CIS 5150, Spring 2024

Some Course Notes and Slides

Notes

  • ** Basics of Algebra and Analysis (manuscript) (html)
  • ** Linear Algebra and Optimization With Applications to Machine Learning, Vol. I and II (html)
  • ** Linear Algebra and Optimization With Applications to Machine Learning, Vol. I. (pdf)
  • ** Linear Algebra and Optimization With Applications to Machine Learning, Vol. II. (pdf)
  • ** Applications of Scientific Computation; EAS205, Some Notes (pdf)
  • ** Solving the Elastic Net and Lasso Regression Problems (pdf)
  • ** Spectral Theory of Unsigned and Signed Graphs
    Applications to Graph Clustering: a Survey (pdf)
  • ** Logarithms and Square Roots of Real Matrices (pdf)
  • ** Chapters 1, 2, 3, 4 on Mathematical Reasoning and Logic, functions, relations, from "Discrete Mathematics, Second Edition:" (pdf)
  • ** Chapter 5 from GMA (2nd edition); Basics of Projective Geometry (pdf)
  • ** Chapter 9 from GMA (2nd edition); The Quaternions and the Spaces S^3, SU(2), SO(3), and RP^3 (pdf)
  • ** Chapter 10 from GMA (2nd edition); Dirichlet-Voronoi Diagrams and Delaunay Triangulations (pdf)

    Slides

  • ** Some Matlab code
  • bezier-parabola (m)
  • bezier-cubic (m)
  • bezier function, degree 2 (m)
  • bezier function, degree 3 (m)
  • Lemniscate (m)
  • Solving a triangular system by backsubstitution, v1 (m)
  • Solving a triangular system by backsubstitution, v2 (m)
  • Solving a triangular system; some examples (m)
  • Computes a point on a curve using de Casteljau's algorithm (m)
  • Linear (affine!) interpolation (m)
  • To display the construction of a point using de Casteljau's algorithm (m)
  • Running de Casteljau's algorithm; examples (m)
  • The Steiner Roman surface (m)

  • ** Example of a Learning Problem   (slides, pdf)
  • ** Motivations: Fitting Data   (slides, pdf)
  • ** Problems, Questions and Motivations; Vector Spaces, Bases, Linear Maps, The dual space   (slides, pdf)
  • ** Matrices and Linear Maps   (slides, pdf)
  • ** Haar Bases and Haar Wavelets   (slides, pdf)
  • ** Direct Sums, Affine Maps   (slides, pdf)
  • ** Determinants and Applications   (slides, pdf)
  • ** Determinants "a la Michael Artin"   (slides, pdf)
  • ** Gaussian, LU, and Choleski Decompositions   (slides, pdf)
  • ** Normed spaces and matrix norms; condition number of a matrix   (slides, pdf)
  • ** Iterative Methods for Solving Linear Systems   (slides, pdf)
  • ** The Dual Space, Duality   (slides, pdf)
  • ** Euclidean Spaces   (slides, pdf)
  • ** QR-Decomposition for Arbitrary Matrices   (slides, pdf)
  • ** Hermitian Spaces   (slides, pdf)
  • ** Eigenvectors and Eigenvalues   (slides, pdf)
  • ** Spectral Theorems in Euclidean and Hermitian Spaces   (slides, pdf)
  • ** Introduction to the Finite Elements Method   (slides, pdf)
  • ** Singular Value Decomposition (SVD) and Polar Form   (slides, pdf)
  • ** Applications of SVD and Pseudo-Inverses   (slides, pdf)
  • ** Quadratic Optimization Problems   (slides, pdf)

  • ** Basic Notions of Topology   (slides, pdf)
  • ** Review of Multivariate Calculus   (slides, pdf)
  • ** Derivatives (Directional, Total), Series   (slides, pdf)
  • ** Extrema of real-valued functions   (slides, pdf)
  • ** Lagrange Multipliers (Equality constraints)   (slides, pdf)
  • ** Introduction to Nonlinear Optimization   (slides, pdf)
  • ** Convex Sets and Convex Functions   (slides, pdf)
  • ** Active Constraints and Qualified Constaints   (slides, pdf)
  • ** The Karush-Kuhn-Tucker Conditions   (slides, pdf)
  • ** Lagrangian Duality   (slides, pdf)
  • ** Weak and Strong Duality   (slides, pdf)
  • ** Handling Equality Constraints Explicitly   (slides, pdf)
  • ** Hard Margin Support Vector Machine: Version I   (slides, pdf)
  • ** Hard Margin Support Vector Machine: Version II   (slides, pdf)
  • ** Dual of the Hard Margin Support Vector Machine   (slides, pdf)
  • ** Introduction to Soft Margin Support Vector Machines   (slides, pdf)
  • ** Soft Margin Support Vector Machines   (slides, pdf)
  • ** Classification of Data Points: Terminology   (slides, pdf)
  • ** Classification of the Data Points in Terms of nu   (slides, pdf)
  • ** Solving SVM Using ADMM   (slides, pdf)
  • ** Ridge Regression   (slides, pdf)
  • ** Ridge Regression: Learning an Affine Function   (slides, pdf)
  • ** Lasso Regression   (slides, pdf)
  • ** Lasso Regression: Learning an Affine Function   (slides, pdf)
  • ** Elastic Net Regression   (slides, pdf)

    Slides on the spectral theory of unsigned and signed graphs
    with applications to graph clustering

  • ** Graphs and graph Laplacians   (slides, pdf)
  • ** Spectral Graph Drawing   (slides, pdf)
  • ** Graph Clustering using Normalized Cuts; 2 clusters   (slides, pdf)
  • ** Graph Clustering using Normalized Cuts; K clusters   (slides, pdf)
  • ** Graph Clustering using Normalized Cuts; Finding a discrete solution   (slides, pdf)
  • ** Signed Graphs ;   (slides, pdf)
  • ** Graph Clustering Using Ratio Cuts   (slides, pdf)
  • ** Appendix; Rayleigh Ratios, Rayleigh-Ritz Theorem, Courant-Fischer Theorem   (slides, pdf)

    Other slides

  • ** Some slides for CIS7000. Groups and Group Actions   (slides, pdf)
  • ** Some slides for CIS7000. Group Representations   (slides, pdf)
  • ** Some slides for CIS7000. Fourier Analysis on a Locally Compact Abelian Group   (slides, pdf)
  • ** Some slides for CIS7000. Analysis on Compact Groups and Representations
    Tensor Products of Representations and "Hom" Representations
    Fourier Transform and Cotransform   (slides, pdf)
  • ** Some slides for CIS7000. Matrix Representations of SL(2), SU(2) and SO(3)   (slides, pdf)
  • ** Some slides for CIS7000. Induced Representations and G-bundles   (slides, pdf)
  • ** Some slides for CIS7000. Steerable Families   (slides, pdf)
  • ** Some slides for CIS7000. Feature Fields and
    Promoting the Fourier transform from H to R^d \rtimes H (slides, pdf)
  • ** Some slides for CIS7000. Correlation of the Space of Feature Fields
    Equivariant Correlation G-Kernels when G = R^d \rtimes H
    Equivariant Correlation G-Kernels, General Case
    Equivariant Correlation X_{in}-Kernels   (slides, pdf)

  • ** Rotation Logic (talk given at the Robotics Symposium, Sept. 27, 2013) (slides, pdf)
  • ** Some Mathematical Methods in Machine Learning (Two lectures (each 1h 25mn)
    given in Paris at ENS Cachan, Sept. 8, 2020) (slides, pdf)
  • ** Dirichlet-Voronoi Diagrams and Delaunay Triangulations (pdf)
  • ** The Quaternions and the Spaces S^3, SU(2), SO(3), and RP^3 (pdf)

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    published by:

    Jean Gallier