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kNN.py
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kNN.py
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import heapq
import numpy as np
import matplotlib.pyplot as plt
import sys
class Node(object):
def __init__(self, axis=None, val=[], left=None, right=None):
self.axis = axis
self.point = val
self.left = left
self.right = right
self.dflag = 0
class KDtree(object):
def __init__(self, point, k):
self.dim = len(point[0])
self.k = k
self.Kbest = []
self.alpha = 0.8
self.root = self.fit(point)
def fit(self, point, depth=0):
if len(point) <= 0 or len(point[0]) == 0:
return None
axis = depth % self.dim
array = [p[axis] for p in point]
# print(len(point))
median = self.find_median(0, len(array)-1, array, len(array)//2)
median = median[len(array)//2]
index = array.index(median)
left = [i for i in point if i[axis] < median]
right = [i for i in point if i[axis] > median]
return Node(axis = axis,
val = point[index],
left = self.fit(point=left, depth=depth+1),
right = self.fit(point=right, depth=depth+1))
def find_median(self, l, r, a, index):
i,j = l,r
mid = l + (r-l)//2
x = a[mid]
while (i<=j):
while a[i] < x:
i+=1
while x < a[j]:
j-=1
if i<=j:
a[i],a[j] = a[j],a[i]
i +=1
j -=1
if l<j and index <= j:
a = self.find_median(l, j, a, index)
elif i<r and i <= index:
a = self.find_median(i, r, a, index)
return a
def calc(self, root):
if root is None:
return 0
return self.calc(root.left) + self.calc(root.right) + 1
def calcD(self, root):
if root is None:
return 0
return self.calcD(root.left) + self.calcD(root.right) + root.dflag
def flatten(self, root, flat_a=[]):
if root is None:
return flat_a
flat_a = self.flatten(root.left)
if root.dflag == 0:
flat_a.append(root.point)
flat_a = self.flatten(root.right)
return flat_a
def FLAG(self, root):
if root is None:
return 0
calc = self.calc(root)
return not root.dflag and (self.alpha * calc <= max(self.calc(root.left), self.calc(root.right))
or self.alpha * calc <= self.calcD(root))
def add(self, root, point, depth=0):
axis = depth % self.dim
if root is None:
root = Node(axis=axis, val=point, left=None, right=None)
else:
if point[root.axis] < root.point[root.axis]:
root.left = self.add(root.left, point, depth=depth+1)
elif root.point[axis] < point[root.axis]:
root.right = self.add(root.right, point, depth=depth+1)
if self.FLAG(root):
root = self.rebuild(root, depth)
return root
def delete(self, root, point, depth=0):
if root is None:
return None
else:
if all(root.point == point):
root.dflag = 1
elif point[root.axis] < root.point[root.axis]:
root.left = self.delete(root.left, point, depth=depth+1)
elif root.point[root.axis] < point[root.axis]:
root.right = self.delete(root.right, point, depth=depth+1)
if self.FLAG(root):
root = self.rebuild(root, depth)
return root
def rebuild(self, root, depth):
flat_a = self.flatten(root=root)
return self.fit(flat_a, depth=depth)
def find_Knearest(self, point, root=None):
if root is None:
self.Kbest = []
root = self.root
if root.left is not None or root.right is not None:
if point[root.axis] < root.point[root.axis] and root.left is not None:
self.find_Knearest(point, root=root.left)
elif root.right is not None:
self.find_Knearest(point, root=root.right)
dis = sum(list(map(lambda x,y : abs(x-y), root.point, point)))
if len(self.Kbest) < self.k:
heapq.heappush(self.Kbest,(-dis, root.point))
if dis < abs(heapq.nsmallest(1, self.Kbest, lambda d:d[0])[0][0]):
heapq.heappop(self.Kbest)
heapq.heappush(self.Kbest, (-dis, root.point))
if abs(root.point[root.axis]-point[root.axis]) < abs(heapq.nsmallest(1, self.Kbest, lambda d:d[0])[0][0]):
if root.right is not None and point[root.axis] < root.point[root.axis]:
self.find_Knearest(point, root=root.right)
elif root.left is not None and point[root.axis] >= root.point[root.axis]:
self.find_Knearest(point, root=root.left)
return self.Kbest
def gen_data(x1, x2):
y = np.sin(x1) * 1 / 2 + np.cos(x2) * 1 / 2 + 0.1 * x1
return y
def load_data():
x1_train = np.linspace(0, 50, 1000)
x2_train = np.linspace(-10, 10, 1000)
data_train = [[x1, x2, gen_data(x1, x2) + np.random.random(1)[0] - 0.5] for x1, x2 in zip(x1_train, x2_train)]
x1_test = np.linspace(0, 50, 100) + np.random.random(100) * 0.5
x2_test = np.linspace(-10, 10, 100) + 0.02 * np.random.random(100)
data_test = [[x1, x2, gen_data(x1, x2)] for x1, x2 in zip(x1_test, x2_test)]
return np.array(data_train), np.array(data_test)
def main():
train, test = load_data()
x_train, y_train = train[:, :], train[:, 2]
x_test, y_test = test[:, :], test[:, 2] # 同上，但这里的y没有噪声
t = KDtree([x_train[0]], k=13)
for point in x_train[1:]:
t.root=t.add(t.root, point, 0)
# t.root=t.delete(t.root, point, 0)
t.root=t.rebuild(t.root, 0)
result = [t.find_Knearest(i)[-1][-1] for i in x_test]
result = [i[-1] for i in result]
result = [np.average(i) for i in result]
#
print(len(result))
plt.plot(result)
plt.plot(y_test)
plt.show()
return 0
if __name__ == "__main__":
main()
# t = KDtree([[]],1)
# a = [3,2,1,5,4,3,2] # 1,2,2,3,3,4,5
# a = [4,5,6,3,6,8,4] # 3,4,4,5,6,6,8
# a = [0,2,1,1,5,6,7] # 0,1,1,2,5,6,7
# s = t.find_median(0, len(a)-1, a, len(a)//2)
# s = s[len(a)//2]
# print(s)