In the present era of data deluge, massive amounts of data are constantly harvested from diverse information sources in various domains, ranging from science and technology to business and telecommunications. Petabytes of high-dimensional data from multimodal imaging systems, social media, recommender systems, and large-scale research experiments, all require sophisticated solutions to information representation, dimensionality-reduction, and data analysis. In response to these Big Data challenges, this course will present the basic signal processing and machine learning tools, which enable to sense, represent, recover, and process high-dimensional data from low-dimensional features or measurements. The context of the course is sketched below:
- Dimensionality Reduction: Principle Component Analysis, Singular Value Decomposition, Feature extraction.
- Dictionary Learning: Classical alternating optimization methods, such as K-SVD.
- Compressed Sensing and Data Recovery: Greedy approximation algorithms, convex optimization algorithms.
- Supervised learning: Regression methods, classification methods, Support Vector Machines, AdaBoost, Naive Bayes.
- Data mining: k-Nearest Neighbors, PageRank.
- Unsupervised learning: Data clustering methods, the K-means algorithm, Expectation Maximization.
- Overview of data mining applications: context-based image retrieval, video data mining.