# CS 531: High Dimensional Data Science

January 2021

The objective is to understand the theoretical foundations of high dimensional data science. This is an elective course offered to undergraduate and postgraduate students.

## Time

• Monday: 5-6.30pm
• Tuesday: 5-6.30pm

## Pre-requisite

1. Algorithm Design
2. Probability - video lectures by Prof.John Tsitsiklis
3. Linear algebra - video lectures by Prof. Gilbert Strang
4. Linear algebra - video lectures by 3blue1brown
5. Single variable Calculus - video lecture by Prof. David Jerison

## Books

1. Foundations of Data science by Blum, Hopcroft and Kannan - online pdf
2. Understanding machine learning by Shai Shalev-Shwartz and Shai Ben-David

• NIL

## Syllabus (not necessarily in this order)

1. High Dimensional Space - The geometry of high dimension, properties of unit ball, Random projects and Johnson-Lindenstrauss Lemma, Separating gaussians
2. Singular Value Decomposition (SVD) - Introduction to SVD, best k-rank approximations, left singular vectors, power method for SVD, applications of SVD.
3. Compressed sensing

We expect every student to follow the highest standards of integrity and academic honesty. Copying/sharing code in exams, homeworks, labs are not allowed. All answers have to be written in your own words. You need to cite any idea you have taken from internet or text book to answer a question. See the IIT Goa policy for academic malpractices.

## Course Schedule

# Date Topic Video Resources Other Resources
Introduction to Linear algebra
1 1/2/21 Vectors: magnitude & direction, linear combination, independence, span, basic, norms, inner product, orthogonal vectors
2 2/2/21 Matrices: column/row vectors, special matrices, matrix addition, matrix times a vector - multiple ways to see this, matrix multiplication, rank of a matrix, special matrices - identity matrix, diagonal matrix, inverse matrix
3 8/2/21 Eigen values and vectors: Computing them, Properties, Special matrices and their eigen values and eigen vectors Youtube PDF
4 9/2/21 Eigen values and vectors: Properties of eigen values and eigen vectors, Diagonalization Youtube PDF
7 22/2/21 Discussion on sample linear algebra questions google drive
10 1/3/21 Singular Value Decomposition (SVD) google drive
11 2/3/21 Best k-rank approximation google drive
12 8/3/21 Principle component analysis google drive
13 10/3/21 Computing eigen values google drive
14 Mid semester exam