數據挖掘——聚類算法

一、問題描述

分別用k均值、合併聚類和DBSCAN聚類算法對鳶尾花數據集聚類，並檢驗結果是否與數據標籤一致。

二、實驗目的

學習聚類算法。

三、實驗內容

1. 分別用k均值、合併聚類和DBSCAN聚類算法對鳶尾花數據集聚類，並檢驗結果是否與數據標籤一致。

2. 數據導入

3.主要代碼

四、實驗結果及分析

原始數據

1. k均值model = KMeans(n_clusters = 3,max_iter = 100)

2. 合併聚類agg = AgglomerativeClustering(n_clusters=4)

3. DBSCAN聚類算法dbscan = db.DBSCAN(eps=0.2, min_sample = 3)

五、完整代碼

agglomerative_clustering.py

import numpy as np
import heapq

class AgglomerativeClustering:
    def __init__(self, n_clusters = 1):
        self.k = n_clusters
            
    def fit_transform(self, X):
        m, n = X.shape
        C, centers = {}, {}
        assignments = np.zeros(m)
        for id in range(m):
            C[id] = [id]
            centers[id] = X[id]
            assignments[id] = id 
        H = []
        for i in range(m):
            for j in range(i+1, m):
                d = np.linalg.norm(X[i] - X[j], 2)
                heapq.heappush(H, (d, [i, j]))     
        new_id = m 
        while len(C) > self.k:
            distance, [id1, id2] = heapq.heappop(H)
            if id1 not in C or id2 not in C:
                continue
            C[new_id] = C[id1] + C[id2]
            for i in C[new_id]:
                assignments[i] = new_id
            del C[id1], C[id2], centers[id1], centers[id2]
            new_center = sum(X[C[new_id]]) / len(C[new_id])
            for id in centers:
                center = centers[id]
                d = np.linalg.norm(new_center - center, 2)
                heapq.heappush(H, (d, [id, new_id]))
            centers[new_id] = new_center
            new_id += 1
        return np.array(list(centers.values())), assignments
    

dbscan3.py

import numpy as np

class DBSCAN:
    def __init__(self, eps = 0.5, min_sample = 5):
        self.eps = eps
        self.min_sample = min_sample
            
    def get_neighbors(self, X, i):
        m = len(X)
        distances = [np.linalg.norm(X[i] - X[j], 2) for j in range(m)]
        neighbors_i = [j for j in range(m) if distances[j] < self.eps]
        return neighbors_i
    
    def grow_cluster(self, X, i, neighbors_i, id):
        self.assignments[i] = id
        Q = neighbors_i
        t = 0
        while t < len(Q):
            j = Q[t]
            t += 1
            if self.assignments[j] == 0:
                self.assignments[j] = id
                neighbors_j = self.get_neighbors(X, j)
                if len(neighbors_j) > self.min_sample:
                    Q += neighbors_j
               
    def fit_transform(self, X):
        self.assignments = np.zeros(len(X))
        id = 1
        for i in range(len(X)):
            if self.assignments[i] != 0:
                continue
            neighbors_i = self.get_neighbors(X, i)
            if len(neighbors_i) > self.min_sample:
                self.grow_cluster(X, i, neighbors_i, id)
                id += 1
        return self.assignments

flower.py

from sklearn import datasets
import numpy as np
import matplotlib.pyplot as plt
from week15.k_means import KMeans
from week15.agglomerative_clustering import AgglomerativeClustering
import week15.dbscan3 as db

from sklearn.model_selection import train_test_split
iris = datasets.load_iris()
X = iris["data"][:, (0, 1)]
y = 2* (iris["target"] == 0).astype(np.int)-1
X_train, X_test, y_train, y_test = train_test_split(X ,y ,test_size=0.4,random_state=5)

plt.figure(-1)
plt.scatter(X[:, 0],X[:, 1])

#k均值
model = KMeans(n_clusters = 3,max_iter = 100)
centers, assignments = model.fit_transform(X)
plt.figure(0)
plt.scatter(X[:, 0], X[:, 1], c = assignments)
plt.scatter(np.array(centers)[:,0],np.array(centers)[:,1],c = 'r',s=80)
plt.show()

#合併聚類
agg = AgglomerativeClustering(n_clusters=4)
agg_center, agg_assignments = agg.fit_transform(X)
plt.figure(0)
plt.scatter(X[:, 0], X[:, 1])
plt.scatter(agg_center[:, 0], agg_center[:, 1], c='b',marker='*',s = 300)

#DBSCAN聚類算法
dbscan = db.DBSCAN(eps=0.2, min_sample = 3)
db_assignments = dbscan.fit_transform(X)
plt.figure(0)
plt.scatter(X[:, 0], X[:, 1], c = db_assignments)

plt.show()

k_means.py

import numpy as np

class KMeans:
    def __init__(self, n_clusters = 1, max_iter = 50, random_state=0):
        self.k = n_clusters
        self.max_iter = max_iter
        np.random.seed(random_state)
         
    def assign_to_centers(self, centers, X):
        assignments = []
        for i in range(len(X)):
            distances = [np.linalg.norm(X[i] - centers[j], 2) for j in range(self.k)] 
            assignments.append(np.argmin(distances))
        return assignments 
    
    def adjust_centers(self, assignments, X):
        new_centers = []
        for j in range(self.k):
            cluster_j = [X[i] for i in range(len(X)) if assignments[i] == j]
            new_centers.append(np.mean(cluster_j, axis=0))
        return new_centers  
            
    def fit_transform(self, X):
        idx = np.random.randint(0, len(X), self.k)
        centers = [X[i] for i in idx]
        for iter in range(self.max_iter):
            assignments = self.assign_to_centers(centers, X)
            centers = self.adjust_centers(assignments, X)
        return np.array(centers), np.array(assignments)