add cluster

jiagu/cluster/__init__.py

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+# -*-coding:utf-8-*-
+
+from .kmeans import KMeans
+from .dbscan import DBSCAN
+

jiagu/cluster/base.py

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+# -*-coding:utf-8-*-
+
+import numpy as np
+
+
+def elu_distance(a, b):
+    """计算两点之间的欧氏距离并返回"""
+    dist = np.sqrt(np.sum(np.square(np.array(a) - np.array(b))))
+    return dist
+

jiagu/cluster/dbscan.py

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+# -*-coding:utf-8-*-
+"""
+ * Copyright (C) 2019 OwnThink.
+ *
+ * Name        : dbscan.py - 聚类
+ * Author      : zengbin93 <zeng_bin8888@163.com>
+ * Version     : 0.01
+ * Description : DBSCAN 算法实现
+"""
+
+import random
+import numpy as np
+from collections import OrderedDict
+
+from .base import elu_distance
+
+
+class DBSCAN(object):
+    def __init__(self, eps, min_pts):
+        self.eps = eps
+        self.min_pts = min_pts
+
+    def _find_cores(self, X):
+        """遍历样本集找出所有核心对象"""
+        cores = set()
+        for di in X:
+            if len([dj for dj in X if elu_distance(di, dj) <= self.eps]) >= self.min_pts:
+                cores.add(di)
+        return cores
+
+    def train(self, X):
+        """输入数据，完成 KMeans 聚类
+
+        :param X: list of tuple / np.array
+            输入数据特征，[n_samples, n_features]，如：[[0.36, 0.37], [0.483, 0.312]]
+        :return: OrderedDict
+        """
+        if isinstance(X, np.ndarray):
+            X = [tuple(x) for x in X.tolist()]
+
+        # 确定数据集中的全部核心对象集合
+        cores = self._find_cores(X)
+        not_visit = set(X)
+
+        k = 0
+        clusters = OrderedDict()
+        while len(cores):
+            not_visit_old = not_visit
+            # 随机选取一个核心对象
+            core = list(cores)[random.randint(0, len(cores) - 1)]
+            not_visit = not_visit - set(core)
+
+            # 查找所有密度可达的样本
+            core_deque = [core]
+            while len(core_deque):
+                coreq = core_deque[0]
+                coreq_neighborhood = [di for di in X if elu_distance(di, coreq) <= self.eps]
+
+                # 若coreq为核心对象，则通过求交集方式将其邻域内未被访问过的样本找出
+                if len(coreq_neighborhood) >= self.min_pts:
+                    intersection = not_visit & set(coreq_neighborhood)
+                    core_deque += list(intersection)
+                    not_visit = not_visit - intersection
+
+                core_deque.remove(coreq)
+            cluster_k = not_visit_old - not_visit
+            cores = cores - cluster_k
+            clusters[k] = list(cluster_k)
+            k += 1
+
+        return clusters

jiagu/cluster/kmeans.py

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+# -*-coding:utf-8-*-
+"""
+ * Copyright (C) 2019 OwnThink.
+ *
+ * Name        : kmeans.py - 聚类
+ * Author      : zengbin93 <zeng_bin8888@163.com>
+ * Version     : 0.01
+ * Description : KMeans 算法实现
+"""
+
+import numpy as np
+import random
+from collections import OrderedDict
+
+from .base import elu_distance
+
+
+class KMeans(object):
+    def __init__(self, k, max_iter=100):
+        """
+
+        :param k: int
+            类簇数量，如 k=5
+        :param max_iter: int
+            最大迭代次数，避免不收敛的情况出现导致无法退出循环，默认值为 max_iter=100
+        """
+        self.k = k
+        self.max_iter = max_iter
+
+        self.centroids = None   # list
+        self.clusters = None    # OrderedDict
+
+    def _update_clusters(self, dataset):
+        """
+        对dataset中的每个点item, 计算item与centroids中k个中心的距离
+        根据最小距离将item加入相应的簇中并返回簇类结果cluster
+        """
+        clusters = OrderedDict()
+        centroids = self.centroids
+
+        k = len(centroids)
+        for item in dataset:
+            a = item
+            flag = -1
+            min_dist = float("inf")
+
+            for i in range(k):
+                b = centroids[i]
+                dist = elu_distance(a, b)
+                if dist < min_dist:
+                    min_dist = dist
+                    flag = i
+
+            if flag not in clusters.keys():
+                clusters[flag] = []
+            clusters[flag].append(item)
+
+        self.clusters = clusters
+
+    def _update_centroids(self):
+        """根据簇类结果重新计算每个簇的中心，更新 centroids"""
+        centroids = []
+        for key in self.clusters.keys():
+            centroid = np.mean(self.clusters[key], axis=0)
+            centroids.append(centroid)
+        self.centroids = centroids
+
+    def _quadratic_sum(self):
+        """计算簇内样本与各自中心的距离，累计求和。
+
+        sum_dist刻画簇内样本相似度, sum_dist越小则簇内样本相似度越高
+        计算均方误差，该均方误差刻画了簇内样本相似度
+        将簇类中各个点与质心的距离累计求和
+        """
+        centroids = self.centroids
+        clusters = self.clusters
+
+        sum_dist = 0.0
+        for key in clusters.keys():
+            a = centroids[key]
+            dist = 0.0
+            for item in clusters[key]:
+                b = item
+                dist += elu_distance(a, b)
+            sum_dist += dist
+        return sum_dist
+
+    def train(self, X):
+        """输入数据，完成 KMeans 聚类
+
+        :param X: list of list / np.array
+            输入数据特征，[n_samples, n_features]，如：[[0.36, 0.37], [0.483, 0.312]]
+        :return: OrderedDict
+        """
+        if isinstance(X, np.ndarray):
+            X = X.tolist()
+
+        # 随机选择 k 个 example 作为初始类簇均值向量
+        self.centroids = random.sample(X, self.k)
+
+        self._update_clusters(X)
+        current_dist = self._quadratic_sum()
+        old_dist = 0
+        iter_i = 0
+
+        while abs(current_dist - old_dist) >= 0.00001:
+            self._update_centroids()
+            self._update_clusters(X)
+            old_dist = current_dist
+            current_dist = self._quadratic_sum()
+
+            iter_i += 1
+            if iter_i > self.max_iter:
+                break
+
+        return self.clusters
+
+

test/test_cluster.py

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+# -*-coding:utf-8-*-
+import unittest
+import numpy as np
+import matplotlib.pyplot as plt
+from pprint import pprint
+
+from jiagu.cluster.kmeans import KMeans
+from jiagu.cluster.dbscan import DBSCAN
+
+
+def load_dataset():
+    # 西瓜数据集4.0  编号，密度，含糖率
+    # 数据集来源：《机器学习》第九章 周志华教授
+    data = '''
+    1,0.697,0.460,
+    2,0.774,0.376,
+    3,0.634,0.264,
+    4,0.608,0.318,
+    5,0.556,0.215,
+    6,0.403,0.237,
+    7,0.481,0.149,
+    8,0.437,0.211,
+    9,0.666,0.091,
+    10,0.243,0.267,
+    11,0.245,0.057,
+    12,0.343,0.099,
+    13,0.639,0.161,
+    14,0.657,0.198,
+    15,0.360,0.370,
+    16,0.593,0.042,
+    17,0.719,0.103,
+    18,0.359,0.188,
+    19,0.339,0.241,
+    20,0.282,0.257,
+    21,0.748,0.232,
+    22,0.714,0.346,
+    23,0.483,0.312,
+    24,0.478,0.437,
+    25,0.525,0.369,
+    26,0.751,0.489,
+    27,0.532,0.472,
+    28,0.473,0.376,
+    29,0.725,0.445,
+    30,0.446,0.459'''
+
+    data_ = data.strip().split(',')
+    dataset = [(float(data_[i]), float(data_[i + 1])) for i in range(1, len(data_) - 1, 3)]
+    return np.array(dataset)
+
+
+def show_dataset():
+    dataset = load_dataset()
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    ax.scatter(dataset[:, 0], dataset[:, 1])
+    plt.title("Dataset")
+    plt.show()
+
+
+class TestCluster(unittest.TestCase):
+    def test_a_kmeans(self):
+        print("=" * 68, '\n')
+        print("test k-means ... ")
+        X = load_dataset()
+        print("shape of X: ", X.shape)
+
+        k = 4
+        km = KMeans(k=k, max_iter=100)
+        clusters = km.train(X)
+        pprint(clusters)
+        self.assertEqual(len(clusters), k)
+        pprint({k: len(v) for k, v in clusters.items()})
+        print("\n\n")
+
+    def test_b_dbscan(self):
+        print("=" * 68, '\n')
+        print("test dbscan ... ")
+        X = load_dataset()
+        ds = DBSCAN(eps=0.11, min_pts=5)
+        clusters = ds.train(X)
+        pprint(clusters)
+        self.assertTrue(len(clusters) < len(X))
+        # self.assertEqual(len(clusters), 6)
+        pprint({k: len(v) for k, v in clusters.items()})
+
+
+if __name__ == '__main__':
+    unittest.main()