Dimensionality Reduction in Data Science

This book provides a practical and fairly comprehensive  review of Data Science through the vision of Dimensionality Education as well as  tackling problems based on observations and data collected in the real world.  State-of-the-art solutions from statistics, computer science and mathematical results are explained from the point of view of a practitioner in a domain science such as biology, cyber security, chemistry, sports science and more. Quantitative and qualitative assessments methods are described  to implement and validate the solutions back in the real world where the problems originated.  The ability to generate, gather and store volumes of data in the order of tera- and exo-bytes daily has far outpaced the ability to derive useful information with available computational resources for many domains. This book focuses on data science and problem definition, data cleansing, feature selection and extraction, statistical, geometric, information-theoretic, biomolecular and machine learning methods for dimensionality reduction of big datasets and problem solving, as well as a comparative assessment of solutions in a real-world setting.This book targets professionals working within this related field with at least an undergraduate degree in any science area, particularly quantitative. Readers should be able to follow examples in this book that introduce each method or technique. These motivating examples are followed by precise definitions of the technical concepts required and presentation of the results in general situations. These concepts require a degree of abstraction that can be followed by re-interpreting concepts like in the original example(s). Finally, each section closes with solutions to the original problem(s) afforded by these techniques, perhaps in various ways to compare and contrast dis/advantages to other solutions.