CS-303 Coding Assignment: Diffusion Maps & Optimization

Name: Aditya Prakash Borate
Roll No.: 23110065

This repository contains the Python code implementation for the coding assignment of course CS-303 (March 6, 2025). The assignment covers two main problems:

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Problem 1: Data Visualization using Diffusion Maps

• Goal: Apply Diffusion Maps, a manifold learning technique, for dimensionality reduction and clustering of the UCI Human Activity Recognition (HAR) time-series dataset.
• Tasks:
  • Preprocessing HAR time-series data (segmentation, distance calculation using DTW and Euclidean).
  • Constructing similarity matrices and the Diffusion Kernel (using DTW).
  • Computing the normalized graph Laplacian and embedding data into 2 or 3 diffusion coordinates.
  • Clustering (K-Means/DBSCAN) the embeddings and evaluating performance (ARI, Silhouette Score).
  • Visualizing embeddings and comparing Diffusion Maps with raw features, PCA, and t-SNE.
  • (Explorative) Implementing Multiscale Diffusion Maps and Spectral Clustering.
• Dataset: UCI HAR Dataset

Problem 2: Derivative-Free Optimization Methods

• Goal: Explore and compare the performance of Nelder-Mead (Simplex), Simulated Annealing (SA), and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) on benchmark functions and a machine learning hyperparameter tuning task.
• Tasks:
  • Benchmarking: Optimizing Rosenbrock, Rastrigin, and Ackley functions. Comparing convergence speed and accuracy.
  • Hyperparameter Tuning: Tuning SVM (kernel type, C, gamma) for MNIST classification using the three optimization methods.
  • Analysis: Comparing methods based on test accuracy, function evaluations required, stability over multiple runs, and robustness to initial conditions.
  • Visualization: Plotting optimization trajectories (2D/3D), convergence speed, hyperparameter search landscape, and final SVM performance (e.g., confusion matrix).