更新 function.py

function.py

@@ -41,74 +41,64 @@ name = "严锡好"
 
 
 # 这里写自己的代码实现
-def mahalanobis_distance(x1, x2, cov_inv, mean):
-    """
-    计算两点之间的马氏距离。
-    
-    Args:
-    x1 (numpy array): 第一个点。
-    x2 (numpy array): 第二个点。
-    cov_inv (numpy array): 协方差矩阵的逆矩阵。
-    mean (numpy array): 数据集的均值。
-    
-    Returns:
-    float: 两点之间的马氏距离。
-    """
-    delta = x1 - x2
-    dist = delta @ cov_inv @ delta.T
-    return np.sqrt(dist)
+class KDNode:
+    def __init__(self, data, left=None, right=None, label=None):
+        self.data = data
+        self.left = left
+        self.right = right
+        self.label = label
 
-def classify0(inX, dataSet, labels, k=3):
-    """
-    使用马氏距离的 KNN 分类算法。
+class KDTree:
+    def __init__(self, data, labels, k=3):
+        self.k = k
+        self.root = self.build_tree(data, labels)
 
-    Args:
-    - inX (numpy array): 输入待分类的样本。
-    - dataSet (numpy array): 训练数据集。
-    - labels (list or numpy array): 训练集对应的标签。
-    - k (int): kNN 算法参数，默认值为 3。
+    def build_tree(self, data, labels, depth=0):
+        if not data:
+            return None
+        indices = np.argsort(data[:, depth % data.shape[1]])
+        median_idx = indices[len(indices) // 2]
+        node = KDNode(data[median_idx], label=labels[median_idx])
+        node.left = self.build_tree(data[indices[:median_idx]], labels[indices[:median_idx]], depth + 1)
+        node.right = self.build_tree(data[indices[median_idx + 1:]], labels[indices[median_idx + 1:]], depth + 1)
+        return node
 
-    Returns:
-    - int: 预测的分类标签。
-    """
-    # 计算训练数据集的协方差矩阵和均值
-    cov_matrix = np.cov(dataSet, rowvar=False)
-    mean = np.mean(dataSet, axis=0)
-    cov_inv = np.linalg.inv(cov_matrix + np.eye(cov_matrix.shape[0]) * 1e-5)  # 加上一个小的单位矩阵以避免奇异矩阵
-    
-    # 计算待分类样本与训练集中每个样本的马氏距离
-    distances = np.array([mahalanobis_distance(inX, x, cov_inv, mean) for x in dataSet])
-    
-    # 获取距离最近的 k 个样本的索引
-    sortedDistIndices = distances.argsort()[:k]
-    
-    # 获取这些样本对应的标签
-    classCount = {}
-    for i in sortedDistIndices:
-        voteLabel = labels[i]
-        classCount[voteLabel] = classCount.get(voteLabel, 0) + 1
-    
-    # 选择出现次数最多的标签作为预测标签
-    sortedClassCount = sorted(classCount.items(), key=lambda x: x[1], reverse=True)
-    return sortedClassCount[0][0]
+    def find_nearest_neighbors(self, point, node=None, depth=0, neighbors=None):
+        if not node:
+            return
+        dist = np.linalg.norm(point - node.data)
+        if neighbors is None:
+            neighbors = [(dist, node.label)]
+        else:
+            neighbors = [(n[0], n[1]) for n in neighbors if n[0] < dist] + [(dist, node.label)]
+        neighbors.sort(key=lambda x: x[0])
+        if len(neighbors) < self.k:
+            self.find_nearest_neighbors(point, node.left, depth + 1, neighbors)
+            self.find_nearest_neighbors(point, node.right, depth + 1, neighbors)
+        else:
+            if depth % point.shape[0] != point.shape[0] - 1:
+                self.find_nearest_neighbors(point, node.left, depth + 1, neighbors)
+            if depth % point.shape[0] != point.shape[0] - 1:
+                self.find_nearest_neighbors(point, node.right, depth + 1, neighbors)
 
+    def predict(self, point):
+        neighbors = []
+        self.find_nearest_neighbors(point, self.root, 0, neighbors)
+        neighbors.sort(key=lambda x: x[0])
+        labels = [n[1] for n in neighbors]
+        return np.argmax(np.bincount(labels))
 
 def load_data(file_path):
-    """
-    加载 TSV 格式数据文件。
-    """
     data = np.loadtxt(file_path, delimiter="\t")
     features = data[:, :-1]
     labels = data[:, -1].astype(int)
     return features, labels
 
-
 if __name__ == "__main__":
-    # 以下代码可用于测试，可自行随意修改
     train_file = "datingTrainSet2.tsv"
     train_data, train_labels = load_data(train_file)
+    kdt = KDTree(train_data, train_labels, k=3)
 
-    # 测试一个样本
     test_sample = np.array([65915, 3.868359, 0.128078])
-    predicted_label = classify0(test_sample, train_data, train_labels)
+    predicted_label = kdt.predict(test_sample)
     print(f"The predicted label for the test sample is: {predicted_label}")