IST - Applications of Linear Algebra in Machine Learning and Data Science (2026)

Speakers and Syllabus

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Prof. K. N. Raghavan
Professor, Krea University

6

1.Foundations of Linear Algebra for Data Science (Linear Algebra Recap)
This section covers the essential concepts of linear algebra, emphasizing those most relevant to data science. It will serve as a refresher and delve deeper into topics crucial for advanced applications.

        ◦ Vector spaces, subspaces, and linear transformations.
        ◦ Matrices, determinants, and eigenvalues/eigenvectors.
        ◦ Matrix decompositions (SVD, QR, etc.) and their applications.
        ◦ Norms, inner products, and orthogonality.
        ◦ Applications to systems of linear equations and least squares problems.
Prof. Neeldhara Misra
Associate Professor, IIT Gandhinagar		 12

2.Dimensionality Reduction and Linear Models 
This section combines techniques for reducing the dimensionality of high-dimensional data with the study of fundamental linear models in machine learning.

Dimensionality Reduction & Feature Extraction:

  • Principal Component Analysis (PCA).
  • Linear Discriminant Analysis (LDA).
  • Non-negative Matrix Factorization (NMF) and Independent Component Analysis (ICA).
  • Applications in image processing, signal processing, and data visualization.

 

Linear Models for Machine Learning:

  • Linear regression (ordinary least squares, ridge regression, lasso).
  • Logistic regression and support vector machines (SVMs).
  • Regularization techniques and optimization algorithms (e.g., gradient descent).

 

 
Prof. Palash Dey
Assistant Professor at IIT Kharagpur		 9

3.Advanced Topics and Emerging Applications
This section covers more advanced topics that build upon the foundational sections, including the role of linear algebra in modern deep learning and large-scale data analysis.

  • Tensor decompositions and their applications.
  •  Randomized linear algebra for large-scale data.
  •  Applications in recommender systems and natural language processing.
Prof. M. Rajesh Kannan
Associate Professor, IIT Hyderabad		 9

4.Spectral Methods in ML
This section introduces the application of spectral graph theory to clustering and data analysis, a powerful set of techniques in unsupervised learning.

         ◦Graphs, Adjacency matrices, and the Graph Laplacian (standard and normalized).
        ◦ Eigenvalues/eigenvectors of the Laplacian and their connection to graph properties.
        ◦ Graph partitioning problem.
        ◦ Spectral Clustering algorithms and their analysis.
        ◦ Laplacian Eigenmaps and dimensionality reduction.

 

 Course Associates:

  • Pragya Arora (IIT Gandhinagar)
  • Paras Arya (IIT Gandhinagar)
  • Saraswati Nanoti (IIT Gandhinagar)
  • Abhay Jayarajan (IIT Hyderabad)
  • Rahul Roy (IIT Hyderabad).
  • Mr. Mohana Rahul, IIT Hyderabad

Course Associates will assist with tutorial sessions and hands-on labs.

References
    1. Gilbert Strang: Linear Algebra and Learning from Data, Wellesley-Cambridge Press, 2019.
    2. Gene H. Golub and Charles F. Van Loan: Matrix Computations, 4th Edition, Johns Hopkins University Press.
    3. Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong: Mathematics for Machine Learning, Cambridge University Press, 2020.
    4. Trevor Hastie, Robert Tibshirani, and Jerome Friedman: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition, Springer.
    5. Ian Goodfellow, Yoshua Bengio, and Aaron Courville: Deep Learning, MIT Press.
    6. Ulrike von Luxburg: A Tutorial on Spectral Clustering, Statistics and Computing, Vol. 17, No. 4, 2007.
    7. Dan Spielman, Lecture notes on ”Spectral and Algebraic Graph Theory” (2025).
    8. Bojan Mohar, Some applications of Laplace eigenvalues of graphs, Graph symmetry (Montreal, PQ, 1996), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci.,497, 225–275, Kluwer Acad. Publ., Dordrecht, 1997.

Time Table

 

Week -One

 

Date

9.30-11.00

11.00-11.30

11.30-1.00

1.00-2.30

2.30-3.30

3.30-4.00

4.00-5.00

18/05(Mon)

KNR

T

NM

L

KNR,PRA,PA

T

NM,SN,AJ

19/05(Tue)

KNR

T

NM

L

KNR,PRA,PA

T

NM,SN,AJ

20/05(Wed)

KNR

T

NM

L

KNR,PRA,PA

T

NM,SN,AJ

21/05(Thu)

KNR

T

NM

L

KNR,PRA,PA

T

NM,SN,AJ

22/05(Fri)

NM

T

NM

L

NM,PRA,PA

T

NM,SN,AJ

23/05(Sat)

NM

T

NM

L

NM,PRA,PA

T

NM,SN,AJ

 

 

Week-Two

Date

9.30-11.00

11.00-11.30

11.30-1.00

1.00-2.30

2.30-3.30

3.30-4.00

4.00-5.00

25/05(Mon)

PD

T

RK

L

PD,PRA,PA

T

RK,RR,MR

26/05(Tue)

PD

T

RK

L

PD,PRA,PA

T

RK,RR,MR

27/05(Wed)

PD

T

RK

L

PD,PRA,PA

T

RK,RR,MR

28/05(Thu)

PD

T

RK

L

PD,PRA,PA

T

RK,RR,MR

29/05(Fri)

PD

T

RK

L

PD,PRA,PA

T

RK,RR,MR

30/05(Sat)

PD

T

RK

L

PD,PRA,PA

T

RK,RR,MR

 

  • S1 : Section 1 (Foundations of Linear Algebra : Prof. K. N. Raghavan)
  • S2 : Section 2 (Dimensionality Reduction and Linear Models : Prof. Neeldhara Misra)
  • S3 : Section 3 (Advanced Topics : Prof. Palash Dey)
  • S4 : Section 4 (Spectral and Clustering Methods : Prof. M. Rajesh Kannan )
  • Lec : Lecture Session (1.5 hours)
  • Tut: Tutorial/Lab Session (1 hour)
  •  T : Tea
  •  L : Lunch
  •  KNR : Prof. K. N. Raghavan
  •  NM : Prof. Neeldhara Misra
  •  PD : Prof. Palash Dey
  •  RK : Prof. M. Rajesh Kannan
  •  PRA: Pragya Arora
  •  PA : Paras Arya
  •  SN : Saraswati Nanoti
  •  AJ : Abhay Jayarajan
  •  RR : Rahul Roy
  •  MR : Mohanarahul

 

 

 

 

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