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https://github.com/robcyberlab/image-pixel-clustering

🌀Image Pixel Clustering📏
https://github.com/robcyberlab/image-pixel-clustering

clustering data-science data-visualization dbscan-clustering euclidean-distances hierarchical-clustering image-processing kmeans-clustering machine-learning python single-linkage-clustering

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🌀Image Pixel Clustering📏

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# 🌀Image Pixel Clustering📏



Note: Due to privacy policies, I am not allowed to post the dataset publicly.



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## Table of Contents📋

1. [Overview](#overview)

2. [Clustering Techniques](#clustering-techniques)

3. [Dataset Description](#dataset-description)

4. [Distance Metric](#distance-metric)

5. [Neighbor-Based Clustering](#neighbor-based-clustering)



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## Overview📖

In this laboratory, we will test at least two of the following clustering techniques:

- **k-means**

- **Single Linkage**



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## Clustering Techniques🌀

The focus of this lab is to experiment with and understand the following clustering methods:



1. **k-means**  

   - **Description**: A partition-based clustering algorithm that divides data into `k` clusters, where each data point belongs to the cluster with the nearest mean (centroid).  

   - **Steps**:

     1. Initialize `k` centroids randomly or using specific initialization methods (e.g., k-means++).

     2. Assign each point to the nearest centroid using a distance metric (e.g., Euclidean distance).

     3. Update centroids by calculating the mean position of points in each cluster.

     4. Repeat steps 2-3 until convergence (i.e., centroids stabilize or a maximum number of iterations is reached).

   - **Key Benefits**: Simple and efficient for large datasets.

   - **Limitations**: Sensitive to the initial placement of centroids and may converge to a local minimum.



2. **Single Linkage**  

   - **Description**: A hierarchical clustering method that merges clusters based on the minimum distance between any two points in the clusters.

   - **Steps**:

     1. Treat each data point as an individual cluster.

     2. Compute the distance between all pairs of clusters.

     3. Merge the two clusters with the smallest distance.

     4. Repeat steps 2-3 until all points are in a single cluster or the desired number of clusters is achieved.

   - **Key Feature**: Preserves spatial relationships by linking clusters through their closest members.

   - **Applications**: Effective for identifying elongated or irregularly shaped clusters.

   - **Limitation**: Can be sensitive to outliers, as single linkage focuses only on the nearest points.



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## Dataset Description📊

The dataset consists of images containing black pixels. Each point will have the following features:

- **x-coordinate**

- **y-coordinate**



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## Distance Metric📏

### Euclidean Distance Formula 🌐



The Euclidean distance measures how far apart two points are in a space. For two points on a 2D plane, we can think of them as having **x** and **y** coordinates. To find out how far apart the two points are, we use this formula:



$$

text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

$$



Where:

- **(x₁, y₁)** and **(x₂, y₂)** are the coordinates of the two points.

- **(x₂ - x₁)** is the horizontal distance between the points.

- **(y₂ - y₁)** is the vertical distance between the points.

- Squaring the differences and adding them together gives the total squared distance.

- Finally, we take the square root to get the actual distance between the points.



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### Simple Steps to Calculate:

1. **Subtract** the x-coordinates of the two points: \( x_2 - x_1 \)

2. **Subtract** the y-coordinates of the two points: \( y_2 - y_1 \)

3. **Square** each difference.

4. **Add** the squared differences.

5. **Take the square root** of the sum to get the distance.



This will give you the "straight line" distance between the two points, as if you were measuring with a ruler.



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## Neighbor-Based Clustering🌍

Perform clustering on points from the previous lab, considering only the points in **neighboring "cells"**. Compare the **number of distance function calls** between this approach and classic methods.



This technique leverages spatial locality to reduce computation overhead, providing insights into the efficiency of clustering based on spatial constraints.



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