python實現基於密度的DBscan 聚類算法(含代碼和數據

DBscan算法是典型的基於密度的聚類算法，假定類別可以通過樣本分佈的緊密程度決定。在DBscan算法中，將樣本密集的一個區域內的點作爲一個cluster，再將相連的clueter聚合爲一個cluster。

• 把所有的數據點區分並標記爲核心點、邊界點和噪音點
  刪除噪音點
• 所有在半徑Eps內的核心點間由邊相連
• 聯通的核心點作爲一組成爲一個cluster
• 分配每一個邊界點到它所落入的核心點半徑範圍內的cluster中

若在某點半徑Eps內有>=minPts個點，則該點就是核心點，
若點不是核心點，但是被其他核心點包括，則爲邊界點
若又不是核心點，又沒被包括，則爲離羣點(噪音點

1. 距離選擇
   DBscan對不同的距離指標總體上效果差異不大，選擇歐式距離作爲距離指標。
2. 參數選擇
   在DBscan中不需要預先決定cluster的數目，算法自動決定聚類的數目，但是需要設定Eps和MinPts兩個參數。在本實驗中對掃描半徑Eps和最小包含點MinPts 的取值如下：
   minPts = [3 4 5 6 7 8 9]
   Eps = [0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29]

dbscan.py

import numpy as np
import data_utils as du

def get_cores_area(data, dist_matrix, eps, minPts):
    core_points = {}
    if dist_matrix is None:
        dist_matrix = pairwise_distance(data, data)

    for i, core_near_dis in enumerate(dist_matrix):
        inner_points = []	# 包含的點
        for j, dis in enumerate(core_near_dis):
            if i == j:
                continue
            if dis < eps:
                inner_points.append(j)
            if len(inner_points) >= minPts:
                core_points[i] = inner_points	# 標記核心點族羣所包含的點
    return core_points

# 計算兩點歐式距離
def pairwise_distance(x, y):
    xx = np.sum(x * x, axis=1, keepdims=True)
    yy = np.sum(y * y, axis=1, keepdims=True)
    xy = np.matmul(x, y.T)
    d = xx + yy.T - 2 * xy
    return d


def dbscan(data, eps, minPts):
    dist_matrix = pairwise_distance(data, data)
    cores_area = get_cores_area(data, dist_matrix, eps, minPts)
    clusters = []
    while len(cores_area) > 0:
        cluster = set()
        visit_set = set()
        core, nears = cores_area.popitem()
        visit_set.add(core)
        visit_set.update(nears)
        while len(visit_set) > 0:
            point = visit_set.pop()
            cluster.add(point)
            if point in cores_area:
                visit_set.update(cores_area.pop(point))
        clusters.append(cluster)

    cluster = np.zeros(len(data))
    for i, c in enumerate(clusters):
        for item in c:
            cluster[item] = i
    return cluster


if __name__ == '__main__':
    # print("----DBscan----")
    data, labels = du.read_data()
    eps_set = np.arange(0.15, 0.3, 0.01).round(2)
    minPts_set = np.arange(3, 10, 1)
    for eps in eps_set:
        for minPts in minPts_set:
            print("eps=", eps, ", minPts=", minPts)
            cluster = dbscan(data, eps, minPts)
            purity, fscore, precision, recall = du.standard(cluster)
            print("purity=", purity, ", F-score=", fscore)
    # print("----------------")

data_utils.py

import pandas as pd
import numpy as np


def read_data():
    pf = pd.read_csv('Frogs_MFCCs.csv', encoding='utf-8')
    data = np.array(pf)
    f_data = data[:, 0:22].astype(np.float)
    return f_data, data[:, 22]

def standard(cluster):
    data, labels = read_data()
    label_set = sorted(list(set(labels)))
    purity = get_purity(cluster, labels, label_set)
    fscore, precision, recall, TP, FP, FN, TN = f_score(cluster, labels)
    return purity, fscore, precision, recall

if __name__ == '__main__':
    f_data, labels = read_data()
    label_set = list(set(labels))

代碼及數據下載：https://download.csdn.net/download/SAM2un/12036441