Nonlinear Dimensionality Reduction Techniques

This book proposes tools for analysis of multidimensional and metric data, by establishing a state-of-the-art of the existing solutions and developing new ones. It mainly focuses on visual exploration of these data by a human analyst, relying on a 2D or 3D scatter plot display obtained through Dimensionality Reduction (DR). Performing diagnosis of an energy system requires identifying relations between observed monitoring variables and the associated internal state of the system. Dimensionality reduction, which allows to represent visually a multidimensional dataset, constitutes a promising tool to help domain experts to analyse these relations. This book reviews existing techniques for visual data exploration and dimensionality reduction, and proposes new solutions to challenges in that field. In order to perform diagnosis of energy systems, domain experts need to establish relations between the possible states of a given system and the measurement of a set of monitoring variables.
Classical dimensionality reduction techniques such as tSNE and Isomap are presented, as well as the new unsupervised technique ASKI and the supervised methods ClassNeRV and ClassJSE. A new approach, MING for local map quality evaluation, is also introduced. These methods are then applied to the representation of expert-designed fault indicators for smart-buildings, I-V curves for photovoltaic systems and acoustic signals for Li-ion batteries.