Machine Learning Academy · Ders

K-Means: Ağırlık Merkezleri, Atama ve Güncelleme Adımları

K-Means: Ağırlık Merkezleri, Atama ve Güncelleme Adımları, CoddyKit'te ücretsiz bir Machine Learning Academy dersidir. Bu, 4 dersinin 1. dersidir. Aşağıdan dersin tamamını ücretsiz okuyabilir, sonra tarayıcıda yerleşik kod editörü ve 7/24 yapay zeka koçu ile uygulamalı olarak pratik yapabilirsin. Bu, Machine Learning Academy öğrenme yolunun bir parçasıdır ve ilerlemeniz web ve CoddyKit uygulaması arasında senkronize olur. Machine Learning Academy kursu toplamda 4 dersten oluşur.

Bu dersin bazı bölümleri henüz çevrilmemiş olup İngilizce olarak gösterilmektedir.

What Is K-Means Clustering?

K-Means is an unsupervised algorithm that partitions n data points into k non-overlapping clusters. Unlike supervised learning, there are no labels — the algorithm discovers structure purely from the feature values. K-Means is fast, scalable, and widely used for customer segmentation, image compression, and anomaly detection.

The Three-Step Algorithm

K-Means repeats three steps until convergence: 1) Initialise — randomly place k centroids in feature space. 2) Assignment — assign every point to the nearest centroid. 3) Update — move each centroid to the mean of its assigned points. The loop stops when assignments no longer change.

Computing Distance to Centroids

In each assignment step, the Euclidean distance from every point to every centroid is computed. A point is assigned to the centroid with the smallest distance. For a point x and centroid c, the squared distance is sum((x_i - c_i)^2). Using squared distance avoids the expensive square-root and gives the same ordering.

import numpy as np

def assign_clusters(X, centroids):
    # X: (n, d), centroids: (k, d)
    distances = np.linalg.norm(X[:, np.newaxis] - centroids, axis=2)  # (n, k)
    return np.argmin(distances, axis=1)  # label for each point

X = np.array([[1, 2], [3, 4], [5, 6], [8, 8]])
centroids = np.array([[2, 2], [7, 7]])
labels = assign_clusters(X, centroids)
print(labels)  # [0, 0, 0, 1]

The Update Step: Recomputing Centroids

After assignment, each centroid is relocated to the arithmetic mean of all points currently in its cluster. If a cluster becomes empty (no points assigned), the centroid is usually re-initialised randomly or removed. This mean-shift minimises the total within-cluster sum of squares (WCSS) — also called inertia.

import numpy as np

def update_centroids(X, labels, k):
    d = X.shape[1]
    new_centroids = np.zeros((k, d))
    for c in range(k):
        points = X[labels == c]
        if len(points) > 0:
            new_centroids[c] = points.mean(axis=0)
    return new_centroids

X = np.array([[1, 2], [3, 4], [5, 6], [8, 8]])
labels = np.array([0, 0, 0, 1])
print(update_centroids(X, labels, k=2))

Tracing Convergence by Hand

Consider four 1D points: 1, 2, 8, 9 and k=2. Init: centroids = [1, 8]. Iter 1 assignment: 1→C0, 2→C0, 8→C1, 9→C1. Iter 1 update: C0=1.5, C1=8.5. Iter 2 assignment: unchanged. Converged in 2 iterations! In higher dimensions convergence may take more steps, but the logic is identical.

Inertia: Measuring Cluster Compactness

Inertia (WCSS) is the sum of squared distances between each point and its cluster centroid. Lower inertia means tighter, more compact clusters. K-Means minimises inertia at each update step, but the algorithm is not guaranteed to find the global minimum — it can get stuck in local optima depending on initialisation.

from sklearn.cluster import KMeans
import numpy as np

X = np.array([[1, 2], [1, 4], [1, 0],
              [10, 2], [10, 4], [10, 0]])

km = KMeans(n_clusters=2, random_state=42)
km.fit(X)

print('Inertia:', km.inertia_)
print('Labels:', km.labels_)
print('Centroids:', km.cluster_centers_)

K-Means++ Initialisation

Random centroid initialisation often leads to slow convergence or poor local optima. K-Means++ (the scikit-learn default via init='k-means++') seeds centroids more intelligently: the first centroid is chosen randomly, and each subsequent centroid is selected with probability proportional to its squared distance from the nearest already-chosen centroid. This spreads starting points and consistently finds better solutions.

from sklearn.cluster import KMeans
import numpy as np

X = np.random.randn(300, 2)

# Default: k-means++ initialisation
km = KMeans(n_clusters=3, init='k-means++', n_init=10, random_state=0)
km.fit(X)
print('Inertia with k-means++:', round(km.inertia_, 2))

# Compare with random init
km_rand = KMeans(n_clusters=3, init='random', n_init=10, random_state=0)
km_rand.fit(X)
print('Inertia with random init:', round(km_rand.inertia_, 2))

Visualising Cluster Assignments

Plotting cluster assignments on a 2D scatter shows the Voronoi partition — the decision boundaries where each point's nearest centroid changes. Plotting centroids as large stars and colouring points by cluster label makes convergence intuitive. This visualisation also reveals when clusters overlap or have unequal sizes.

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

X, _ = make_blobs(n_samples=300, centers=3, cluster_std=0.6, random_state=0)
km = KMeans(n_clusters=3, random_state=0)
labels = km.fit_predict(X)

plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='tab10', s=30)
plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1],
            c='black', s=200, marker='*', label='Centroids')
plt.legend()
plt.title('K-Means Clusters')
plt.show()

Multiple Restarts and n_init

Because K-Means can converge to local optima, scikit-learn runs the algorithm n_init times with different random seeds and keeps the result with the lowest inertia. The default is n_init=10. For small datasets 10 is usually sufficient; for large or tricky datasets you may raise it to 20 or 50. Always check the final inertia against the best-run inertia to diagnose poor convergence.

from sklearn.cluster import KMeans
import numpy as np

X = np.random.randn(500, 5)

km = KMeans(n_clusters=4, n_init=20, random_state=0)
km.fit(X)

print('Best inertia over 20 runs:', round(km.inertia_, 2))
print('Number of iterations until convergence:', km.n_iter_)

Limitations of K-Means

K-Means has several well-known weaknesses: 1) Assumes spherical clusters — it struggles with elongated or crescent shapes. 2) Sensitive to outliers — a distant outlier pulls the centroid away from the true cluster mean. 3) Requires k upfront — you must know or estimate the number of clusters before fitting. 4) Feature scale matters — always standardise features before running K-Means so large-scale variables do not dominate distances.

Running K-Means with scikit-learn

In practice, using sklearn.cluster.KMeans is the standard approach. Key parameters: n_clusters (k), init (default 'k-means++'), n_init, max_iter (default 300), and random_state. After fitting, km.labels_ contains cluster assignments, km.cluster_centers_ holds centroid positions, and km.inertia_ reports WCSS.

from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_iris

X, _ = load_iris(return_X_y=True)

scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

km = KMeans(n_clusters=3, random_state=42)
km.fit(X_scaled)

print('Cluster sizes:', {i: (km.labels_ == i).sum() for i in range(3)})
print('Inertia:', round(km.inertia_, 2))

Quick Check

Test your understanding of K-Means clustering concepts from this lesson.

Lesson Recap

In this lesson you learned: K-Means iterates assignment and update steps until cluster memberships stabilise, inertia (WCSS) measures compactness and is minimised by each update, and K-Means++ initialisation and multiple restarts help avoid poor local optima. Next up we explore how to choose the right value of k using the elbow method and silhouette score.

Sıkça Sorulan Sorular

“K-Means: Ağırlık Merkezleri, Atama ve Güncelleme Adımları” dersi ücretsiz mi?

Evet — “K-Means: Ağırlık Merkezleri, Atama ve Güncelleme Adımları” dersin tüm metni burada web'de ücretsiz olarak okunabilir. Etkileşimli olarak pratik yapmak (yerleşik kod editörü ve 7/24 yapay zeka koçu) ve Machine Learning Academy kursunun geri kalanını açmak için CoddyKit PRO'ya yükselt. Machine Learning Academy kursu toplamda 4 dersten oluşur.

“K-Means: Ağırlık Merkezleri, Atama ve Güncelleme Adımları” dersinde ne öğreneceğim?

K-Means algoritmasının üç yinelemesini elle izleyecek, noktaları en yakın ağırlık merkezlerine atayacak, ağırlık merkezlerini yeniden hesaplayacak ve 2B saçılım grafiğinde yakınsamayı gözlemleyeceksi… Machine Learning Academy ile uygulamalı kodu tarayıcıda doğrudan çalıştırarak pratik yaparsın ve 7/24 yapay zeka koçu dersi çalışırken sorularını yanıtlar.

Machine Learning Academy öğrenmeye başlamak için deneyim gerekli mi?

Önceden deneyim gerekmez. CoddyKit'te Machine Learning Academy, başlangıçtan ileri seviyeye kadar yapılandırıldığı için buradan başlayabilir veya başından başlayıp kendi hızında ilerleme yapabilirsin. Bu, 4 dersinin 1. dersidir.

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Bu Machine Learning Academy dersinde kod yazıp çalıştırabilir miyim?

Evet. Her Machine Learning Academy dersi yerleşik bir kod editörü içerir, bu sayede tarayıcıda gerçek kod yazıp çalıştırabilir ve anlık yapay zeka geri bildirimi alırsın — yerel kurulum gerekli değildir.

Bu kursun tüm dersleri

K-Means: Ağırlık Merkezleri, Atama ve Güncelleme Adımları
K Seçimi: Dirsek Yöntemi ve Siluet Skoru
DBSCAN: Çekirdek Noktalar, Sınır Noktaları ve Gürültü
Müşteri Segmentasyonu için Kümeleme: Baştan Sona Örnek

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