Principal component analysis (PCA) is a widely used technique for dimension reduction,
data processing, and feature extraction. The three tasks are particularly useful and important …

Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

The article begins with a review of the main approaches for interpretation the results from
principal component analysis (PCA) during the last 50–60 years. The simple structure …

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional
data, due to their simple geometric interpretations and typically attractive computational …

The paper deals with the estimation of a high dimensional covariance with a conditional
sparsity structure and fast diverging eigenvalues. By assuming a sparse error covariance …

Sparse coding—that is, modelling data vectors as sparse linear combinations of basis
elements—is widely used in machine learning, neuroscience, signal processing, and …

Statistical Foundations of Data Science gives a thorough introduction to commonly used
statistical models, contemporary statistical machine learning techniques and algorithms …

In this paper we survey the primary research, both theoretical and applied, in the area of
robust optimization (RO). Our focus is on the computational attractiveness of RO …

Deep neural networks (DNNs) are computationally/memory-intensive and vulnerable to
adversarial attacks, making them prohibitive in some real-world applications. By converting …

This paper deals with the computational complexity of conditions which guarantee that the
NP-hard problem of finding the sparsest solution to an underdetermined linear system can …