[Machine_Learning]PAM vs K-Means with Outliers

데이터 셋 생성

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs

X, _ = make_blobs(n_samples=50, centers=1, cluster_std=0.5, random_state=42)

#outliers
outliers = np.array([[3, 3], [3, -3], [-3, 3], [-3, -3]])
X_with_outliers = np.vstack([X, outliers])

#data view
plt.scatter(X_with_outliers[:, 0], X_with_outliers[:, 1], c='blue', s=50)
plt.scatter(outliers[:, 0], outliers[:, 1], c='red', s=100, marker='x')
plt.title('Data with Outliers')
plt.xlabel('X1')
plt.ylabel('X2')
plt.grid(True)
plt.savefig('./graph.png')

 

K-means

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans


X, _ = make_blobs(n_samples=50, centers=1, cluster_std=0.5, random_state=42)

#outliers
outliers = np.array([[3, 3], [3, -3], [-3, 3], [-3, -3]])
X_with_outliers = np.vstack([X, outliers])

kmeans = KMeans(n_clusters=1, random_state=42)
kmeans.fit(X_with_outliers)
kmeans_centroid = kmeans.cluster_centers_

#data view
plt.scatter(X_with_outliers[:, 0], X_with_outliers[:, 1], c='blue', s=50)
plt.scatter(outliers[:, 0], outliers[:, 1], c='red', s=100, marker='x')
plt.scatter(kmeans_centroid[:, 0], kmeans_centroid[:, 1], c='green', s=200, marker='*')
plt.title('K-means Centroid with Outliers')
plt.xlabel('X1')
plt.ylabel('X2')
plt.grid(True)
plt.savefig('./graph1.png')
kmeans_centroid

 

PAM

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans


X, _ = make_blobs(n_samples=50, centers=1, cluster_std=0.5, random_state=42)

#outliers
outliers = np.array([[3, 3], [3, -3], [-3, 3], [-3, -3]])
X_with_outliers = np.vstack([X, outliers])

#functions
def manhattan_distance(point1, point2):
    return np.sum(np.abs(np.array(point1) - np.array(point2)))

def assign_to_clusters(data, medoids):
    distances = np.array([[manhattan_distance(dp, medoid) for medoid in medoids] for dp in data])
    return np.argmin(distances, axis=1)

def compute_cost(data, medoids, clusters):
    return np.sum([manhattan_distance(data[i], medoids[clusters[i]]) for i in range(len(data))])

def pam_clustering(data, initial_medoids):
    medoids = initial_medoids
    clusters = assign_to_clusters(data, medoids)
    current_cost = compute_cost(data, medoids, clusters)
    history = [(medoids, clusters, current_cost)]
    
    changed = True
    while changed:
        changed = False
        for data_idx in range(len(data)):
            for medoid_idx in range(len(medoids)):
                if not np.array_equal(data[data_idx], medoids[medoid_idx]):
                    new_medoids = np.array(medoids)
                    new_medoids[medoid_idx] = data[data_idx]
                    new_clusters = assign_to_clusters(data, new_medoids)
                    new_cost = compute_cost(data, new_medoids, new_clusters)
                    if new_cost < current_cost:
                        current_cost = new_cost
                        clusters = new_clusters
                        medoids = np.array(new_medoids)
                        changed = True
        history.append((medoids, clusters, current_cost))
    return history

#pam calc
initial_medoid_pam = np.array([X_with_outliers[0]])
pam_history_pam = pam_clustering(X_with_outliers, initial_medoid_pam)
final_medoid_pam = pam_history_pam[-1][0]

#data view
plt.scatter(X_with_outliers[:, 0], X_with_outliers[:, 1], c='blue', s=50)
plt.scatter(outliers[:, 0], outliers[:, 1], c='red', s=100, marker='x')
plt.scatter(final_medoid_pam[:, 0], final_medoid_pam[:, 1], c='purple', s=200, marker='^')
plt.title('PAM Medoid with Outliers')
plt.xlabel('X1')
plt.ylabel('X2')
plt.grid(True)
plt.savefig('./graph2.png')
final_medoid_pam