Week 1 : Introduction to vectors, properties and applications
Week 2 : Introduction to matrices and Applications – Circuits, Graphs, Social Networks, Traffic flow
Week 3 : Eigenvalue decomposition, properties and Applications – Principal component analysis (PCA), Eigenfaces for facial recognition
Week 4 : Singular value decomposition (SVD) and Applications – Beamforming in MIMO, Dimensionality reduction, Rate maximization in wireless, MUSIC algorithm
Week 5 : Linear regression and Least Squares. Applications: System identification, linear regression, Support vector machines (SVM), kernel SVMs
Week 6 : Optimal linear MMSE estimation. Applications – MMSE Receiver, Market prediction and forecasting, ARMA models
Week 7 : Data analytics: Recommender systems, user rating prediction, NETFLIX problem
Week 8 : Structure of FFT/ IFFT matrices, properties, System model for OFDM/ SC-FDMA, Signal processing in OFDM systems. Modeling of Dynamical systems – Examples: Robots, Chemical plants. Solution of autonomous linear dynamical systems (LDS), solution of with inputs and outputs
Week 9 : Modeling of Dynamical systems – Examples: Robots, Chemical plants. Solution of autonomous linear dynamical systems (LDS), solution of with inputs and outputs
Week 10 : Unsupervised learning: Centroid based clustering, probabilistic model based clustering and EM algorithm
Week 11 : Linear perceptron. Training a perceptron – stochastic gradient. Compressive sensing, orthogonal matching pursuit for sparse signal estimation
Week 12 : Discrete time Markov chains – Applications: supply chain management, forecasting, Operations research – resource and inventory management.
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