shen, D. Srivastava and T. Yu,
Differentially Private Spatial Decompositions, ICDE 2012.
"""
logging.debug("post-processing...")
budget = self.getCountBudget() # ## count budget for h+1 levels
H = Params.maxHeight
# ## Phase 1 (top-down)
queue = deque()
self.root.n_count *= budget[self.root.n_depth] ** 2
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
for subnode in [curr.nw, curr.ne, curr.sw, curr.se]:
subnode.n_count = curr.n_count + subnode.n_count * (budget[subnode.n_depth] ** 2)
queue.append(subnode)
# ## Phase 2 (bottom-up)
self.root.update_count()
# ## Phase 3 (top-down)
queue = deque()
E_root = 0
for i in range(H + 1):
E_root += 4 ** i * budget[H - i] * budget[H - i]
self.root.n_count /= E_root
self.root.n_F = 0
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
h = H - curr.n_depth - 1 # ## height of curr's children
E_h = 0
for i in range(h + 1):
E_h += 4 ** i * budget[H - i] * budget[H - i]
for subnode in [curr.nw, curr.ne, curr.sw, curr.se]:
subnode.n_F = curr.n_F + curr.n_count * (budget[curr.n_depth] ** 2)
subnode.n_count = (subnode.n_count - 4 ** h * subnode.n_F) / E_h
queue.append(subnode)
def pruning(self):
"""
If the tree is grown without the stopping condition of minLeafSize, prune it here after post processing
"""
logging.debug("pruning...")
queue = deque()
queue.append(self.root)
while len(queue) > 0:
curr = queue.popleft()
if curr.n_isLeaf is False:
if curr.n_count <= self.param.minPartSize:
curr.n_isLeaf = True
else:
queue.append(curr.nw)
queue.append(curr.ne)
queue.append(curr.sw)
queue.append(curr.se)
def buildIndex(self):
budget_c = self.getCountBudget()
logging.debug('encoding coordinates...')
RES = self.param.Res # order of Hilbert curve
ndata = self.realData.shape[1]
hidx = np.zeros(ndata)
for i in range(ndata):
hx, hy = self.get_Hcoord(self.realData[0, i], self.realData[1, i], RES)
hidx[i] = self.h_encode(hx, hy, RES)
hidx = np.sort(hidx)
logging.debug('building index...')
self.root.n_data = hidx
self.root.n_box = (0, 2 ** (2 * RES) - 1)
self.root.n_count = self.getCount(self.root, budget_c[0])
stack = deque()
stack.append(self.root)
tree = [self.root]
leaf_li = [] # storage of all leaves
nleaf = 0 # leaf counter
max_depth = -1
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # curr is a leaf node
if curr.n_depth < Params.maxHeight:
remainingEps = sum(budget_c[curr.n_depth + 1:])
curr.n_count = self.getCount(curr, remainingEps)
nleaf += 1
curr.n_isLeaf = True
leaf_li.append(curr)
else: # curr needs to split
curr.n_budget -= 1
tmp = self.getCoordinates(curr)
if tmp is False: # if split fails
stack.append(curr)
continue
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(), KNode() # create sub-nodes
split_prm, split_sec1, split_sec2, nw_node.n_data, ne_node.n_data, sw_node.n_data, se_node.n_data = tmp
nw_node.n_box = (curr.n_box[0], split_sec1)
ne_node.n_box = (split_sec1, split_prm)
sw_node.n_box = (split_prm, split_sec2)
se_node.n_box = (split_sec2, curr.n_box[1])
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
sub_node.n_count = self.getCount(sub_node, budget_c[sub_node.n_depth])
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
tree.append(sub_node)
curr.n_data = None
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
# # convert hilbert values in leaf nodes to real coordinates and update bounding box
logging.debug('decoding and updating bounding box...')
for leaf in leaf_li:
bbox = np.array([[1000.0, 1000.0], [-1000.0, -1000.0]], dtype='float64')
for hvalue in leaf.n_data:
hx, hy = self.h_decode(int(hvalue), RES)
x, y = self.get_Rcoord(hx, hy, RES)
bbox[0, 0] = x if x < bbox[0, 0] else bbox[0, 0]
bbox[1, 0] = x if x > bbox[1, 0] else bbox[1, 0]
bbox[0, 1] = y if y < bbox[0, 1] else bbox[0, 1]
bbox[1, 1] = y if y > bbox[1, 1] else bbox[1, 1]
leaf.n_box = bbox
# # update bounding box bottom-up
tree = sorted(tree, cmp=self.cmp_node)
logging.debug('updating box for each node in the tree...')
for node in tree:
if node.n_data is None:
node.n_box = np.zeros((2, 2))
node.n_box[0, 0] = min(node.ne.n_box[0, 0], node.nw.n_box[0, 0], node.se.n_box[0, 0],
node.sw.n_box[0, 0])
node.n_box[0, 1] = min(node.ne.n_box[0, 1], node.nw.n_box[0, 1], node.se.n_box[0, 1],
node.sw.n_box[0, 1])
node.n_box[1, 0] = max(node.ne.n_box[1, 0], node.nw.n_box[1, 0], node.se.n_box[1, 0],
node.sw.n_box[1, 0])
node.n_box[1, 1] = max(node.ne.n_box[1, 1], node.nw.n_box[1, 1], node.se.n_box[1, 1],
node.sw.n_box[1, 1])
class Kd_cell(Kd_pure):
""" Kd tree based on syntatic data generation and a grid structure. See
Y. Xiao, L. Xiong, and C. Yuan, Differentially private data release
through multidimensional partitioning, in SDM Workshop, VLDB, 2010
"""
def __init__(self, data, param):
self.param = param
self.differ = Differential(self.param.Seed)
self.mapp = None
self.root = KNode()
self.realData = data
self.root.n_box = None
self.root.n_budget = Params.maxHeight
def getCountBudget(self):
count_eps = self.param.Eps * 0.5
H = Params.maxHeight
if self.param.geoBudget == 'none':
return [count_eps / (H + 1) for _ in range(H + 1)]
elif self.param.geoBudget == 'aggressive':
unit = count_eps / (2 ** (H + 1) - 1)
return [unit * 2 ** i for i in range(H + 1)]
elif self.param.geoBudget == 'quadratic':
unit = count_eps * (np.sqrt(2) - 1) / (2 ** (0.5 * (H + 1)) - 1)
return [unit * 2 ** (0.5 * i) for i in range(H + 1)]
elif self.param.geoBudget == 'optimal':
unit = count_eps * ((2 ** (1.0 / 3)) - 1) / (2 ** ((1.0 / 3) * (H + 1)) - 1)
return [unit * 2 ** ((1.0 / 3) * i) for i in range(H + 1)]
elif self.param.geoBudget == 'quartic':
unit = count_eps * ((2 ** (1.0 / 4)) - 1) / (2 ** ((1.0 / 4) * (H + 1)) - 1)
return [unit * 2 ** ((1.0 / 4) * i) for i in range(H + 1)]
else:
logging.error('No such geoBudget scheme')
sys.exit(1)
def synthetic_gen(self):
"""Apply a grid structure on the domain and perturb the count using half
of the available privacy budget """
logging.debug('generating synthetic map...')
data = self.realData
unit = Params.unitGrid
x_min = np.floor(Params.LOW[0] / unit) * unit
x_max = np.ceil(Params.HIGH[0] / unit) * unit
y_min = np.floor(Params.LOW[1] / unit) * unit
y_max = np.ceil(Params.HIGH[1] / unit) * unit
x_CELL = int(np.rint((x_max - x_min) / unit))
y_CELL = int(np.rint((y_max - y_min) / unit))
self.root.n_box = np.array([[x_min, y_min], [x_max, y_max]])
self.mapp = np.zeros((x_CELL, y_CELL)) - 1 # ## initialize every cell with -1
for i in range(Params.NDATA): # ## populate the map
point = data[:, i]
cell_x = int(np.floor((point[0] - x_min) / unit))
cell_y = int(np.floor((point[1] - y_min) / unit))
if self.mapp[cell_x, cell_y] != -1:
self.mapp[cell_x, cell_y] += 1
else:
self.mapp[cell_x, cell_y] = 1
for i in range(x_CELL): # ## perturb the counts
for j in range(y_CELL):
if self.mapp[i, j] != -1:
self.mapp[i, j] += np.rint(self.differ.getNoise(1, 0.5 * self.param.Eps))
else:
self.mapp[i, j] = np.rint(self.differ.getNoise(1, 0.5 * self.param.Eps))
# if noisy count is negative, ignore the noise and generate no points
if self.mapp[i, j] < 0:
self.mapp[i, j] = 0
def cell_setLeaf(self, curr):
""" Throw away the counts based on the syntatic data """
curr.n_count = 0
return
def testLeaf(self, curr):
if (curr.n_count <= self.param.minPartSize) or (curr.n_depth == Params.maxHeight) or (
self.uniform_test(curr, self.param.cellDistance)):
return True
return False
def uniform_test(self, curr, distance):
""" One of the stopping conditions: cell is uniform according to some threshold 'distance') """
unit = Params.unitGrid
x_min = int(np.rint((curr.n_box[0, 0] - self.root.n_box[0, 0]) / unit))
x_max = int(np.rint((curr.n_box[1, 0] - self.root.n_box[0, 0]) / unit))
y_min = int(np.rint((curr.n_box[0, 1] - self.root.n_box[0, 1]) / unit))
y_max = int(np.rint((curr.n_box[1, 1] - self.root.n_box[0, 1]) / unit))
data = self.mapp[x_min:x_max, y_min:y_max]
total = np.sum(data)
avg = total / ((x_max - x_min) * (y_max - y_min))
dist = np.sum(np.abs(data - avg))
if dist > distance:
return False
else:
return True
def buildIndex(self):
stack = deque()
stack.append(self.root)
nleaf = 0 # leaf counter
max_depth = -1
self.root.n_count = np.sum(self.mapp)
while len(stack) > 0:
curr = stack.popleft()
if curr.n_depth > max_depth:
max_depth = curr.n_depth
if self.testLeaf(curr) is True: # curr is a leaf node
nleaf += 1
curr.n_isLeaf = True
self.cell_setLeaf(curr)
else: # curr needs to split
curr.n_budget -= 1
tmp = self.getCoordinates(curr)
nw_node, ne_node, sw_node, se_node = KNode(), KNode(), KNode(), KNode() # create sub-nodes
nw_coord, ne_coord, count_tmp = tmp
x_nw, y_nw = nw_coord
x_se, y_se = ne_coord
nw_node.n_box = np.array([[curr.n_box[0, 0], y_nw], [x_nw, curr.n_box[1, 1]]])
ne_node.n_box = np.array([[x_nw, y_se], [curr.n_box[1, 0], curr.n_box[1, 1]]])
sw_node.n_box = np.array([[curr.n_box[0, 0], curr.n_box[0, 1]], [x_se, y_nw]])
se_node.n_box = np.array([[x_se, curr.n_box[0, 1]], [curr.n_box[1, 0], y_se]])
c_t = 0
for sub_node in [nw_node, ne_node, sw_node, se_node]:
sub_node.n_depth = curr.n_depth + 1
sub_node.n_count = count_tmp[c_t]
sub_node.n_budget = curr.n_budget
stack.append(sub_node)
c_t += 1
curr.nw, curr.ne, curr.sw, curr.se = nw_node, ne_node, sw_node, se_node
# end of while
logging.debug("number of leaves: %d" % nleaf)
logging.debug("max depth: %d" % max_depth)
def getCoordinates(self, curr):
dim_1 = curr.n_depth % Params.NDIM # primary split dimension
UNIT = Params.unitGrid
x_min = int(np.rint((curr.n_box[0, 0] - self.root.n_box[0, 0]) / UNIT))
x_max = int(np.rint((curr.n_box[1, 0] - self.root.n_box[0, 0]) / UNIT))
y_min = int(np.rint((curr.n_box[0, 1] - self.root.n_box[0, 1]) / UNIT))
y_max = int(np.rint((curr.n_box[1, 1] - self.root.n_box[0, 1]) / UNIT))
total = np.sum(self.mapp[x_min:x_max, y_min:y_max])
if dim_1 == 0:
for i in range(x_max - x_min):
if np.sum(self.mapp[x_min:x_min + i + 1, y_min:y_max]) >= total / 2:
break
split_prm = (x_min + i + 1) * UNIT + self.root.n_box[0, 0]
half_1 = np.sum(self.mapp[x_min:x_min + i + 1, y_min:y_max])
half_2 = np.sum(self.mapp[x_min + i + 1:x_max, y_min:y_max])
for j in range(y_max - y_min):
if np.sum(self.mapp[x_min:x_min + i + 1, y_min:y_min + j + 1]) >= half_1 / 2:
break
split_sec1 = self.root.n_box[0, 1] + (y_min + j + 1) * UNIT
n_sw = np.sum(self.mapp[x_min:x_min + i + 1, y_min:y_min + j + 1])
n_nw = np.sum(self.mapp[x_min:x_min + i + 1, y_min + j + 1:y_max])
for k in range(y_max - y_min):
if np.sum(self.mapp[x_min + i + 1:x_max, y_min:y_min + k + 1]) >= half_2 / 2:
break
split_sec2 = self.root.n_box[0, 1] + (y_min + k + 1) * UNIT
n_se = np.sum(self.mapp[x_min + i + 1:x_max, y_min:y_min + k + 1])
n_ne = np.sum(self.mapp[x_min + i + 1:x_max, y_min + k + 1:y_max])
return (split_prm, split_sec1), (split_prm, split_sec2), (n_nw, n_ne, n_sw, n_se)
else:
for i in range(y_max - y_min):
if np.sum(self.mapp[x_min:x_max, y_min:y_min + i + 1]) >= total / 2:
break
split_prm = self.root.n_box[0, 1] + (y_min + i + 1) * UNIT
half_1 = np.sum(self.mapp[x_min:x_max, y_min:y_min + i + 1])
half_2 = np.sum(self.mapp[x_min:x_max, y_min + i + 1:y_max])
for j in range(x_max - x_min):
if np.sum(self.mapp[x_min:x_min + j + 1, y_min:y_min + i + 1]) >= half_1 / 2:
break
split_sec1 = (x_min + j + 1) * UNIT + self.root.n_box[0, 0]
n_sw = np.sum(self.mapp[x_min:x_min + j + 1, y_min:y_min + i + 1])
n_se = np.sum(self.mapp[x_min + j + 1:x_max, y_min:y_min + i + 1])
for k in range(x_max - x_min):
if np.sum(self.mapp[x_min:x_min + k + 1, y_min + i + 1:y_max]) >= half_2 / 2:
break
split_sec2 = (x_min + k + 1) * UNIT + self.root.n_box[0, 0]
n_nw = np.sum(self.mapp[x_min:x_min + k + 1, y_min + i + 1:y_max])
n_ne = np.sum(self.mapp[x_min + k + 1:x_max, y_min + i + 1:y_max])
return (split_sec2, split_prm), (split_sec1, split_prm), (n_nw, n_ne, n_sw, n_se)
def populate_synthetic_tree(self):
""" Populate real data to the synthetic tree """
logging.debug('populating synthetic tree...')
a_data = self.realData
ndata = a_data.shape[1]
for i in range(ndata):
ptx = a_data[0, i]
pty = a_data[1, i]
leaf = self.root.find_subnode(ptx, pty)
leaf.n_count += 1
# traverse the tree and update leaf counts
stack = deque()
stack.append(self.root)
while len(stack) > 0:
cur_node = stack.popleft()
if cur_node.n_isLeaf is True: # leaf
cur_node.n_count += self.differ.getNoise(1, 0.5 * self.param.Eps)
else:
stack.append(cur_node.nw)
stack.append(cur_node.ne)
stack.append(cur_node.sw)
stack.append(cur_node.se)
