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Linear Algebra

Linear Algebra

Steve Brunton via YouTube Direct link

A Compressed Overview of Sparsity

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A Compressed Overview of Sparsity

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Linear Algebra

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  1. 1 A Compressed Overview of Sparsity
  2. 2 2016 AIAA AVIATION Forum: Flow Control - Steve Brunton
  3. 3 Singular Value Decomposition (SVD): Overview
  4. 4 Singular Value Decomposition (SVD): Mathematical Overview
  5. 5 Singular Value Decomposition (SVD): Matrix Approximation
  6. 6 Singular Value Decomposition (SVD): Dominant Correlations
  7. 7 The Frobenius Norm for Matrices
  8. 8 SVD Method of Snapshots
  9. 9 Matrix Completion and the Netflix Prize
  10. 10 Unitary Transformations
  11. 11 Linear Systems of Equations, Least Squares Regression, Pseudoinverse
  12. 12 Least Squares Regression and the SVD
  13. 13 Linear Systems of Equations
  14. 14 Linear Regression
  15. 15 Principal Component Analysis (PCA)
  16. 16 SVD and Optimal Truncation
  17. 17 SVD: Image Compression [Matlab]
  18. 18 SVD: Image Compression [Python]
  19. 19 Unitary Transformations and the SVD [Matlab]
  20. 20 Unitary Transformations and the SVD [Python]
  21. 21 Linear Regression 1 [Matlab]
  22. 22 Linear Regression 2 [Matlab]
  23. 23 Linear Regression 1 [Python]
  24. 24 Linear Regression 2 [Python]
  25. 25 Linear Regression 3 [Python]
  26. 26 SVD and Alignment: A Cautionary Tale
  27. 27 Principal Component Analysis (PCA) [Matlab]
  28. 28 Principal Component Analysis (PCA) 1 [Python]
  29. 29 Principal Component Analysis (PCA) 2 [Python]
  30. 30 SVD: Eigenfaces 1 [Matlab]
  31. 31 SVD: Eigenfaces 2 [Matlab]
  32. 32 SVD: Eigenfaces 3 [Matlab]
  33. 33 SVD: Eigenfaces 4 [Matlab]
  34. 34 SVD: Eigen Action Heros [Matlab]
  35. 35 SVD: Eigenfaces 3 [Python]
  36. 36 SVD: Eigenfaces 2 [Python]
  37. 37 SVD: Eigenfaces 1 [Python]
  38. 38 SVD: Optimal Truncation [Matlab]
  39. 39 SVD: Optimal Truncation [Python]
  40. 40 SVD: Importance of Alignment [Python]
  41. 41 SVD: Importance of Alignment [Matlab]
  42. 42 Randomized SVD Code [Matlab]
  43. 43 Randomized SVD Code [Python]
  44. 44 Randomized Singular Value Decomposition (SVD)
  45. 45 Randomized SVD: Power Iterations and Oversampling
  46. 46 Fourier Analysis: Overview
  47. 47 Fourier Series: Part 1
  48. 48 Fourier Series: Part 2
  49. 49 Inner Products in Hilbert Space
  50. 50 Complex Fourier Series
  51. 51 Fourier Series [Matlab]
  52. 52 Fourier Series [Python]
  53. 53 Fourier Series and Gibbs Phenomena [Matlab]
  54. 54 Fourier Series and Gibbs Phenomena [Python]
  55. 55 The Fourier Transform
  56. 56 The Fourier Transform and Derivatives
  57. 57 The Fourier Transform and Convolution Integrals
  58. 58 Parseval's Theorem
  59. 59 Solving the Heat Equation with the Fourier Transform
  60. 60 The Discrete Fourier Transform (DFT)
  61. 61 Computing the DFT Matrix
  62. 62 The Fast Fourier Transform (FFT)
  63. 63 The Fast Fourier Transform Algorithm
  64. 64 Denoising Data with FFT [Matlab]
  65. 65 Denoising Data with FFT [Python]
  66. 66 Computing Derivatives with FFT [Matlab]
  67. 67 Computing Derivatives with FFT [Python]
  68. 68 Solving PDEs with the FFT [Matlab]
  69. 69 Solving PDEs with the FFT [Python]
  70. 70 Why images are compressible: The Vastness of Image Space
  71. 71 What is Sparsity?
  72. 72 Sparsity and Parsimonious Models: Everything should be made as simple as possible, but no simpler
  73. 73 Compressed Sensing: Overview
  74. 74 Compressed Sensing: Mathematical Formulation
  75. 75 Compressed Sensing: When It Works
  76. 76 Sparsity and the L1 Norm
  77. 77 Solving PDEs with the FFT, Part 2 [Matlab]
  78. 78 Solving PDEs with the FFT, Part 2 [Python]
  79. 79 The Spectrogram and the Gabor Transform
  80. 80 Spectrogram Examples [Matlab]
  81. 81 Spectrogram Examples [Python]
  82. 82 Uncertainty Principles and the Fourier Transform
  83. 83 Wavelets and Multiresolution Analysis
  84. 84 Image Compression and the FFT
  85. 85 Sparse Sensor Placement Optimization for Reconstruction
  86. 86 Sparse Sensor Placement Optimization for Classification
  87. 87 Sparse Representation (for classification) with examples!
  88. 88 Image Compression with Wavelets (Examples in Python)
  89. 89 Image Compression with the FFT (Examples in Matlab)
  90. 90 Image Compression and Wavelets (Examples in Matlab)
  91. 91 Image Compression and the FFT (Examples in Python)
  92. 92 Beating Nyquist with Compressed Sensing, part 2
  93. 93 Underdetermined systems and compressed sensing [Matlab]
  94. 94 Underdetermined systems and compressed sensing [Python]
  95. 95 Beating Nyquist with Compressed Sensing
  96. 96 Robust Regression with the L1 Norm
  97. 97 Robust Regression with the L1 Norm [Matlab]
  98. 98 Robust Regression with the L1 Norm [Python]
  99. 99 Beating Nyquist with Compressed Sensing, in Python
  100. 100 PySINDy: A Python Library for Model Discovery
  101. 101 The Laplace Transform: A Generalized Fourier Transform
  102. 102 Laplace Transforms and Differential Equations
  103. 103 Laplace Transform Examples
  104. 104 Sparsity and Compression: An Overview
  105. 105 Data-Driven Resolvent Analysis

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