python实现LSH算法

LSH（局部敏感哈希）是一种用于高维数据的近似最近邻搜索的技术。以下是Python实现LSH算法的步骤：

1. 安装必要的库：numpy和bitarray。可以使用以下命令进行安装：

   pip install numpy bitarray

2. 导入库：

   import numpy as np
   from bitarray import bitarray

3. 定义哈希函数：

   def hash_vector(v, planes):
       return "".join(['1' if np.dot(v, plane) > 0 else '0' for plane in planes])

4. 定义LSH类：

   class LSH:
       def __init__(self, num_planes, input_dim):
           self.num_planes = num_planes
           self.input_dim = input_dim
           self.planes = np.random.normal(size=(num_planes, input_dim))
           self.hash_tables = {}
           for i in range(num_planes):
               self.hash_tables[i] = {}
   
       def add(self, v, label):
           hash_val = hash_vector(v, self.planes)
           for i in range(self.num_planes):
               if hash_val[i] not in self.hash_tables[i]:
                   self.hash_tables[i][hash_val[i]] = bitarray(self.input_dim)
                   self.hash_tables[i][hash_val[i]].setall(0)
               self.hash_tables[i][hash_val[i]][label] = 1
   
       def query(self, v):
           hash_val = hash_vector(v, self.planes)
           candidates = None
           for i in range(self.num_planes):
               if hash_val[i] not in self.hash_tables[i]:
                   return None
               if candidates is None:
                   candidates = self.hash_tables[i][hash_val[i]]
               else:
                   candidates = candidates & self.hash_tables[i][hash_val[i]]
           return candidates

5. 创建LSH对象并添加数据：

   lsh = LSH(num_planes=10, input_dim=100)
   for i in range(1000):
       v = np.random.normal(size=100)
       lsh.add(v, i)

6. 查询最近邻：

   query_v = np.random.normal(size=100)
   candidates = lsh.query(query_v)
   if candidates is not None:
       distances = np.linalg.norm(query_v - candidates, axis=1)
       nearest_neighbor = np.argmin(distances)