Experiment-kNN/function.py

# function.py
import numpy as np
import os

"""
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。

注意事项:
- 在 function.py 中实现 kNN 分类算法。
- 可以自行导入其他库，需要在 requirements.txt 添加依赖，若未在 requirements.txt 中添加使用到的依赖，则无法自动评测，成绩为零。
- 自动评测脚本仅会加载 classify 和 load_data 函数，请勿修改函数名。
- 训练集和测试集需手动下载解压，并放入当前目录下。

测评环境:
- CPU: Intel Xeon(R) CPU E3-1231 v3 @ 3.40GHz
- OS: Ubuntu 22.04.4 LTS
- Python: 3.10.12
- numpy: 2.1.1
"""


"""
请在这里填写学号和姓名，不填写即成绩无效。
"""
id = "202210423215"
name = "章程鸿·"


import numpy as np
import os
from collections import Counter


def classify(input_vector, dataSet, labels, k=2):
    """
    使用 KNN 算法对输入样本进行分类。

    参数:
            - input_vector (numpy array): 输入待分类的样本（1xN）。
            - dataSet (numpy array): 训练数据集（MxN）。
    - labels (list or numpy array): 训练集对应的标签。
    - k (int): kNN 算法参数，默认值为 2。

    返回:
    - int: 预测的分类标签。
    """
    # 计算马氏距离
    centered_dataSet = dataSet - np.mean(dataSet, axis=0)
    centered_input_vector = input_vector - np.mean(dataSet, axis=0)
    cov_matrix = np.cov(centered_dataSet.T)
    if np.linalg.det(cov_matrix) == 0:
        raise ValueError("协方差矩阵不可逆")
    inv_cov_matrix = np.linalg.inv(cov_matrix)
    mahalanobis_distances = np.sqrt(np.sum(centered_input_vector.dot(inv_cov_matrix) * centered_input_vector, axis=1))

    sorted_indices = mahalanobis_distances.argsort()
    k_nearest_distances = mahalanobis_distances[sorted_indices[:k]]
    k_nearest_labels = labels[sorted_indices[:k]]

    # 计算权重（距离的倒数）
    weights = 1 / k_nearest_distances
    # 归一化权重
    weights /= weights.sum()

    # 计算加权投票
    weighted_votes = np.zeros((10,))
    for label, weight in zip(k_nearest_labels, weights):
        weighted_votes[label] += weight

    return np.argmax(weighted_votes)


def load_dataset(directory):
    """
    加载数据集中的图像，并将其转换为特征向量和标签。

    参数:
    - directory (str): 数据文件夹路径。

    返回:
            - np.array: 特征数据（Mx1024）。
            - np.array: 标签数据（Mx1）。
    """
    feature_list = []
    label_list = []
    for file in os.listdir(directory):
        file_path = os.path.join(directory, file)
        feature_vector = img_to_vector(file_path)
        feature_list.append(feature_vector)
        label_list.append(int(file.split('_')[0]))
    feature_matrix = np.array(feature_list)
    label_array = np.array(label_list)

    # 特征缩放
    feature_matrix = feature_matrix / 255.0
    return feature_matrix, label_array


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。
    """
    vector = np.zeros((1024,))
    with open(filename) as file:
        for i, line in enumerate(file):
            vector[i * 32:i * 32 + 32] = np.array([int(char) for char in line.strip()])
    return vector


if __name__ == "__main__":
    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"
    )
    predicted_label = classify(
        np.array([int(char) for char in test_data]).reshape(1, 1024),
        train_data,
        train_labels,
    )

    print(f"预测的标签: {predicted_label}")