Mathematical Methods for Data Analysis
Master essential mathematical techniques for data analysis, including vector spaces, clustering algorithms, and optimization methods.
Master essential mathematical techniques for data analysis, including vector spaces, clustering algorithms, and optimization methods.
This comprehensive course explores the mathematical foundations crucial for modern data analysis. Students learn advanced mathematical methods including vector spaces, metrics, Hilbert spaces, and linear transformations. The curriculum combines theoretical concepts with practical applications through case studies of machine learning algorithms like k-means clustering and gradient descent. Special emphasis is placed on understanding mathematical formulations and computational methods for exploiting data structures.
Instructors:
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What you'll learn
Master vector spaces, metrics, and convergence concepts
Understand and apply clustering algorithms including k-means
Explore Hilbert spaces and kernel methods in machine learning
Implement regression and classification techniques
Develop optimization skills using gradient descent
Skills you'll gain
This course includes:
PreRecorded video
Graded assignments, Exams
Access on Mobile, Tablet, Desktop
Limited Access access
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There are 5 modules in this course
This graduate-level course explores mathematical methods essential for data analysis, combining theoretical foundations with practical applications. The curriculum covers vector spaces, metrics, convergence, inner products, and Hilbert spaces, along with their applications in machine learning algorithms. Through case studies, students learn to apply these mathematical concepts to real-world problems such as clustering and classification. The course emphasizes both mathematical formulations and computational methods, providing a deep understanding of how mathematical tools can be used to analyze complex data structures.
Introduction to Mathematical Analysis Tools for Data Analysis
Module 1
Vector Spaces, Metrics and Convergence
Module 2
Inner Product, Hilbert Space
Module 3
Linear Functions and Differentiation
Module 4
Linear Transformations and Higher Order Differentiations
Module 5
Fee Structure
Instructor
7 Courses
A Distinguished Scholar in Mathematical Imaging and Data Sciences
Jianfeng Cai serves as Professor in the Department of Mathematics at The Hong Kong University of Science and Technology, where he has established himself as a leading expert in mathematical foundations of imaging and data sciences. After completing his Bachelor's degree from Fudan University and PhD from the Chinese University of Hong Kong in 2007, he worked at several prestigious institutions including the National University of Singapore, UCLA, and University of Iowa before joining HKUST in 2015. His research focuses on theoretical and algorithmic foundations of problems related to information, data, and signals, with particular emphasis on efficient representation, sensing, and analysis of high-dimensional data. His groundbreaking work has garnered over 6,500 citations for a single paper on matrix completion algorithms, while his research has found applications in medical imaging, compressed sensing, signal processing, and machine learning. Named a highly cited researcher in mathematics by Clarivate Analytics in 2017 and 2018, his contributions include pioneering work in image restoration, matrix completion, and blind motion deblurring. Beyond his research, he actively supervises numerous PhD students while maintaining collaborations across multiple disciplines and institutions. His current office is located in Room 3438 at HKUST, where he continues to advance the field of mathematical imaging and data sciences through innovative research and mentorship.
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