A literature survey of matrix methods for data science

Abstract

Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial role in enabling and improving data science computations with many new developments being fueled by the availability of data and computing resources. We highlight the role of various different factorizations and the power of changing the representation of the data as well as discussing topics such as randomized algorithms, functions of matrices, and high-dimensional problems. We briefly touch upon the role of techniques from numerical linear algebra used within deep learning.

References in corpus (63)

• Modularity and community structure in networks
• Semi-Supervised Classification with Graph Convolutional Networks
• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• The structure and dynamics of multilayer networks
• Spectral Networks and Locally Connected Networks on Graphs
• Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
• Kernel methods in machine learning
• Deep Convolutional Networks on Graph-Structured Data
• Higher-order organization of complex networks
• Subgraph Centrality in Complex Networks
• Graph Convolutional Matrix Completion
• Deep Learning using Linear Support Vector Machines
• Spectral redemption: clustering sparse networks
• Tensorizing Neural Networks
• Neural Ordinary Differential Equations
• Motifs in Temporal Networks
• Sketching as a Tool for Numerical Linear Algebra
• Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1
• Stable Architectures for Deep Neural Networks
• The Physics of Communicability in Complex Networks
• Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition
• Spectral properties of the Laplacian of multiplex networks
• On Tensors, Sparsity, and Nonnegative Factorizations
• The Why and How of Nonnegative Matrix Factorization
• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
• Randomized Kaczmarz solver for noisy linear systems
• Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
• Randomized Iterative Methods for Linear Systems
• A Practical Randomized CP Tensor Decomposition
• Fast approximation of matrix coherence and statistical leverage
• Improving CUR Matrix Decomposition and the Nyström Approximation via Adaptive Sampling
• Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond
• Hypergraph model of social tagging networks
• Randomized Low-Rank Dynamic Mode Decomposition for Motion Detection
• Fast and Guaranteed Tensor Decomposition via Sketching
• A literature survey of low-rank tensor approximation techniques
• Fast matrix computations for pair-wise and column-wise commute times and Katz scores
• Tensor Networks for Big Data Analytics and Large-Scale Optimization Problems
• Spectral Theory of Unsigned and Signed Graphs. Applications to Graph Clustering: a Survey
• Sparse and Non-Negative BSS for Noisy Data
• Practical Gauss-Newton Optimisation for Deep Learning
• Total variation regularization of the $3$-D gravity inverse problem using a randomized generalized singular value decomposition
• NMF with Sparse Regularizations in Transformed Domains
• Randomized Numerical Linear Algebra: Foundations & Algorithms
• Clustering Signed Networks with the Geometric Mean of Laplacians
• Accurate, Fast and Scalable Kernel Ridge Regression on Parallel and Distributed Systems
• Labeled Graph Generative Adversarial Networks
• The Power Mean Laplacian for Multilayer Graph Clustering
• Limited-memory polynomial methods for large-scale matrix functions
• Higher-order Weighted Graph Convolutional Networks
• NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks
• Layer-Parallel Training of Deep Residual Neural Networks
• Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formats
• Tensorizing Generative Adversarial Nets
• Preconditioned Krylov solvers for kernel regression
• Perturbations of CUR Decompositions
• Fast Approximation of the Gauss-Newton Hessian Matrix for the Multilayer Perceptron
• Refining the Structure of Neural Networks Using Matrix Conditioning
• MUSCO: Multi-Stage Compression of neural networks
• Fast and Accurate Gaussian Kernel Ridge Regression Using Matrix Decompositions for Preconditioning
• Newton Methods for Convolutional Neural Networks
• Semi-Supervised Classification on Non-Sparse Graphs Using Low-Rank Graph Convolutional Networks
• $L^{\gamma }$-PageRank for Semi-Supervised Learning

Cited by in corpus (5)

• Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks
• Orientations and matrix function-based centralities in multiplex network analysis of urban public transport
• Learning in High-Dimensional Feature Spaces Using ANOVA-Based Fast Matrix-Vector Multiplication
• On the rational approximation of Markov functions,with applications to the computation of Markovfunctions of Toeplitz matrices
• Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products