def kdtree_knn_search(root: Node, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
#搜索query点的邻近点
if root is None:
return False #1、节点不存在
if root.is_leaf():
# compare the contents of a leaf
leaf_points = db[root.point_indices, :] #获取叶子节点的所有点
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
return False #2、叶子节点
# 作业2
# 提示：仍通过递归的方式实现搜索
# 屏蔽开始
if root.value >= query[root.axis]:
if kdtree_knn_search(root.left, db, result_set, query):
return True
elif math.fabs(root.value - query[root.axis]) < result_set.worst_dist:
return kdtree_knn_search(root.right, db, result_set, query)
return False #3、左右子树都不满足，就需要返回上一层树，所以为False
else:
if kdtree_knn_search(root.right, db, result_set, query):
return True
elif math.fabs(root.value - query[root.axis]) < result_set.worst_dist:
return kdtree_knn_search(root.left, db, result_set, query)
return False #3、左右子树都不满足，就需要返回上一层树，所以为False
# 屏蔽结束
return False
def kdtree_knn_search(root: Node, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf():
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
return False
# 作业2
# 提示：仍通过递归的方式实现搜索
# 屏蔽开始
# search in the left or right by axis, and search in the circle, whose radius is fixed
if query[root.axis] <= root.value:
kdtree_knn_search(root.left, db, result_set, query)
if math.fabs(query[root.axis] - root.value) < result_set.worstDist():
kdtree_knn_search(root.right, db, result_set, query)
else:
kdtree_knn_search(root.right, db, result_set, query)
if math.fabs(query[root.axis] - root.value) < result_set.worstDist():
kdtree_knn_search(root.left, db, result_set, query)
# 屏蔽结束
return False
def kdtree_knn_search(root: Node, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf():
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
return False
if query[root.axis] <= root.value:
kdtree_knn_search(root.left, db, result_set, query)
if math.fabs(query[root.axis] -
root.value) < result_set.get_worst_dist():
kdtree_knn_search(root.right, db, result_set, query)
else:
kdtree_knn_search(root.right, db, result_set, query)
if math.fabs(query[root.axis] -
root.value) < result_set.get_worst_dist():
kdtree_knn_search(root.left, db, result_set, query)
return False
def octree_knn_search(root: Octant, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf and len(root.point_indices) > 0:
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
# check whether we can stop search now
return inside(query, result_set.worstDist(), root)
morton_code = 0
if query[0] > root.center[0]:
morton_code = morton_code | 1
if query[1] > root.center[1]:
morton_code = morton_code | 2
if query[2] > root.center[2]:
morton_code = morton_code | 4
if octree_knn_search(root.children[morton_code], db, result_set, query):
return True
for c, child in enumerate(root.children):
if c == morton_code or child is None:
continue
if False == overlaps(query, result_set.worstDist(), child):
continue
if octree_knn_search(child, db, result_set, query):
return True
return inside(query, result_set.worstDist(), root)
def knn_search(root: Node, result_set: KNNResultSet, key):
if root is None:
return False
# compare the root itself 第一步 query的点和root计算worst
result_set.add_point(math.fabs(root.key - key), root.value)
if result_set.worstDist(
) == 0: # A special case - if the worst distance is 0, no need to search anymore
return True
if root.key >= key: # query point < root.key, search left
# iterate left branch first
if knn_search(root.left, result_set,
key): # if key!= query, need to go through one subtree.
return True # ( knn_search root 里面root是none返回false, key == query时候 worstDist=0，返回true,不然就一直迭代)
elif math.fabs(root.key - key) < result_set.worstDist(
): ## May not need to search for the other subtree, depends on worst distance.
return knn_search(root.right, result_set, key)
return False
else:
# iterate right branch first
if knn_search(root.right, result_set, key):
return True
elif math.fabs(root.key - key) < result_set.worstDist():
return knn_search(root.left, result_set, key)
return False
def kdtree_knn_search(root: Node, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf(): # 是叶子 不会被分割 ，直接丢到结果集里面
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
return False
if query[root.axis] <= root.value: ## axis维度上的查询点 在根节点的左边
kdtree_knn_search(root.left, db, result_set,
query) # q[axis] inside the partition
if math.fabs(query[root.axis] - root.value) < result_set.worstDist():
kdtree_knn_search(root.right, db, result_set,
query) # |q[axis] - splitting_value| < w
else:
kdtree_knn_search(root.right, db, result_set, query)
if math.fabs(query[root.axis] - root.value) < result_set.worstDist():
kdtree_knn_search(root.left, db, result_set, query)
return False
def kdtree_knn_search(root: Node, db: np.ndarray, result_set: KNNResultSet, query: np.ndarray):
if root is None:
return False
if root.is_leaf():
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
return False
# 作业2
# 提示：仍通过递归的方式实现搜索
# 屏蔽开始
root.value = (middle_left_point_value + middle_right_point_value) * 0.5
root.left = kdtree_recursive_build(root.left,
db,
point_indices_sorted[0:middle_right_idx],
axis_round_robin(axis, dim=db.shape[1])
leaf_size)
# bi-divide, and get the right-son tree
root.right = kdtree_recursive_build(root.right,
db,
point_indices_sorted[middle_right_idx:]),
axis_round_robin(axis, dim=db.shape[1]),
leaf_size)
def knn_search(root:Node,result_set:KNNResultSet,key):
if root is None:
return False
# compare the root itself
#计算worst_dist ,并把当前root.value(index二叉树)里的值加入到resut_set 中
result_set.add_point(math.fabs(root.key - key),root.value)
# A special case – if the worst distance is 0, no need to search anymore
if result_set.worstDist() == 0:
return True
# iterate left branch first
if root.key >= key:
# If key != query, need to go through one subtree
if knn_search(root.left, result_set, key):
return True
# May not need to search for the other subtree, depends on worst distance
elif math.fabs(root.key-key) < result_set.worstDist():
return knn_search(root.right, result_set, key)
return False
else:
# iterate right branch first
if knn_search(root.right, result_set, key):
return True
elif math.fabs(root.key-key) < result_set.worstDist():
return knn_search(root.left, result_set, key)
return False
def kdtree_knn_search(root: Node, db: np.ndarray, result_set: KNNResultSet, query: np.ndarray):
if root is None:
return False
if root.is_leaf():
# compare the contents of a leaf, put into the result set
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
return False
# 作业2
# 提示：仍通过递归的方式实现搜索
# 屏蔽开始
if query[root.axis] < root.value: # query[axis] inside the partition
kdtree_knn_search(root.left, db, result_set, query)
if math.fabs(query[root.axis] - root.value) < result_set.worstDist(): # |query[axis]-splitting_value| < w
kdtree_knn_search(root.right, db, result_set, query)
else:
kdtree_knn_search(root.right, db, result_set, query)
if math.fabs(query[root.axis] - root.value) < result_set.worstDist():
kdtree_knn_search(root.left, db, result_set, query)
# 屏蔽结束
return False
def main():
# configuration
leaf_size = 32
min_extent = 0.0001
k = 8
radius = 1
N = 100000 # 对N个点做搜索
# read data
filename = "../000000.bin"
db_np = read_velodyne_bin(filename)
root = kd_tree_construction(db_np, leaf_size)
depth = [0]
max_depth = [0]
traverse_kdtree(root, depth, max_depth)
knn_result_set = KNNResultSet(k)
query = db_np[0, :]
kd_tree_knn_search(root, db_np, knn_result_set, query)
print(knn_result_set)
radius_result_set = RadiusNNResultSet(radius)
kd_tree_radius_search(root, db_np, radius_result_set, query)
print(radius_result_set)
def main():
# configuration
db_size = 64
dim = 3
leaf_size = 4
k = 1
db_np = np.random.rand(db_size, dim)
root = kdtree_construction(db_np, leaf_size=leaf_size)
depth = [0]
max_depth = [0]
traverse_kdtree(root, depth, max_depth)
print("tree max depth: %d" % max_depth[0])
query = np.asarray([0, 0, 0])
result_set = KNNResultSet(capacity=k)
kdtree_knn_search(root, db_np, result_set, query)
print(result_set)
diff = np.linalg.norm(np.expand_dims(query, 0) - db_np, axis=1)
nn_idx = np.argsort(diff)
nn_dist = diff[nn_idx]
print(nn_idx[0:k])
print(nn_dist[0:k])
print("Radius search:")
query = np.asarray([0, 0, 0])
result_set = RadiusNNResultSet(radius=0.5)
kdtree_radius_search(root, db_np, result_set, query)
print(result_set)
def main():
# configuration
db_size = 100
k = 5
radius = 2.0
data = np.random.permutation(db_size).tolist()
root = None
for i, point in enumerate(data):
root = insert(root, point, i) # values = i, 数据中点的索引，对后面的NN搜索有用。
print("data = ", data)
query_key = 6
result_set = KNNResultSet(capacity=k) ## k等于5 查找与 query_key最近的k个数据
knn_search(root, result_set, query_key)
print('kNN Search:')
print('index - distance')
print(result_set)
result_set = RadiusNNResultSet(radius=radius)
radius_search(root, result_set, query_key)
print('Radius NN Search:')
print('index - distance')
print(result_set)
def main():
# 生成模拟数据
db_size = 64
dim = 3
leaf_size = 4
k = 8
db_np = np.random.rand(db_size, dim)
root = kdtree_construction(db_np, leaf_size=leaf_size)
# 测试Kd-Tree遍历
depth = [0]
max_depth = [0]
traverse_kdtree(root, depth, max_depth)
print("Tree max depth: %d" % max_depth[0])
# 测试KNN search
query = np.asarray([0, 0, 0])
result_set = KNNResultSet(capacity=k)
kdtree_knn_search(root, db_np, result_set, query)
print(result_set)
# 测试brute-force法
diff = np.linalg.norm(np.expand_dims(query, 0) - db_np, axis=1)
nn_idx = np.argsort(diff)
nn_dist = diff[nn_idx]
print(nn_idx[0:k])
print(nn_dist[0:k])
# 测试Radius search
result_set = RadiusNNResultSet(radius=0.5)
kdtree_radius_search(root, db_np, result_set, query)
print(result_set)
def main():
# configuration
db_size = 100
k = 5
radius = 2.0
#data = np.random.permutation(db_size).tolist()
data = [3, 4, 7, 0, 6, 5, 1, 2]
root = None
for i, point in enumerate(data):
root = insert(root, point, i)
query_key = 6
result_set = KNNResultSet(capacity=k)
knn_search(root, result_set, query_key)
print('kNN Search:')
print('index - distance')
print(result_set)
result_set = RadiusNNResultSet(radius=radius)
radius_search(root, result_set, query_key)
print('Radius NN Search:')
print('index - distance')
print(result_set)
def kdtree_contribute_Matrix(S, K):
N = len(S)
A = np.zeros((N, N))
leaf_size = 4
root = kdtree.kdtree_construction(S, leaf_size=leaf_size)
for i in range(N):
query = S[i]
result_set = KNNResultSet(capacity=K)
kdtree.kdtree_knn_search(root, S, result_set, query)
index = result_set.knn_output_index()
for j in index:
A[i][j] = 1 #
A[j][i] = A[i][j]
if i == j:
A[i][j] = 0
return A
def main():
# configuration
N = 64000
D = 3
leaf_size = 4
min_extent = 0.05
k = 8
r = 0.372
# generate point cloud:
point_cloud = np.random.rand(N, D)
octree = OCTree(point_cloud=point_cloud,
leaf_size=leaf_size,
min_extent=min_extent)
# octree.traverse()
# random query test:
for _ in range(100):
# generate query point:
query = np.random.rand(D)
# 01 -- knn: brute-force as baseline:
dists = np.linalg.norm(point_cloud - query, axis=1)
sorting_idx = np.argsort(dists)
brute_force_result = {i for i in sorting_idx[:k]}
knn_result_set = KNNResultSet(capacity=k)
octree.knn_search(query, knn_result_set)
knn_result = {i.index for i in knn_result_set.dist_index_list}
assert len(brute_force_result - knn_result) == 0
# 02 -- rnn: brute-force as baseline:
dists = np.linalg.norm(point_cloud - query, axis=1)
brute_force_result = {i for i, d in enumerate(dists) if d <= r}
rnn_result_set = RadiusNNResultSet(radius=r)
octree.rnn_search(query, rnn_result_set)
rnn_result = {i.index for i in rnn_result_set.dist_index_list}
assert len(brute_force_result - rnn_result) == 0
print('[OCTree kNN & RNN Random Query Test]: Successful')
begin_t = time.time()
print("[OCTree]: RNN search normal:")
for i in range(100):
query = np.random.rand(3)
rnn_result_set = RadiusNNResultSet(radius=0.5)
octree.rnn_search(query, rnn_result_set)
# print(result_set)
print("\tSearch takes %.3fms\n" % ((time.time() - begin_t) * 1000))
begin_t = time.time()
print("[OCTree]: RNN search fast:")
for i in range(100):
query = np.random.rand(3)
rnn_result_set = RadiusNNResultSet(radius=0.5)
octree.rnn_fast_search(query, rnn_result_set)
# print(result_set)
print("\tSearch takes %.3fms\n" % ((time.time() - begin_t) * 1000))
def octree_knn_search(root: Octant, db: np.ndarray, result_set: KNNResultSet, query: np.ndarray):
if root is None:
return False
if root.is_leaf and len(root.point_indices) > 0:
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
# check whether we can stop search now
return inside(query, result_set.worstDist(), root)
# 提前结束：核心-八叉树对3个维度有限制；
# 结束条件：其实是两个方向：向下递归，向上回溯
# 1-当一个节点返回True时，表示找到knn了，维度限制导致不会有更优的了，不再向下，立即结束；
# 2-最坏距离球如果 inside 当前节点，不需要再向上回溯检查其他节点，立即结束；
# 跳过条件：在检查
# 1. search the first relevant child:
# 找到最近的孩子，根据查询点的莫顿码
morton_code = 0
if query[0] > root.center[0]:
morton_code = morton_code | 1
if query[1] > root.center[1]:
morton_code = morton_code | 2
if query[2] > root.center[2]:
morton_code = morton_code | 4
if octree_knn_search(root.children[morton_code],
db,
result_set,
query):
return True
# 2. check other children
for c, child in enumerate(root.children):
if c == morton_code or child is None:
continue
if False == overlaps(query, result_set.worstDist(), child):
continue
if octree_knn_search(child, db, result_set, query):
return True
# final check of if we can stop search
return inside(query, result_set.worstDist(), root)
def octree_knn_search(root: Octant, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf and len(root.point_indices) > 0:
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
# check whether we can stop search now
#判断需要查询的点query,和半径为result_set.worstDist()构成的球，是否在octant内，该octant为叶子节点。
#如果在内则不需要去查询其他的Octant
return inside(query, result_set.worstDist(), root)
# 作业7
# 屏蔽开始
#如果不是叶子节点，先找到查询点属于哪个子Octant
children_idx = 0
if query[0] > root.center[0]: # x轴
children_idx = children_idx | 1
if query[1] > root.center[1]: # y轴
children_idx = children_idx | 2
if query[2] > root.center[2]: # z轴
children_idx = children_idx | 4
#如果在这个子octant中发现，查询点在该子octant中，同时由worst_dist构成的球也被octant包含，所以直接返回
if octree_knn_search(root.children[children_idx], db, result_set, query):
return True
#如果不满足上边的情况则需要遍历其他子octant
for c, child in enumerate(root.children):
if c == children_idx or child == None:
continue
if overlaps(query, result_set.worstDist(), child) == False:
continue
if octree_knn_search(root.children[c], db, result_set, query):
return True
# 屏蔽结束
# final check of if we can stop search
return inside(query, result_set.worstDist(), root)
def octree_knn_search(root: Octant, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf and len(root.point_indices) > 0:
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
# check whether we can stop search now
return inside(query, result_set.worstDist(), root)
# 作业7
# 屏蔽开始
child_idx = 0
# 判断所查询点在八叉树的位置
if query[0] > root.center[0]:
child_idx = child_idx | 1
if query[1] > root.center[1]:
child_idx = child_idx | 2
if query[2] > root.center[2]:
child_idx = child_idx | 4
# 递归判断是否在该区域就可以找到足够多的点
if octree_knn_search(root.children[child_idx], db, result_set, query):
return True
# 没有在查询点区域找到，对其他区域进行搜索
for c, child in enumerate(root.children):
if c == child_idx or child is None: # 搜索区域没有点或所搜索到查询点区域，skip
continue
if False == overlaps(query, result_set.worstDist(),
child): # 搜索区域与查询点和最坏距离构成的球面没有交点，skip
continue
if octree_knn_search(child, db, result_set,
query): # 其他情况可以进入搜索区域搜索（递归）
return True
# 屏蔽结束
# final check of if we can stop search
return inside(query, result_set.worstDist(), root)
def octree_knn_search(root: Octant, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf and len(root.point_indices) > 0:
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
# check whether we can stop search now
return inside(query, result_set.worstDist(), root)
# 作业7
# 屏蔽开始
# Determine & search the most relevant child
morton_code = 0
if query[0] > root.center[0]:
morton_code = morton_code | 1
if query[1] > root.center[1]:
morton_code = morton_code | 2
if query[2] > root.center[2]:
morton_code = morton_code | 4
if octree_knn_search(root.children[morton_code], db, result_set, query):
return True
# check other children
for c, child in enumerate(root.children):
if c == morton_code or child is None:
continue
# if an octant is not overlapping with query ball, skip
if overlaps(query, result_set.worstDist(), child) == False:
continue
if octree_knn_search(child, db, result_set, query):
return True
# 屏蔽结束
# final check of if we can stop search
return inside(query, result_set.worstDist(),
root) # if query ball is inside an octant, stop
def kdtree_knn_search(root: Node, db: np.ndarray, result_set: KNNResultSet,
query: np.ndarray):
if root is None:
return False
if root.is_leaf():
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
return False
# 作业2
# 提示：仍通过递归的方式实现搜索
# 屏蔽开始
# 屏蔽结束
return False
def octree_knn_search(root: Octant, db: np.ndarray, result_set: KNNResultSet, query: np.ndarray):
if root is None:
return False
if root.is_leaf and len(root.point_indices) > 0:
# compare the contents of a leaf
leaf_points = db[root.point_indices, :]
diff = np.linalg.norm(np.expand_dims(query, 0) - leaf_points, axis=1)
for i in range(diff.shape[0]):
result_set.add_point(diff[i], root.point_indices[i])
# check whether we can stop search now
return inside(query, result_set.worstDist(), root)
# 作业7
# 屏蔽开始
# 屏蔽结束
# final check of if we can stop search
return inside(query, result_set.worstDist(), root)
def KDTreeBenchmark(root_dir,
files,
k,
leaf_size,
radius,
feature=None,
feature2=None):
construction_time_sum = 0
knn_time_sum = 0
radius_time_sum = 0
brute_time_sum = 0
iteration_num = 0
for file in files:
if file.find('bin') == -1:
continue
iteration_num += 1
filename = os.path.join(root_dir, file)
db_np = read_velodyne_bin(filename)
begin_t = time.time()
root = kdtree.kdtree_construction(db_np, leaf_size, feature, feature2)
construction_time_sum += time.time() - begin_t
query = db_np[0, :]
begin_t = time.time()
result_set = KNNResultSet(capacity=k)
kdtree.kdtree_knn_search(root, db_np, result_set, query)
print("result set from KD Tree\n", result_set)
knn_time_sum += time.time() - begin_t
# print("--------")
begin_t = time.time()
result_set = RadiusNNResultSet(radius=radius)
kdtree.kdtree_radius_search(root, db_np, result_set, query)
#print(result_set)
radius_time_sum += time.time() - begin_t
#print("--------")
begin_t = time.time()
diff = np.linalg.norm(np.expand_dims(query, 0) - db_np, axis=1)
nn_idx = np.argsort(diff)
nn_dist = diff[nn_idx]
#print(nn_idx[0:k])
#print(nn_dist[0:k])
brute_time_sum += time.time() - begin_t
depth = [0]
max_depth = [0]
kdtree.traverse_kdtree(root, depth, max_depth)
print("tree depth: %d, max depth: %d" % (depth[0], max_depth[0]))
print("Kdtree: build %.3f, knn %.3f, radius %.3f, brute %.3f" %
(construction_time_sum * 1000 / iteration_num, knn_time_sum * 1000 /
iteration_num, radius_time_sum * 1000 / iteration_num,
brute_time_sum * 1000 / iteration_num))
def correctness_base():
# points = read_velodyne_bin("000000.bin")[0:100000, :]
points = read_test_file("../test.txt")
point_indices = np.array(range(points.shape[0]))
print(points.shape)
K = 8
query_point = points[1000]
leaf_size = 32
radius = 0.5
print("******** KNN search (build with median) ***********")
start = time.time()
root = kdtree_construction(points, leaf_size)
build = time.time()
knn_result_set = KNNResultSet(K)
kdtree_knn_search(root, points, knn_result_set, query_point)
end = time.time()
print("KDTree build takes {}ms".format(1000 * (build - start)))
print("KDTree KNN search takes {}ms".format(1000 * (end - build)))
print("Comparision times = {}".format(knn_result_set.comparision_count))
knn_result_set.list()
print("")
def fit(self, data):
#TODO
#step1 随机选取 K个数据点 作为聚类的中心
self.centers_ = data[random.sample(range(data.shape[0]),
self.k_)] #random.sample(list,num)
old_centers = np.copy(self.centers_) #存储old_centers
#step2 E-Step(expectation)：N个点、K个中心，求N个点到K个中心的nearest-neighbor
#kd-tree config
leaf_size = 1
k = 1 # 结果每个点选取属于自己的类中心
for _ in range(self.max_iter_):
labels = [[] for i in range(self.k_)] #用于分类所有数据点
root = kdtree.kdtree_construction(
self.centers_, leaf_size=leaf_size) #对中心点进行构建kd-tree
for i in range(data.shape[0]): #对每一个点在4个中心点中进行 1-NN的搜索
result_set = KNNResultSet(capacity=k)
query = data[i]
kdtree.kdtree_knn_search(root, self.centers_, result_set,
query) #返回对应中心点的索引
# labels[result_set.output_index].append(data[i])
#print(result_set)
output_index = result_set.knn_output_index()[0] #获取最邻近点的索引
labels[output_index].append(data[i]) #将点放入类中
#step3 M-Step(maximization)：更新中心点的位置，把属于同一个类的数据点求一个均值，作为这个类的中心值
for i in range(self.k_): #求K类里，每个类的的中心点
points = np.array(labels[i])
self.centers_[i] = points.mean(axis=0) #取点的均值，作为新的聚类中心
# print(points)
# print(self.centers_[i])
if np.sum(
np.abs(self.centers_ - old_centers)
) < self.tolerance_ * self.k_: # 如果前后聚类中心的距离相差小于self.tolerance_ * self.k_ 输出
break
old_centers = np.copy(self.centers_) #保存旧中心点
self.fitted = True
Point_Show(self.centers_)
def main():
# configuration
db_size = 1280
dim = 3
leaf_size = 4
k = 1
db_np = np.random.rand(db_size, dim)#生成size×dim的array，每个数都是0-1之间的随机数
radius_time_sum = 0
brute_time_sum = 0
root = kdtree_construction(db_np, leaf_size)
# root = kdtree_construction_median(db_np, leaf_size)
# depth = [0]
# max_depth = [0]
# traverse_kdtree(root, depth, max_depth)
# print("tree max depth: %d" % max_depth[0])
query = np.asarray([0, 0, 0])
result_set = KNNResultSet(capacity=k)
kdtree_knn_search(root, db_np, result_set, query)
# print(result_set)
#
diff = np.linalg.norm(np.expand_dims(query, 0) - db_np, axis=1)
nn_idx = np.argsort(diff)
nn_dist = diff[nn_idx]
# print(nn_idx[0:k])
# print(nn_dist[0:k])
print("Radius search:")
query = np.asarray([7, 3, 4])
begin_t = time.time()
result_set = RadiusNNResultSet(radius = 2)
kdtree_radius_search(root, db_np, result_set, query)
radius_time_sum = time.time() - begin_t
# print(result_set)
begin_t = time.time()
diff = np.linalg.norm(np.expand_dims(query, 0) - db_np, axis=1)
nn_idx = np.argsort(diff)
nn_dist = diff[nn_idx]
brute_time_sum = time.time() - begin_t
print('KD-tree: radius_search/brute',radius_time_sum/brute_time_sum)
def knn_search(root: Node, result_set: KNNResultSet, key):
if root is None:
return False
# compare the root itself
result_set.add_point(math.fabs(root.key - key), root.value)
if result_set.worstDist() == 0:
return True
if root.key >= key:
# iterate left branch first
if knn_search(root.left, result_set, key):
return True
elif math.fabs(root.key-key) < result_set.worstDist():
return knn_search(root.right, result_set, key)
return False
else:
# iterate right branch first
if knn_search(root.right, result_set, key):
return True
elif math.fabs(root.key-key) < result_set.worstDist():
return knn_search(root.left, result_set, key)
return False
def main():
# 生成模拟数据
db_size = 3000
dim = 3
leaf_size = 4
min_extent = 0.0001
k = 8
db_np = np.random.rand(db_size, dim)
root = octree_construction(db_np, leaf_size, min_extent)
# 测试Octree遍历
depth = [0]
max_depth = [0]
traverse_octree(root, depth, max_depth)
print("Tree max depth: %d" % max_depth[0])
# 测试KNN search
query = np.asarray([0, 0, 0])
result_set = KNNResultSet(capacity=k)
octree_knn_search(root, db_np, result_set, query)
print(result_set)
# 测试brute-force法
diff = np.linalg.norm(np.expand_dims(query, 0) - db_np, axis=1)
nn_idx = np.argsort(diff)
nn_dist = diff[nn_idx]
print(nn_idx[0:k])
print(nn_dist[0:k])
# 测试Radius search (normal)
begin_t = time.time()
print("Radius search normal:")
for i in range(100):
query = np.random.rand(3)
result_set = RadiusNNResultSet(radius=0.5)
octree_radius_search(root, db_np, result_set, query)
print("Search takes %.3fms\n" % ((time.time() - begin_t) * 1000))
# 测试Radius search (fast)
begin_t = time.time()
print("Radius search fast:")
for i in range(100):
query = np.random.rand(3)
result_set = RadiusNNResultSet(radius=0.5)
octree_radius_search_fast(root, db_np, result_set, query)
print("Search takes %.3fms\n" % ((time.time() - begin_t) * 1000))
def main():
# configuration
N = 64000
D = 3
leaf_size = 4
k = 8
r = 0.372
point_cloud = np.random.rand(N, D)
kd_tree = KDTree(
point_cloud = point_cloud,
init_axis = 0,
leaf_size = leaf_size
)
# kd_tree.traverse()
# random query test:
for _ in range(100):
# generate query point:
query = np.random.rand(D)
# 01 -- knn: brute-force as baseline:
dists = np.linalg.norm(point_cloud - query, axis=1)
sorting_idx = np.argsort(dists)
brute_force_result = {i for i in sorting_idx[:k]}
knn_result_set = KNNResultSet(capacity=k)
kd_tree.knn_search(query, knn_result_set)
knn_result = {i.index for i in knn_result_set.dist_index_list}
assert len(brute_force_result - knn_result) == 0
# 02 -- rnn: brute-force as baseline:
dists = np.linalg.norm(point_cloud - query, axis=1)
brute_force_result = {i for i, d in enumerate(dists) if d <= r}
rnn_result_set = RadiusNNResultSet(radius = r)
kd_tree.rnn_search(query, rnn_result_set)
rnn_result = {i.index for i in rnn_result_set.dist_index_list}
assert len(brute_force_result - rnn_result) == 0
print('[KDTree kNN & RNN Random Query Test]: Successful')
def main():
# configuration
db_size = 64
dim = 3
leaf_size = 4
k = 1
db_np = np.random.rand(db_size, dim)
print('db_np = ', db_np)
root = kdtree_construction(db_np, leaf_size=leaf_size)
depth = [0]
max_depth = [0]
traverse_kdtree(root, depth, max_depth)
print("tree max depth: %d" % max_depth[0])
query = np.asarray([0, 0, 0])
result_set = KNNResultSet(capacity=k)
kdtree_knn_search(root, db_np, result_set, query)
print(result_set)
