import numpy as np import os from sklearn.neighbors import KDTree """ 实验说明: - 自行编写实现数据加载与 kNN 的手写数字分类算法。 - 函数输入: 待分类的样本 input_vector, 训练数据集 dataSet, 训练集对应的标签 labels。 - 函数返回: 预测的分类标签。 请在这里填写学号和姓名,不填写即成绩无效。 """ id = "202210423213" name = "熊浩燃" def classify(input_vector, dataSet, labels, k=1, distance_metric='euclidean', weighted=False): """ KNN 分类算法。 Args: - input_vector (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1。 - distance_metric (str): 距离度量方式,支持'euclidean'和'manhattan'。 - weighted (bool): 是否使用加权投票。 Returns: - int: 预测的分类标签。 """ # 选择距离度量 if distance_metric == 'euclidean': distances = np.linalg.norm(dataSet - input_vector, axis=1) elif distance_metric == 'manhattan': distances = np.sum(np.abs(dataSet - input_vector), axis=1) else: raise ValueError(f"Unsupported distance metric: {distance_metric}") # 获取距离最近的 k 个样本的索引 nearest_neighbors_indices = distances.argsort()[:k] # 获取这些样本的标签 nearest_labels = np.array(labels)[nearest_neighbors_indices] if weighted: # 使用加权投票:距离越近,权重越大 nearest_distances = distances[nearest_neighbors_indices] weights = 1 / (nearest_distances + 1e-5) # 防止距离为0 weighted_vote = np.bincount(nearest_labels, weights=weights) predicted_label = weighted_vote.argmax() else: predicted_label = np.bincount(nearest_labels).argmax() return predicted_label def classify_with_kdtree(input_vector, dataSet, labels, k=1): """ 使用 KD-tree 进行加速的 kNN 分类算法。 Args: - input_vector (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1。 Returns: - int: 预测的分类标签。 """ tree = KDTree(dataSet) # 构建 KD-tree dist, indices = tree.query(input_vector.reshape(1, -1), k=k) # 查询最近邻 nearest_labels = np.array(labels)[indices[0]] predicted_label = np.bincount(nearest_labels).argmax() return predicted_label def load_dataset(directory): """ 从文件夹中加载数据,若不自行正确实现,则无法通过评测,不记录成绩。 Args: - directory (str): 数据文件夹路径。 Returns: - np.array: 特征数据。 - np.array: 标签数据。 """ labels = [] data_list = [] for filename in os.listdir(directory): if filename.endswith(".txt"): # 确保读取的是 txt 文件 label = int(filename.split('_')[0]) labels.append(label) vector = img_to_vector(os.path.join(directory, filename)) data_list.append(vector) return np.array(data_list), np.array(labels) def img_to_vector(filename): """ 将二值图像转换为向量。 Args: - filename (str): 图像文件路径。 Returns: - np.array: 二值图像向量。 """ with open(filename, 'r') as f: # 确保使用文本模式读取 lines = f.readlines() vector = np.zeros((1024,), dtype=int) # 将其改为 (1024,) 的一维数组 for i in range(32): for j in range(32): vector[32 * i + j] = int(lines[i][j]) return vector if __name__ == "__main__": # 测试代码 train_data, train_labels = load_dataset("trainingDigits") test_data = ( "00000000000000110000000000000000" "00000000000011111000000000000000" "00000000000011111100000000000000" "00000000001111111110000000000000" "00000000001111111110000000000000" "00000000001111111100000000000000" "00000000011111111000000000000000" "00000000111111111000000000000000" "00000000111111110000000000000000" "00000000111111110000000000000000" "00000000111111110000000000000000" "00000000111111110000000000000000" "00000000111111100000000000000000" "00000001111111100000000000000000" "00000001111111100000000000000000" "00000001111111100000000000000000" "00000001111111111111000000000000" "00000001111111111111111000000000" "00000001111111111111111100000000" "00000011111111111111111110000000" "00000011111111111111111110000000" "00000001111111111111111110000000" "00000001111111111111111110000000" "00000000111111111100111111100000" "00000000111111111000111111100000" "00000000011111111001111111100000" "00000000011111111111111111000000" "00000000001111111111111111000000" "00000000000111111111111111000000" "00000000000011111111111100000000" "00000000000001111111110000000000" "00000000000000000111100000000000" ) test_vector = np.array([int(char) for char in test_data]).reshape(1, 1024) # 使用默认的欧氏距离和不加权的投票机制 predicted_label = classify(test_vector, train_data, train_labels) print(f"预测的标签(普通分类): {predicted_label}") # 使用 KD-tree 进行加速的分类 predicted_label_kdtree = classify_with_kdtree(test_vector, train_data, train_labels) print(f"预测的标签KD-tree 加速: {predicted_label_kdtree}")