【Basic】Image Segmentation in MATLAB: Using K-means Clustering for Image Segmentation

## 2.1 K-Means Clustering Algorithm Principle

The K-means clustering algorithm is an unsupervised machine learning technique that partitions data points into K clusters. The principle of the algorithm is as follows:

***Initialization:** Randomly select K data points as the initial cluster centers.
***Assignment:** Assign each data point to the cluster center closest to it.
***Update:** Calculate the average of all data points in each cluster and use it as the new cluster center.
***Repeat:** Repeat the assignment and update steps until the cluster centers no longer change or a predefined number of iterations is reached.

Ultimately, the algorithm divides the data points into K clusters, with each cluster consisting of data points closest to its center.

## 2. K-Means Clustering Algorithm

### 2.1 K-Means Clustering Algorithm Principle

The K-means clustering algorithm is an unsupervised learning technique used to partition data points into K clusters. The goal is to find a set of cluster centers such that the sum of distances from each data point to its nearest cluster center is minimized.

**Algorithm Principle:**

1. **Initialization:** Randomly select K data points as the initial cluster centers.
2. **Assignment:** Assign each data point to the nearest cluster center.
3. **Update:** Recalculate the center of each cluster as the average of all data points within it.
4. **Repeat:** Repeat steps 2 and 3 until the cluster centers no longer change or the maximum number of iterations is reached.

### 2.2 K-Means Clustering Algorithm Steps

**Steps:**

1. **Determine the K value:** Decide the number of clusters to divide into.
2. **Initialize cluster centers:** Randomly select K data points as the initial cluster centers.
3. **Calculate distances:** Compute the distance from each data point to each cluster center.
4. **Assign clusters:** Assign each data point to the nearest cluster center.
5. **Update cluster centers:** Recalculate the center of each cluster as the average of all its data points.
6. **Repeat:** Repeat steps 3-5 until the cluster centers no longer change or the maximum number of iterations is reached.

**Code Block:**

import numpy as np
import matplotlib.pyplot as plt

# Data points
data = np.array([[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]])

# K value
K = 2

# Initialize cluster centers
centroids = np.array([[1, 2], [9, 10]])

# Distance calculation function
def distance(x, y):
    return np.linalg.norm(x - y)

# Cluster assignment function
def assign_cluster(data, centroids):
    clusters = np.zeros(len(data))
    for i in range(len(data)):
        distances = [distance(data[i], centroid) for centroid in centroids]
        clusters[i] = np.argmin(distances)
    return clusters

# Cluster center update function
def update_centroids(data, clusters, K):
    new_centroids = np.zeros((K, 2))
    for i in range(K):
        cluster_data = data[clusters == i]
        new_centroids[i] = np.mean(cluster_data, axis=0)
    return new_centroids

# Maximum iterations
max_iterations = 10

# Iterate
for i in range(max_iterations):
    clusters = assign_cluster(data, centroids)
    centroids = update_centroids(data, clusters, K)

# Visualization
plt.scatter(data[:, 0], data[:, 1], c=clusters)
plt.scatter(centroids[:, 0], centroids[:, 1], c='r', marker='x')
plt.show()

**Code Logic Analysis:**

***Initialization:** Randomly initialize K cluster centers.
***Distance calculation:** Calculate the Euclidean distance from each data point to each cluster center.
***Cluster assignment:** Assign each data point to the