Module I: Dimension Reduction

This module provides a comprehensive framework for analyzing complex data by combining linear algebra with statistical theory. It covers Spectral Decomposition and Singular Value Decomposition (SVD), covariance and geometric projections onto different subspaces. The core focus is Principal Component Analysis (PCA), a method to simplify large datasets by identifying dominant patterns that explain the most variation, with applications in image processing.

TAs: Parth Gupte, Pramath Haritz
Schedule
Date & Time Tuesday-Thursday; From 2.30 pm to 4.00 pm
Classroom B308 (December 9, 16, 18, 23, 30 and January 1), EE Department, IISc
Duration December 9, 2025 - January 1, 2026
Meeting Link Join Class
Announcements
Date Title Description
December 29, 2025 Extra Class Added

There will be an extra class on January 1, 2026.
December 25, 2025 Christmas Break

There will be no class on December 25, 2025.
December 9, 2025 Dataset for experimentation

The dataset used for experimentation is available at this link
Lectures
Resources

A. Blum, J. Hopcroft, and R. Kannan (2020) Foundations of Data Sciences, Cambridge University Press

Open Resource

J. M. Lewis, S. Lakshmivarahan and S. K. Dhall (2006) Dynamic Data Assimilation: a least squares approach, Cambridge University Press

Open Resource

J. Wang (2012) Geometric Structure of High-Dimensional Data and Dimensionality Reduction, Springer

Open Resource

S. Mirniaharikandehei, M. Heidari, G. Danala, S. Lakshmivarahan, and Bin Zheng (2021) Applying a random projection algorithm to optimize machine learning model for predicting peritoneal metastasis in gastric cancer patients using CT images”, Computer Methods and Programs in BIOMEDICINE, Vol 200, 105937

Open Resource

M. Heidari, S. Lakshmivarahan, S. Mirniaharikandehei, G. Danala, Sai Kiran R. Maryada, and Bin Zheng (2021) 'Applying a Random Projection Algorithm to Optimize Machine Learning Model for Breast Lesion Classification,' inIEEE Transactions on Biomedical Engineering, Vol 68, 2764-2775

Open Resource

Heidari, Morteza, et al. "Applying a Random Projection Algorithm to Generate Optimal Feature Vector and Improve Performance of Machine Learning Model for Breast Lesion Classification."

Open Resource

Mirniaharikandehei, Seyedehnafiseh, et al. "Applying a random projection algorithm to optimize machine learning model for predicting peritoneal metastasis in gastric cancer patients using CT images." Computer methods and programs in biomedicine 200 (2021): 105937.

Open Resource

Heidari, Morteza, et al. "Applying a random projection algorithm to optimize machine learning model for breast lesion classification." IEEE Transactions on Biomedical Engineering 68.9 (2021): 2764-2775.

Open Resource