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WEEK 12 CS2004 – Bin Packing and Data Clustering

Algorithms and Their Applications - CS2004 (2024-2025)

1. Introduction to Topics Covered

  • Overview of topics studied so far:
  • Concepts of Computation and Algorithms
  • Comparative analysis of algorithms
  • Mathematical foundations including Big-Oh notation
  • Computational Complexity
  • Data structures
  • Sorting Algorithms
  • Graph traversal algorithms
  • Heuristic Search techniques
  • Hill Climbing and Simulated Annealing methods
  • Parameter Optimization Applications
  • Evolutionary Computation
  • Swarm Intelligence

2. Focus of Current Lecture

  • We will delve into specific algorithms:
  • Bin Packing (brief overview)
  • Data Clustering (in-depth analysis)

3. Bin Packing Introduction

  • Definition: The bin packing problem involves the task of fitting a number of items into the smallest number of bins (containers), each with a specified capacity.
  • Example: Given items of sizes (x1, x2, \ldots, x_n) that need to fit into bins of capacity (c).
  • If items are sized 5, 1, 4, 2, 3 and capacity is 6, the goal is to minimize the number of bins used.

4. Applications of Bin Packing

  • Numerous applications exist, including but not limited to:
  • TV/radio advertisements
  • CD or tape compilations
  • Organizing files in recycle bins.

5. Bin Packing Algorithms

  • Combinatorial Problem: Many methods can address bin packing challenges.
  • First-Fit Decreasing (FFD) Algorithm:
  • Sorts items in descending order before packing.
  • Uses empty bins, numbered sequentially.
  • Each item is placed in the first bin that can accommodate it, starting with the largest item first.
  • Empty bins at the end of packing are ignored.
Example of First-Fit Decreasing
  • Items: 3, 1, 5, 6, 7, 8, 3, 2, 9, 1
  • Bin capacity: 10
  • Sorted order for packing: 9, 8, 7, 6, 5, 3, 3, 2, 1, 1

6. Introduction to Data Clustering

  • Definition: Data clustering is the process of grouping objects into sets (clusters) based on their characteristics/features.
  • Goal: Objects within the same cluster share common traits, typically based on similarity or proximity, while objects in different clusters are dissimilar.
  • Assumption: Each set is mutually exclusive; an object cannot belong to more than one cluster.

7. How Clustering Works

  • The approach involves:
  • Measuring similarities among various data rows based on their feature values (e.g. represented in a feature vector).
  • Clusters can be represented visually if only a few features are considered.

8. Importance of Clustering

  • Utility: Understanding relationships among objects aids in data analysis:
  • Simplifies complex data modeling.
  • Serves as a pre-processing step to further data exploration.
  • Can provide insights into unknown properties of objects.

9. Real-World Applications of Data Clustering

  • Retail Marketing: Clustering assists in identifying household segments based on factors such as:
  • Income levels
  • Household size
  • Occupation
  • Geography
  • Sports Science: Used to analyze players based on performance metrics (points, rebounds, assists, etc.).
  • Health Insurance: Groups households based on medical needs and demographics (doctor visits, chronic conditions, etc.).

10. Clustering Representation

  • Each cluster can be represented by a vector (e.g., C = {1, 2, 3, 1, 2}) denoting membership of objects (rows) to clusters.

11. Measuring Data Similarity

  • Clustering methods rely on distance metrics to determine how closely related data points are:
  • Examples include Euclidean, Correlation, Pearson, Spearman, and Manhattan distances.

12. Evaluating Cluster Worth

  • Assessing the effectiveness of clustering results involves:
  • Selecting appropriate metrics (e.g., density and separation of clusters).
  • Utilizing methods such as the K-Means algorithm, which computes the sum of squared distances within clusters.

13. Challenges in Clustering

  • Determining the correct number of clusters is often difficult:
  • Some methods require predefined clusters, while others find clusters dynamically.

14. Clustering Methods Overview

  • Various approaches exist:
  • Centroid-based (e.g., K-Means)
  • Hierarchical
  • Density-based
  • Distribution-based
  • Optimization algorithms (like Hill Climbing).

15. K-Means Clustering Method

  • Requires prior knowledge of the number of clusters (k).
  • Steps:
  1. Assign objects randomly to clusters.
  2. Compute the new centers of each cluster.
  3. Allocate objects to the nearest center and minimize error.
  4. Repeat until stable centers or a specified iteration is reached.

16. Validating Clustering Results

  • After clustering, verification involves:
  • Checking if the chosen method is effective.
  • Confirming results by comparing with established knowledge.

17. Kappa Metric for Comparing Clusters

  • Kappa metric evaluates agreements between different clustering results:
  • It ranges from -1 to 1, indicating the level of agreement from very poor (>0) to very good (=1).

18. Next Steps in Learning

  • Upcoming topics include Traveling Salesperson Problem and practical lab sessions focusing on K-Means clustering.