更新 function.py

function.py

@@ -6,6 +6,14 @@ import time
 id = "202210423220"
 name = "方子涵"
 
+def mahalanobis_distance(x, y, cov_inv):
+    """
+    计算两点之间的马氏距离。
+    """
+    delta = x - y
+    dist = np.sqrt(delta.dot(cov_inv).dot(delta.T))
+    return dist
+
 def classify(input_vector, dataSet, labels, k=3):
     """
     KNN 分类算法。
@@ -19,18 +27,26 @@ def classify(input_vector, dataSet, labels, k=3):
     Returns:
     - int: 预测的分类标签。
     """
-    # 计算输入向量与数据集中每个向量的欧式距离
+    # 计算数据集的协方差矩阵的逆矩阵
-    diffMat = np.tile(input_vector, (dataSet.shape[0], 1)) - dataSet
+    cov_inv = np.linalg.inv(np.cov(dataSet.T))
-    sqDiffMat = diffMat**2
+    
-    sqDistances = sqDiffMat.sum(axis=1)
+    # 初始化最近邻列表
-    distances = sqDistances**0.5
-    # 获取距离最近的 k 个样本的索引
-    sortedDistIndices = distances.argsort()
     classCount = {}
+    distances = []
+    
+    # 计算输入向量与数据集中每个向量的马氏距离
+    for vector in dataSet:
+        dist = mahalanobis_distance(input_vector, vector, cov_inv)
+        distances.append((dist, labels[np.where(dataSet == vector)[0][0]]))
+    
+    # 根据距离排序
+    distances.sort()
+    
+    # 获取距离最近的 k 个样本的标签
     for i in range(k):
-        voteIlabel = labels[sortedDistIndices[i]]
+        voteIlabel = distances[i][1]
-        # 统计每个类别的出现次数
         classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1
+    
     # 返回出现次数最多的类别
     sortedClassCount = sorted(classCount.items(), key=lambda x: x[1], reverse=True)
     return sortedClassCount[0][0]
@@ -55,7 +71,6 @@ def load_dataset(directory):
         filePath = os.path.join(directory, filename)
         vector = img_to_vector(filePath)
         dataSet[i, :] = vector
-        # 假设文件名的格式为 "label_number.txt"
         label = int(filename.split('_')[0])
         labels.append(label)
     return dataSet, np.array(labels)
@@ -75,11 +90,10 @@ def img_to_vector(filename):
         lines = file.readlines()
         n = 0
         for line in lines:
-            # 去除每行末尾的换行符
             line = line.strip()
             for i in range(len(line)):
                 returnVect[0, n] = int(line[i])
-                n = n + 1
+                n += 1
                 if n >= 1024:
                     break
             if n >= 1024: