Advances in Data Science

Description

This volume highlights recent advances in data science, including image processing and enhancement on large data, shape analysis and geometry processing in 2D/3D, exploration and understanding of neural networks, and extensions to atypical data types such as social and biological signals. The contributions are based on discussions from two workshops under Association for Women in Mathematics (AWM), namely the second Women in Data Science and Mathematics (WiSDM) Research Collaboration Workshop that took place between July 29 and August 2, 2019 at the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, Rhode Island, and the third Women in Shape (WiSh) Research Collaboration Workshop that took place between July 16 and 20, 2018 at Trier University in Robert-Schuman-Haus, Trier, Germany. These submissions, seeded by working groups at the conference, form a valuable source for readers who are interested in ideas and methods developed in interdisciplinary research fields. The book features ideas, methods, and tools developed through a broad range of domains, ranging from theoretical analysis on graph neural networks to applications in health science. It also presents original results tackling real-world problems that often involve complex data analysis on large multi-modal data sources. Preface Project Descriptions Chapter Summary Acknowledgment Contents Part I Image Processing Two-stage Geometric Information Guided Image Reconstruction 1 Introduction 1.1 Background 2 Review of Shearlet Transform 3 Proposed Model and Algorithm 3.1 Stage I: TV-L1-L2 Model 3.2 Stage II: wTV-L1-L2 Model 4 Convergence Analysis 5 Numerical Examples 5.1 Example 1 5.2 Example 2 5.3 Example 3 6 Conclusion and Remarks References Image Edge Sharpening via Heaviside Substitution and Structure Recovery 1 Introduction 2 The Proposed Edge Sharpening Method 2.1 Heaviside Function 2.2 1D Heaviside Function Substitution 2.3 2D Image Extension 3 Structure Recovery 4 Results and Discussions 4.1 Application to Image Super-Resolution 4.1.1 Parameter Issues 4.1.2 Discussions on Different Initial High-Resolution Images 4.1.3 Results with Large Upscaling Factors 4.1.4 Limitations 4.2 Application to Image Deblurring 4.3 Application to Edge Sharpening 5 Conclusions References Two-Step Blind Deconvolution of UPC-A Barcode Images 1 Introduction 2 Our Approach 2.1 Kernel Estimation 2.2 Image Deblurring 3 Convergence Analysis 4 Experiment 4.1 Synthetic Data Experiment 4.2 Real Data Experiment 4.3 Empirical Verification 5 Conclusions References Part II Shape and Geometry An Anisotropic Local Method for Boundary Detection in Images 1 Introduction 1.1 Related Work 2 Anisotropic Locally Adaptive Discriminant Analysis 2.1 Visualizing ALADA 2.2 Maximum Likelihood Estimation p-Value 3 Results 3.1 Berkeley Benchmark Images 3.2 Real Data 4 Conclusions References Towards Learning Geometric Shape Parts 1 Motivation 2 Background Fundamentals 2.1 Blum Medial Axis 2.1.1 Weighted Extended Distance Function 2.1.2 Defining a Clean Skeleton 2.1.3 Bézier Curve Approximation 2.2 Convolutional Neural Networks for Regression 3 A Canonical Parametric Medial Axis 3.1 Canonical Ordering of Linked Medial Branches 3.1.1 WEDF for Canonical Linked Medial Branches 3.2 Extracting a Stable Parametric Medial Axis 3.2.1 Clean Skeletons and a Minimal Skeletal Representation 3.2.2 Reducing Dimension Variability in the Medial Axis: Bézier Fit 4 Learning a Partial Parametric Medial Axis Using CNN 4.1 A Partial Representation of the Shape 4.2 Constructing the Neural Network 5 Results 5.1 General Shape: 1 Branch Model 5.2 Adding a Connected Branch: 2 Branches Model 5.3 Learning Shape Details: 5 Branch Model 6 Discussion and Future Work References Machine Learning in LiDAR 3D Point Clouds 1 Introduction 2 The Data 3 Feature Engineering: Nearest Neighbor Matrix 4 Machine Learning Frameworks 4.1 Dimension Reduction 5 Classification Experiments 6 Summary and Future Research Directions References Part III Machine Learning Fitting Small Piece-Wise Linear Neural Network Models to Interpolate Data Sets 1 Introduction 2 Paper Overview 3 Related Work 4 An Example: Xor Is Not Interpolated by a One-LayerFunction 5 Two Layer One Weight Models 2L1W 5.1 Generic, Strictly Generic and Non-generic Weights 5.2 Definition of a Two Layer One Weight Model 2L1W 5.3 Sequential Variation 6 Two Additional Models 6.1 The Two Layer Sum Model: 2LS 6.2 The Three Layer Binary Model: BIN 7 Summary and Research Directions Appendix: Results on Example 2D Data Sets Appendix: Results on Example 2D Data Sets Description of Sequential Variation Results Description of Model Results Description of Model Results Model Results for the Xor Data Set Model Results for the Generalized Xor Data Set Model Results for the Generalized Xor Data Set Model Graphs for the Synthetic Movie Ratings Data Set Model Graphs for the Cluster Data Set Result Figures References On Large-Scale Dynamic Topic Modeling with Nonnegative CP Tensor Decomposition 1 Introduction 2 Overview and Notations 2.1 NMF-Based Nonnegative Tensor Decompositions 2.1.1 NMF for Matrices 2.1.2 Direct NMF and Fixed NMF 2.2 CANDECOMP/PARAFAC (CP) Decomposition and NNCPD 2.2.1 Methodology of CP Decomposition and NNCPD 2.2.2 Existence and Uniqueness of Rank-r NNCPD 3 Comparison of NNCPD and NMF-Based Nonnegative Tensor Decompositions 3.1 Synthetic Dataset Numerical Experiments 3.1.1 Monotonic Dynamic Topic Modeling Dataset Experiment 3.1.2 Complex Dynamic Topic Modeling Dataset Experiment 3.2 The 20 Newsgroups Dataset Numerical Experiments 3.3 Noise Dataset Robustness Numerical Experiments 3.3.1 Construction of the Noise Dataset 3.3.2 Experiment Output on Noise Dataset 4 Conclusion References A Simple Recovery Framework for Signals with Time-Varying Sparse Support 1 Introduction 1.1 Related Work 1.2 Organization 2 Windowed Framework 2.1 Description of Framework 3 Example MMV Algorithms 3.1 MMV Sparse Randomized Kaczmarz with Prior Information 3.2 Weighted L2,1-Minimization 3.3 Weighted MMV Stochastic Gradient Matching Pursuit 4 Experiments 4.1 Experiments with Synthetic Data 4.2 Experiments with Real-World Data 4.3 Computational Cost 5 Conclusion References Part IV Data Analysis Role Detection and Prediction in Dynamic Political Networks 1 Introduction 2 Related Work 3 Methodology 3.1 Role Discovery 3.2 Dynamic Role Prediction 4 Empirical Evaluation 4.1 Data Processing and Graph Creation 4.2 Feature Calculation 4.3 Role Results and Analysis 4.4 Prediction and Validation Results 5 Conclusion and Future Work References Classifying Sleep States Using Persistent Homology and Markov Chains: A Pilot Study 1 Introduction 2 Sleep State Analysis Using Persistent Homology 2.1 Background 2.1.1 Persistent Homology 2.1.2 Time Series Analysis 2.2 Results 3 Visualizing Sleep Patterns of Eight OSA Patients 4 Conclusion and Future Research Appendix References A Survey of Statistical Learning Techniques as Applied to Inexpensive Pediatric Obstructive Sleep Apnea Data 1 Introduction 2 Pediatric Obstructive Sleep Apnea and Data 2.1 Survey Data 2.2 Craniofacial Data 2.3 Cleaning Data 3 Data Exploration 3.1 Correlation Networks 3.2 Mapper Algorithm 3.3 Singular Value Decomposition 4 Statistical Learning Methods 4.1 Non-Bayesian Supervised Learning 4.2 Bayesian Classifiers 4.3 Unsupervised Learning 4.3.1 Density-Based Spatial Clustering of Applications with Noise (DBSCAN) 4.3.2 Cut-Cluster-Classify (CCC) 4.3.3 Spectral Clustering 4.3.4 Continuous k-Nearest Neighbour Approach (CkNN) 4.3.5 Distance Metrics and Thresholding Density Using qk 5 Results 5.1 Results for Survey Data 5.2 Results for Craniofacial Data 5.2.1 Results: CF Distributions 5.2.2 Results: Classification with Craniofacial Data 5.3 Results for Combined Survey and Craniofacial Data 6 Conclusion and Future Research Appendix References Nonparametric Estimation of Blood Alcohol Concentration from Transdermal Alcohol Measurements Using Alcohol Biosensor Devices 1 Introduction 1.1 Alcohol Biosensor Devices 2 Overview 3 Methods 3.1 Partial Differential Equation Model Simulation 3.1.1 Model Discretization 3.1.2 Simulation of Population Data 3.2 Nonparametric Maximum Likelihood Estimator 3.2.1 Nonparametric Estimation Schema 3.2.2 Reduction to Finite Support 3.3 Nonparametric Adaptive Grid Algorithm 3.3.1 Consistency and Convergence of the NPAG Algorithm 4 Results of the Synthetic Data Experiments 5 Conclusions Appendix References Appendix The Third WiSh Workshop Participants and Affiliations at the Time of the Workshop The Second WiSDM Workshop Participants and Affiliations at the Time of the Workshop