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Chapter
Applications of Dimensionality Reduction to the Diagnosis of Energy Systems
This Chapter presents a few examples of applications of dimensionality reduction for the analysis of data towards the diagnosis of energy systems. These systems encompass smart-buildings (Sect. 8.1), photovolt...
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Chapter
Conclusions
Dimensionality Reduction (DR) enables analysts to perform visual exploration of high dimensional data by providing a low-dimensional representation. On its own, it allows, for instance, to identify at a glance...
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Chapter
Intrinsic Dimensionality
High dimensional data are subject to the curse of dimensionality defined in Sect. 2.1, which hinders their analysis. Yet, in practice, data may be assumed to live in a manifold whose dimensionality is lower th...
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Chapter
Map Interpretation
Map interpretation encompasses several tools enhancing the map with additional information. Some allow to study the link between axes of the data and embedding space, as detailed Sect. 4.1, while other perform...
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Chapter
Stress Functions for Supervised Dimensionality Reduction
In the general case, Dimensionality Reduction (DR) is an unsupervised task. Indeed, it does not necessitate data annotations, as opposed to classification for which the desired output must be provided for a tr...
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Chapter
Data Science Context
This chapter positions Dimensionality Reduction (DR) in the broader context of data science, considering both its use as an automated pre-processing tool extracting variable (manifold learning) for other autom...
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Chapter
Map Evaluation
The purpose of map evaluation is to assess the overall quality of a map. Most often, this quality is quantified by scalar indicators allowing to compare several maps. This may be used to select the best of sev...
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Chapter
Stress Functions for Unsupervised Dimensionality Reduction
Dimensionality Reduction (DR) represents a set of points {ξ i} in a high dimensional metric data space D $$\mathcal...
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Chapter
Optimization, Acceleration and Out of Sample Extensions
This chapter details the challenges involved for the optimization of the stress functions presented in the previous chapters, as well as the solutions effectively used (Sect. 7.1). It then addresses the issue ...
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Article
Phylogeny and Sequence Space: A Combined Approach to Analyze the Evolutionary Trajectories of Homologous Proteins. The Case Study of Aminodeoxychorismate Synthase
During the course of evolution, variations of a protein sequence is an ongoing phenomenon however limited by the need to maintain its structural and functional integrity. Deciphering the evolutionary path of a...
