Research in data science /
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| Author / Creator: | Gasparovic, Ellen. |
|---|---|
| Imprint: | Cham : Springer, 2019. |
| Description: | 1 online resource (302 pages) |
| Language: | English |
| Series: | Association for women in mathematics series ; v. 17 Association for Women in Mathematics Series. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11913430 |
Table of Contents:
- Intro; Preface; The Cross-Disciplinary Field of Data Science; Project Descriptions; Contributed Papers; Acknowledgments; Contents; Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors; 1 Introduction; 1.1 Problem Formulation; 2 Related and Existing Work; 2.1 Sparse Randomized Kaczmarz; 2.2 SRK for MMV; 3 Main Results; 3.1 Corrupted MMV; 4 Experiments; 5 Conclusion; References; The Hubness Phenomenon in High-Dimensional Spaces; 1 Introduction; 2 Background and Related Work; 2.1 The Hubness Phenomenon; 2.2 Intrinsic Dimensionality; 3 Datasets
- 3.1 Synthetic Data; 3.1.1 Data in the Global Space; 3.1.2 Data in Subspaces; 3.2 Real Data; 4 Intrinsic Dimensionality via Hubness; 4.1 Skewness vs. Feature Ranking: How to Rank Features?; 4.2 Hubs and Subspaces; 5 Hubs, Density, and Clustering; 5.1 Hubness and Data Density; 5.2 Distances Between Points; 5.2.1 Results on Synthetic Data; 5.2.2 Results on Real Data; 5.2.3 Class Separation of Histograms; 5.3 Hubness and Purity; 5.3.1 Density vs. Purity; 5.4 Hubs and Seed Subspace Samples; 6 Conclusion and Proposed Research Directions; References
- Heuristic Framework for Multiscale Testing of the Multi-Manifold Hypothesis; 1 Introduction; 1.1 Contributions; 1.2 Outline; 2 Related Work; 2.1 Manifold Learning; 2.2 The (Multi- )Manifold Hypothesis; 2.3 Quantitative Rectifiability; 2.4 Stratified Space Construction; 2.5 Intrinsic Dimension; 3 Methodology; 4 Implementation; 4.1 Variance-Based Local Intrinsic Dimension; 4.2 Nearest Neighbors-Based Methods: Local GMST; 4.3 Dyadic Linear Multi-Manifolds; 4.4 Estimating the Sum of Squared Distances Function: SQD; 5 Experimental Validation; 5.1 Use Case: Sphere-Line; 5.2 Use Case: LiDAR Data
- 3.4 Prediction, Feature Selection, and Classification; 4 Statistical Analysis of Survey Data; 4.1 Data Pre-processing; 4.2 Clustering Analysis; 4.3 Identify Important Variables; 5 Conclusion and Future Research; Appendix; References; The ∞-Cophenetic Metric for Phylogenetic Trees As an Interleaving Distance; 1 Introduction; 2 Categorical Structures; 2.1 Categories with a Flow; 2.2 The Interleaving Distance Associated to a Category with a Flow; 2.3 Interleaving Distances on Thin Categories; 2.4 The ∞-Distance on Rn Is an Interleaving Distance; 3 Combinatorial Structures; 3.1 Merge Trees; 3.2 Merge Trees As Posets