用python实现Recursive Model Index

以下是使用Python实现的递归模型索引（Recursive Model Index，RMI）的代码示例：

import numpy as np
from sklearn.linear_model import LinearRegression

class RMI:
    def __init__(self, data, leaf_size=16, num_steps=10):
        self.leaf_size = leaf_size
        self.num_steps = num_steps
        self.buckets = []
        self.models = []
        self.build(data)
        
    def build(self, data):
        self.min_val = np.min(data)
        self.max_val = np.max(data)
        num_buckets = int(np.ceil(len(data) / self.leaf_size))
        if num_buckets == 1:
            start = 0
            end = len(data)
            bucket_data = data[start:end]
            bucket_min = np.min(bucket_data)
            bucket_max = np.max(bucket_data)
            self.buckets.append((bucket_min, bucket_max))
            self.models.append(None)
        else:
            self.buckets.append((self.min_val, self.max_val))
            self.models.append(None)
            bucket_data = []
            for i in range(num_buckets):
                start = i * self.leaf_size
                end = min((i + 1) * self.leaf_size, len(data))
                bucket_data.append(data[start:end])
            new_data = []
            for i in range(num_buckets):
                bucket_min = np.min(bucket_data[i])
                bucket_max = np.max(bucket_data[i])
                self.buckets.append((bucket_min, bucket_max))
                bucket_values = (bucket_data[i] - bucket_min) / (bucket_max - bucket_min)
                x = np.linspace(0, 1, len(bucket_values))
                model = LinearRegression()
                for j in range(self.num_steps):
                    model.fit(x.reshape(-1, 1), bucket_values)
                    y_pred = model.predict(x.reshape(-1, 1))
                    residuals = bucket_values - y_pred
                    bucket_values = residuals
                self.models.append(model)
                new_data.append(y_pred)
            self.build(np.concatenate(new_data))
            
    def predict(self, query):
        if query < self.min_val or query > self.max_val:
            return -1
        bucket_idx = 0
        while self.models[bucket_idx] is not None:
            bucket_min, bucket_max = self.buckets[bucket_idx]
            if query <= bucket_min:
                bucket_idx = 2 * bucket_idx + 1
            elif query >= bucket_max:
                bucket_idx = 2 * bucket_idx + 2
            else:
                x = np.array([(query - bucket_min) / (bucket_max - bucket_min)])
                model = self.models[bucket_idx]
                for i in range(self.num_steps):
                    y_pred = model.predict(x.reshape(-1, 1))
                    x -= y_pred
                bucket_idx = 2 * bucket_idx + 1 + np.argmax(x)
        leaf_idx = bucket_idx - len(self.models)
        bucket_min, bucket_max = self.buckets[bucket_idx]
        x = np.array([(query - bucket_min) / (bucket_max - bucket_min)])
        model = self.models[bucket_idx]
        for i in range(self.num_steps):
            y_pred = model.predict(x.reshape(-1, 1))
            x -= y_pred
        return leaf_idx * self.leaf_size + np.argmax(x)

相较于RMI，递归模型索引（RMI）可以更好地处理数据分布不均的情况。这里使用了递归的方式构建索引结构，每个节点只有一个模型，如果当前节点的模型为None，则说明该节点是叶子节点，直接保存数据。查询时，从根节点开始递归查找，如果当前节点的模型为None，则说明该节点是叶子节点，根据数据分布计算得到查询值所在叶子节点的索引。