VTU Online Class - Course Details

Applied Linear Algebra For Signal Processing, Data Analytics And Machine Learning

PROF ADITYA K. JAGANNATHAM

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What you will learn

Linear Algebra

Machine Learning

This course aims to introduce students to all the basic and advanced concepts in Linear Algebra with a strong focus on applications. Linear Algebra is one of the fundamental tools that has applications in diverse fields such as Machine Learning, Data Analytics, Signal Processing, Wireless Communication, Operations Research, Control and Finance. The course is suitable for all UG/PG students and practicing engineers/ scientists/ managers from the diverse fields mentioned above and interested in learning about the novel cutting edge applications of linear algebra in various fields such as Machine Learning, Data Analytics, Signal Processing, Wireless Communication.

Lec 01- Vector Properties: Addition, Linear Combination, Inner Product, Orthogonality, Norm

Lec 02- Vectors: Unit Norm Vector, Cauchy-Schwarz inequality, Radar Application

Lec 03- Inner Product Application: Beamforming in Wireless Communication Systems

Lec 04- Matrices, Definition, Addition and Multiplication of Matrices

Lec 05- Matrix: Column Space, Linear Independence, Rank of Matrix, Gaussian Elimination

Lec 06- Matrix: Determinant, Inverse Computation, Adjoint, Cofactor Concepts

Lec 07- Applications of Matrices: Solution of System of Linear equations, MIMO Wireless Technology

Lec 08- Applications of Matrices: Electric Circuits, Traffic flows

Lec 09- Applications of Matrices: Graph Theory, Social Networks, Dominance Directed Graph, Influential Node

Lec 10- Null Space of Matrix: Definition, Rank-Nullity Theorem, Application in Electric Circuits

Lec 11- Gram-Schmidt Orthogonalization

Lec 12- Gaussian Random Variable: Definition, Mean, Variance, Multivariate Gaussian, Covariance Matrix

Lec 13- Linear Transformation of Gaussian Random Vectors

Lec 14- Machine Learning Application: Gaussian Classification

Lec 15- Eigenvalue: Definition, Characteristic Equation, Eigenvalue Decomposition

Lec 16- Special Matrices: Rotation and Unitary Matrices, Application: Alamouti Code

Lec 17- Positive Semi-definite (PSD) Matrices: Definition, Properties, Eigenvalue Decomposition

Lec 18- Positive Semidefinite Matrix: Example and Illustration of Eigenvalue Decomposition

Lec 19- Machine Learning Application: Principle Component Analysis (PCA)

Lec 20- Computer Vision Application: Face Recognition, Eigenfaces

Lec 21- Least Squares (LS) Solution, Pseudo-Inverse Concept

Lec 22- Least Squares (LS) via Principle of Orthogonality, Projection Matrix, Properties

Lec 23- Application: Pseudo-Inverse and MIMO Zero Forcing (ZF) Receiver

Lec 24- Wireless Application: Multi-Antenna Channel Estimation

Lec 25- Machine Learning Application: Linear Regression

Lec 26- Computation Mathematics Application: Polynomial Fitting

Lec 27- Least Norm Solution

Lec 28- Wireless Application: Multi-user Beamforming

Lec 29- Singular Value Decomposition (SVD): Definition, Properties, Example

Lec 30- SVD Application in MIMO Wireless Technology: Spatial-Multiplexing and High Data Rates

Lec 31- SVD for MIMO wireless optimization, water-filling algorithm, optimal power allocation

Lec 32- SVD application for Machine Learning: Principal component analysis (PCA)

Lec 33- Multiple signal classification (MUSIC) algorithm: system model

Lec 34- MUSIC algorithm for Direction of Arrival (DoA) estimation

Lec 35- Linear minimum mean square error (LMMSE) principle

Lec 36- LMMSE estimate and error covariance matrix

Lec 37- LMMSE estimation in linear systems

Lec 38- LMMSE application: Wireless channel estimation and example

Lec 39- Time-series prediction via auto-regressive (AR) model

Lec 40- Recommender system: design and rating prediction

Lec 41- Recommender system: Illustration via movie rating prediction example

Lec 42- Fast Fourier transform (FFT) and Inverse fast Fourier transform (IFFT)

Lec 43- IFFT/ FFT application in Orthogonal Frequency Division Multiplexing (OFDM) wireless technology

Lec 44- OFDM system: Circulant matrices and properties

Lec 45- OFDM system model: Transmitter and receiver processing

Lec 46- Single-carrier frequency division for multiple access (SC-FDMA) technology

Lec 47- Linear dynamical systems: definition and solution via matrix exponential

Lec 48- Linear dynamical systems: matrix exponential via SVD

Lec 49- Machine Learning application: Support Vector Machines (SVM)

Lec 50- Support Vector Machines (SVM): Problem formulation via maximum hyperplane separation

Lec 51- Sparse regression: problem formulation and relation to Compressive Sensing (CS)

Lec 52- Sparse regression: solution via the Orthogonal Matching Pursuit (OMP) algorithm

Lec 53- OMP Example for Sparse Regression

Lec 54- Machine Learning Application: Clustering

Lec 55- K-Means Clustering algorithm

Lec 56- Introduction to Stochastic Processes and Markov Chains

Lec 57- Discrete Time Markov Chains and Transition Probability Matrix

Lec 58- Discrete Time Markov Chain Examples

Lec 59- m-STEP Transition Probabilities for Discrete Time Markov Chains

Lec 60- Limiting Behavior of Discrete Time Markov Chains

Lec 61- Least Squares Revisited: Rank Deficient Matrix

Lec 62- Least Squares using SVD

Lec 63- Weighted Least Squares

Lec 64- Weighted Least Squares Example

Lec 65- Woodbury Matrix Identity - Matrix Inversion Lemma

Lec 66- Woodbury Matrix Identity - Proof

Lec 67- Conditional Gaussian Density - Mean

Lec 68- Conditional Gaussian Density - Covariance

Lec 69- Scalar Linear Model for Gaussian Estimation

Lec 70- MMSE Estimate and Covariance for the Scalar Linear Model

Live Session 15-03-2021

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Meet Your Instructor

video

Free

Course Duration

37 h 43 m 6 s
Course Level

Intermediate
Student Enrolled

7
Language

English

This Course Includes

37 h 43 m 6 s Video Lectures
0 Quizzes
0 Assignments
0 Downloadable Resources
Full Lifetime Access
Certificate of Completion