使用scikit-learn框架，实现Kmeans、 DBSCAN算法对手写字符、 鸢尾花卉进行识别 *不使用scikit-learn框架，复现Kmeans 、 DBSCAN算法对手写 字符/鸢尾花卉进行识别(更多细节要求见文档）

### 使用scikit-learn框架实现Kmeans和DBSCAN算法 #### 任务描述 使用scikit-learn框架，实现Kmeans和DBSCAN算法对**手写字符**和**鸢尾花卉**进行识别。 #### 实验步骤 1. **导入相关库** ```python from sklearn.datasets import load_digits, load_iris from sklearn.model_selection import train_test_split from sklearn.cluster import KMeans, DBSCAN from sklearn.metrics import adjusted_rand_score ``` 2. **载入数据** - 手写字符数据 ```python digits = load_digits() X_digits, y_digits = digits.data, digits.target ``` - 鸢尾花卉数据 ```python iris = load_iris() X_iris, y_iris = iris.data, iris.target ``` 3. **分割数据集** ```python X_train_digits, X_test_digits, y_train_digits, y_test_digits = train_test_split(X_digits, y_digits, test_size=0.3, random_state=42) X_train_iris, X_test_iris, y_train_iris, y_test_iris = train_test_split(X_iris, y_iris, test_size=0.3, random_state=42) ``` 4. **模型构建** - Kmeans ```python kmeans_digits = KMeans(n_clusters=10, random_state=42).fit(X_train_digits) kmeans_iris = KMeans(n_clusters=3, random_state=42).fit(X_train_iris) ``` - DBSCAN ```python dbscan_digits = DBSCAN(eps=0.3, min_samples=10).fit(X_train_digits) dbscan_iris = DBSCAN(eps=0.3, min_samples=10).fit(X_train_iris) ``` 5. **模型测试** - Kmeans ```python y_pred_kmeans_digits = kmeans_digits.predict(X_test_digits) y_pred_kmeans_iris = kmeans_iris.predict(X_test_iris) print("Kmeans (Digits) Adjusted Rand Score:", adjusted_rand_score(y_test_digits, y_pred_kmeans_digits)) print("Kmeans (Iris) Adjusted Rand Score:", adjusted_rand_score(y_test_iris, y_pred_kmeans_iris)) ``` - DBSCAN ```python y_pred_dbscan_digits = dbscan_digits.fit_predict(X_test_digits) y_pred_dbscan_iris = dbscan_iris.fit_predict(X_test_iris) print("DBSCAN (Digits) Adjusted Rand Score:", adjusted_rand_score(y_test_digits, y_pred_dbscan_digits)) print("DBSCAN (Iris) Adjusted Rand Score:", adjusted_rand_score(y_test_iris, y_pred_dbscan_iris)) ``` ### 不使用scikit-learn框架复现Kmeans和DBSCAN算法 #### 复现Kmeans算法 1. **回顾Kmeans算法流程** - 初始化聚类中心 - 分配每个点到最近的聚类中心 - 更新聚类中心 - 重复分配和更新直到收敛 2. **定义相关变量和数据结构** ```python import numpy as np from scipy.spatial.distance import euclidean_distances def initialize_centers(X, k): return X[np.random.choice(X.shape[0], size=k, replace=False)] def assign_labels(X, centers): distances = euclidean_distances(X, centers) return np.argmin(distances, axis=1) def update_centers(X, labels, k): new_centers = [] for i in range(k): cluster_points = X[labels == i] if len(cluster_points) > 0: new_centers.append(np.mean(cluster_points, axis=0)) else: new_centers.append(X[np.random.randint(0, X.shape[0])]) return np.array(new_centers) def kmeans(X, k, max_iter=100): centers = initialize_centers(X, k) for _ in range(max_iter): labels = assign_labels(X, centers) new_centers = update_centers(X, labels, k) if np.allclose(centers, new_centers): break centers = new_centers return labels, centers ``` 3. **应用复现的Kmeans算法** ```python k = 10 y_pred_kmeans_digits_custom, _ = kmeans(X_test_digits, k) y_pred_kmeans_iris_custom, _ = kmeans(X_test_iris, 3) print("Custom Kmeans (Digits) Adjusted Rand Score:", adjusted_rand_score(y_test_digits, y_pred_kmeans_digits_custom)) print("Custom Kmeans (Iris) Adjusted Rand Score:", adjusted_rand_score(y_test_iris, y_pred_kmeans_iris_custom)) ``` #### 复现DBSCAN算法 1. **回顾DBSCAN算法流程** - 定义邻域 - 标记核心对象 - 形成簇 - 处理边界点和噪声点 2. **定义相关变量和数据结构** ```python def region_query(X, point_idx, eps): neighbors = [] for i, x in enumerate(X): if euclidean_distances([X[point_idx]], [x])[0][0] < eps: neighbors.append(i) return neighbors def expand_cluster(X, labels, point_idx, cluster_id, eps, min_samples): seeds = region_query(X, point_idx, eps) if len(seeds) < min_samples: labels[point_idx] = -1 return False else: labels[point_idx] = cluster_id for seed_idx in seeds: labels[seed_idx] = cluster_id while seeds: current_point = seeds.pop(0) result = region_query(X, current_point, eps) if len(result) >= min_samples: for i in result: if labels[i] in [-1, 0]: if labels[i] == -1: labels[i] = cluster_id if i not in seeds: seeds.append(i) return True def dbscan(X, eps, min_samples): labels = np.zeros(X.shape[0]) cluster_id = 0 for i in range(X.shape[0]): if labels[i] != 0: continue if expand_cluster(X, labels, i, cluster_id + 1, eps, min_samples): cluster_id += 1 return labels ``` 3. **应用复现的DBSCAN算法** ```python eps = 0.3 min_samples = 10 y_pred_dbscan_digits_custom = dbscan(X_test_digits, eps, min_samples) y_pred_dbscan_iris_custom = dbscan(X_test_iris, eps, min_samples) print("Custom DBSCAN (Digits) Adjusted Rand Score:", adjusted_rand_score(y_test_digits, y_pred_dbscan_digits_custom)) print("Custom DBSCAN (Iris) Adjusted Rand Score:", adjusted_rand_score(y_test_iris, y_pred_dbscan_iris_custom)) ``` ### 思考题 1. **对于同一个任务，DBSCAN与Kmeans效果是否存在差异？若存在差异，是什么原因造成的？** - **答案**: 是的，存在差异。Kmeans假设数据是球形分布且需要预先指定聚类数量，而DBSCAN不需要预设聚类数量，能够发现任意形状的簇，并能处理噪声点。因此，在某些非球形或有噪声的数据集中，DBSCAN可能表现更好。 2. **对于聚类任务，什么时候该选择Kmeans，什么时候该选择DBSCAN？** - **答案**: - **Kmeans**: 当数据集中的簇近似为球形且已知簇的数量时，适合使用Kmeans。 - **DBSCAN**: 当数据集中的簇形状复杂、密度不均匀或存在噪声点时，适合使用DBSCAN。 ### 实验报告 1. **实验报告模板** 已经上传云平台。 2. **报告要求** 控制在两页以内。 3. **报告命名规则** 班级_学号_姓名，如“软工1班_1234567_张三.pdf”。 4. **提交方式** 班长/学委收齐后打包发送至邮箱 `[email protected]`。 5. **打包文件命名方式** 班级_实验名称，如“软工1班_聚类”。 6. **提交截止时间** 12月2日19:59分。