Sylvain Lespinats - Nonlinear Dimensionality Reduction Techniques: A Data Structure Preservation Approach

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It is my honor to write this foreword. I had the chance to work with Drs. Benot Colange, Sylvain Lespinats, Jakko Peltonen, and Denys Dutykh on ClassNeRV, an original and efficient way to compute supervised dimensionality reduction (DR). I have known Sylvain for years as we explored different aspects of DR interpretation (CheckViz) and proposed an early version of ClassNeRV called ClassiMap. In short, we designed a stress function that directs distortions where they have the least impact on the class structure. We wanted to translate this approach into the probabilistic framework of stochastic neighbor embedding techniques (tSNE, NeRV) with the help of Jaakko, one of NeRVs authors. Jaakko was instrumental to interpret the equations of ClassiMap in the new framework, but we got stuck with the constraints of the KulbackLeibler-based formulation of the stress function. Fortunately, Sylvain and Denys engaged Benot for a PhD to develop new tools to analyze energy-related data. Benot solved our problem in no time, coming up with a very elegant and unexpected solution. I let you discover it in Chap. of this book which outlines the core of Benots PhD project. Long story short, it is my real pleasure to introduce this work.

At a time where we face challenging health, financial, and environmental crises, data are collected, stored, and processed at a larger and larger scale in a tentative to better model these phenomena and tackle these problems. Alas, the human brain did not scale up at the same pace, and we bear the same cognitive power as our millennial ancestors. The consequence is these data need to be drastically summarized for us to understand.

Mathematicians defined many summary statistics, from basic numerical values like quantiles to more advanced statistical models (nonlinear regression, deep neural networks, generative, adversarial, and causal models) and more recently topological ones based on MorseSmale theory and persistent homology, etc. Despite this undoubtful progress on the modelization side, end-users of these approaches still trust more their naked eyes than a few or even many numerical indicators to detect patterns these models could have missed. And they are right, some patterns escape detection by the most advanced of the models, or are detected but not explicitly encoded, pushing the need for more interpretable and even explainable models that let the user know what patterns the model discovered. In short, we will not avoid the need for data visualization and visual analytics, and multidimensional projections and related techniques are among these approaches which can preserve quite a broad range of similarity-based patterns difficult to detect with more automatic models.

I have grown my expertise for 20 years in both these fields, machine learning for clustering, dimension reduction, and topological data analysis on the one hand, and visual analytics for guiding the interpretation of these models, on the other hand, seeking techniques that would bridge the gap between high-dimensional data and human understanding. Therefore, I am well-versed in these domains to appreciate the depth and breadth of the present work and its foreseeable impact.

By reading this book you will touch upon some of the toughest challenges faced by data scientists and domain experts when it comes to explore and analyze high-dimensional continuous data in search of meaningful patterns. The authors propose original approaches to estimate local data intrinsic dimensionality (TIDLE); to compute meaningful maps that account for that information (ASKI) and better preserve the structure of the classes (ClassNeRV, ClassJSE); to help interpret the visual patterns these maps display (MING) avoiding misuse or disuse of the map; to evaluate maps quality with new class-aware indicators; and to map out-of-sample data onto an existing layout. Technical details and context are given with all the necessary explanations for non-experts to enrich their skill set. The proposed techniques are applied to various analytic problems in smart-building, photovoltaics, and batteries that will inspire the practitioner to try out the same in their own domain. At last, students and researchers will find an excellent introduction to the topic and food for thought to further their own research projects. Finally, I hope you will enjoy the reading as I did.

Dr. Hab. Michal Aupetit

Senior Research Scientist at

Qatar Computing Research Institute

Hamad Bin Khalifa University

maupetit@hbku.edu.qa

https://www.hbku.edu.qa/en/staff/dr-michael-aupetit/

A teacher can never truly teach unless he is still learning himself. A lamp can never light another lamp unless it continues to burn its own flame. The teacher who has come to the end of his subject, who has no living traffic with his knowledge but merely repeats his lessons to his students, can only load their minds; he cannot quicken them. minds; he cannot quicken them.