Xanthopoulos P., Pardalos P.M., Trafalis T.B. Robust Data Mining

Springer, 2013. — 67 p. — ISBN: 978-1441998774, e-ISBN: 978-1441998781.Data uncertainty is a concept closely related with most real life applications that involve data collection and interpretation. Examples can be found in data acquired with biomedical instruments or other experimental techniques. Integration of robust optimization in the existing data mining techniques aim to create new algorithms resilient to error and noise.
This work encapsulates all the latest applications of robust optimization in data mining. This brief contains an overview of the rapidly growing field of robust data mining research field and presents the most well known machine learning algorithms, their robust counterpart formulations and algorithms for attacking these problems. This brief will appeal to theoreticians and data miners working in this field.A Brief Overview: Artificial Intelligence, Computer Science/Engineering, Optimization, Statistics.
A Brief History of Robustness: Robust Optimization vs Stochastic Programming.
Least Squares Problems.
Original Problem.
Weighted Linear Least Squares.
Computational Aspects of Linear Least Squares:
Cholesky Factorization, QR Factorization, Singular Value Decomposition.
Least Absolute Shrinkage and Selection Operator.
Robust Least Squares: Coupled Uncertainty.
Variations of the Original Problem: Uncoupled Uncertainty.
Principal Component Analysis.
Problem Formulations:
Maximum Variance Approach, Minimum Error Approach.
Robust Principal Component Analysis.
Linear Discriminant Analysis
Original Problem: Generalized Discriminant Analysis.
Robust Discriminant Analysis.
Support Vector Machines.
Original Problem: Alternative Objective Function.
Robust Support Vector Machines.
Feasibility-Approach as an Optimization Problem: Robust Feasibility-Approach and Robust SVM Formulations.A. Optimality Conditions.
B. Dual Norms.