DBSCAN算法
网上的资料很多，众多资料给出的算法步骤基本是一样的，无好坏但是有详略之分。
它的优点是可以聚类凹形的数据，这是由它根据距离进行聚类的原理决定的。
个人参考的资料是
风弦鹤：DBSCAN聚类算法——机器学习（理论+图解+python代码）
python实现
个人主要使用numpy和原生python集合类对dbscan类进行了实现，如以下代码所示
#dbscan.py
from os import sep
import numpy as np
import matplotlib.pyplot as plt
class dbscan:
# epsilon/eps : threshold distance
# minpts : least points within a center point
def __init__(self, epsilon:float, minpts:int, debug:bool=False):
self.epsilon = epsilon
self.minpts = minpts
self.debug = debug
self.points = None
def train(self, points:np.ndarray):
#calculate core points out of all points
self.points = points
points_num = np.shape(points)[0]
dist_ndarray_2d = np.ndarray((points_num, points_num), dtype=np.float)
for i in range(points_num):# multithread optimization required
dist_ndarray_2d[i] = np.linalg.norm(points[i] - points, ord=2, axis=1)
in_eps_tfarray_2d = dist_ndarray_2d < self.epsilon
iscore_tfarray_1d = np.sum(in_eps_tfarray_2d, axis=1) > self.minpts
if self.debug:print(in_eps_tfarray_2d, iscore_tfarray_1d)
#clustering from center points
#using index as a point
self.K = 0 #cluster counter
self.gamma = {i for i in range(points_num)}#not visited points
self.omega = {i for i in range(points_num) if iscore_tfarray_1d[i] == True}#core points index
self.clusters = list()
while len(self.omega) > 0:
gamma_old = self.gamma
o = self.omega.pop()
Queue = {o,}
while len(Queue) > 0:
q = Queue.pop()
Nq_indexarray_1d = np.where(in_eps_tfarray_2d[q] == True)[0]
Nq = set(Nq_indexarray_1d.tolist())
if len(Nq) >= self.minpts:
delta = Nq & self.gamma
Queue |= delta
self.gamma = self.gamma.difference(delta)
self.K += 1
Ck = gamma_old.difference(self.gamma)
self.omega = self.omega.difference(Ck)
self.clusters.append(Ck)
print(self.clusters)
def print_clusters(self):
if self.clusters is None : print("[-] empty clusters");return
else:
ind = 0
for cluster in self.clusters:
ind += 1
print("cluster", ind, ":", sep=' ')
print(cluster)
def draw_clusters_2d(self):
if self.clusters is None : print("[-] empty clusters");return
elif np.shape(self.points[0]) != (2,) : print("[-] only support 2 dim points");return
else:
print("[+] drawing by matplotlib")
plt.figure(0)
for cluster in self.clusters:
color = (np.random.random(), np.random.random(), np.random.random())
for point_idx in cluster:
plt.scatter(self.points[point_idx][0], self.points[point_idx][1], c=color)
plt.show()
通过代码创建实例并进行训练。画图验证聚类结果。
其中dbscan_testdata.csv这个文件是由个人另外一个程序《快乐单应》改造的程序做出的，类似一个小丑脸的形状（注：2021年年初流行“小丑竟是我自己”，方便考古使用）。
#main.py
import dbscan
import numpy as np
import pandas as pd
yyz_dbscan_cluster_machine = dbscan.dbscan(10, 2)
ndpoints = pd.read_csv("dbscan_testdata.csv", header=None).values
yyz_dbscan_cluster_machine.train(ndpoints)
yyz_dbscan_cluster_machine.print_clusters()
yyz_dbscan_cluster_machine.draw_clusters_2d()
输出结果如下，这些整数均为点的下标
cluster 1 :
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272,
273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288}
cluster 2 :
{17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 242}
cluster 3 :
{512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532,
533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511}
cluster 4 :
{289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309,
310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405}
cluster 5 :
{406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426,
427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496}
作出图像为：
DBSCAN聚类结果
可以看出，根据算法的参数，该dbscan对象成功对于二维点进行聚类。而且对于凹形数据集也具有聚类效果，不过“小丑的嘴”被分成了两半，这是因为参数epsilon的取值较小，调整后效果如下图所示。
调整epsilon之后的效果
可以看出直观上连接的整体不再被割裂。
总结
- DBSCAN算法是一种效果优秀的聚类算法，可以对凹数据集进行聚类。
- 该算法依赖于集合数据结构，而集合在python中被原生实现，也被几乎所有学习python的人熟悉。而使用C++等语言需要使用STL中的集合数据结构。
- 非计算机科班出身、没有系统学过数据结构与算法写这种数学算法会慢点，需要逐步加深对于数据结构和算法相统一的理解。