Mathematical Methods for Data Analysis

Mathematics has been playing an important role in data analysis from the very beginning; for example, Fourier analysis is one of the main tools in the analysis of image and signal data. This course is to introduce some mathematical methods for data analysis. It will cover mathematical formulations and computational methods to exploit specific structures contained in the data. Some special machine learning algorithms are introduced in case studies.

• Vector spaces, metrics and convergence
• Case study: Clustering, k-means, k-medians
• Inner product, Hilbert space
• Case study: Kernel trick, kernel k-means; metrics learning
• Linear functions and differentiation
• Case study: Regression and classification; optimality and gradient descent

• Chapter 1: Introduction to mathematical analysis tools for data analysis
• Chapter 2: Vector spaces, metics and convergence
• Chapter 3: Inner product, Hilber space
• Chapter 4: Linear functions and differentiation
• Chapter 5: Linear transformations and higher order differentations