math-notes.md

Algorithms and methods

Canonical-correlation analysis

• also called: 'CCA'
• https://en.wikipedia.org/wiki/Canonical_correlation
• implemented in: 'Python sklearn.cross_decomposition.CCA', 'SPSS', 'R cancor'
• domain: 'Multivariate statistics'

Linear discriminant analysis

• also called: 'LDA', 'Normal discriminant analysis', 'NDA, 'Discriminant function analysis'
• https://en.wikipedia.org/wiki/Linear_discriminant_analysis
• related to: 'Principal component analysis'

Minimum Covariance Determinant

• also called: 'MCD'
• paper: 'Least Median of Squares Regression (1984)'
• improvement: 'Fast Minimum Covariance Determinant'

Fast Minimum Covariance Determinant

• also called: 'FAST-MCD'
• paper: 'A Fast Algorithm for the Minimum Covariance Determinant Estimator (1998)'
• implemented in: 'sklearn.covariance.MinCovDet'
• input: 'Normal distributed data'
• robust to outliers
• solves: 'Covariance matrix estimation'

Sample covariance matrix

• https://en.wikipedia.org/wiki/Sample_mean_and_covariance
• sensitive to outliers
• solves: 'Covariance matrix estimation'

Maximum likelihood covariance estimator

• https://en.wikipedia.org/wiki/Estimation_of_covariance_matrices#Maximum-likelihood_estimation_for_the_multivariate_normal_distribution
• implemented in: 'sklearn.covariance.EmpiricalCovariance'
• solves: 'Covariance matrix estimation'

Runge–Kutta methods

• https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
• applications: 'Numerical analysis', 'Ordinary differential equation'
• implemented in: 'scipy.integrate.RK45, scipy.integrate.RK23'

Newton–Cotes formulas

• https://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas
• applications: 'Numerical integration'
• implemented in: 'scipy.integrate.newton_cotes'

Recursive Monotone Stable Quadrature

• http://mathworld.wolfram.com/RecursiveMonotoneStableQuadrature.html

Lin's Method

• http://mathworld.wolfram.com/LinsMethod.html