MSc Communications and Signal Processing

1. Introduction of convex sets and convex functions.
2. Illustrate convex optimization problems, including linear programming, quadratic programming, geometric programming, semi-definite programming.
3. Introduce duality theory, including Lagrangian dual function, Lagrange dual problem, weak and strong duality, Interpretation of dual variables, KKT optimality conditions.
4. Illustrate various convex optimization methods and algorithms, such as descent methods, Newton methods, sub-gradient method, interior point method.
5. Provide some applications of convex optimization to signal processing and communications.
6. Introduction to machine learning and optimisation.
7. High-dimensional data representation. Basic multivariate statistical and regression models. Decision tree algorithms and Bayesian learning.
8. Clustering and classification algorithms including SVMs.
9. Introduction to neurons, human visual system and neural networks. Artificial neural networks (feedforward, recurrent) and their learning mechanisms: supervised and unsupervised.
10. Introduction to deep learning neural networks and their implementations.

• To provide a general overview of convex optimization theory and its applications.
•  To introduce various classical convex optimization problems and illustrate how to solve these numerically and analytically. 
• To introduce and practise basic machine learning techniques for multivariate data analysis and engineering applications. 
• To introduce and practise fundamental neural networks and their recent advances, esp. deep learning neural networks and implementations in practical applications.

• Understand the motivation and benefit of using convex optimization and machine learning.
• Establish a good understanding about convex sets and convex functions.
• Recognise typical forms of convex optimizations and their associated optimal solutions.
• Understand fundamental machine learning approaches in problem solving.
• Able to apply machine learning methods in practical data-oriented problems.
• Understand neural networks and basic deep learning networks and their applications.

• To be able to reason about situations arising in the use of optimization and machine learning.
• To be able to design algorithms for obtaining optimal solutions for convex optimization problems.
• To be able to apply problem solving approaches used in machine learning and neural networks in wider engineering tasks.
• To be able to design a machine learning or neural network algorithm or system for a given learning problem.

• To be able to apply convex optimization to practical communication systems.
• To be able to use machine learning tools or libraries in practical applications.

• Develop the capability for mathematical and algorithmic formulation.
• Develop wider problem-solving and data analytical skills in engineering.
• Scientific report writing and presentation.

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Stephen Boyd and Lieven Vandenberghe, Convex Optimization Cambridge University Press.

Chong-Yung Chi and Wei-Chiang Li , Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications, CRC Press.

Richard O. Duda, Peter E. Hart, and David G. Stork, Pattern Classification, 2nd ed. Willey Interscience Publication.

Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer.

Ian Goodfellow, Toshua Bengio, and Aaron Courville, Deep Learning, MIT Press.