Learn · Applied Linear Algebra for Signal Processing, Data Analytics and Machine Learning
Lecture 52 of 70Week 10
Lec 52- Sparse regression: solution via the Orthogonal Matching Pursuit (OMP) algorithm
Prof. Aditya K. Jagannatham · IIT Kanpur
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- Applied Linear Algebra for Signal Processing, Data Analytics and Machine Learning, IIT Kanpur (at NPTEL)
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All the lectures
- 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: Principal 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