He Wang Northeastern

Math4570

Matrix Methods in Data Analysis and Machine Learning

  • Instructor: He Wang

he.wang@northeastern.edu

 

  • The purpose is page to help students to choose courses. Python Example codes, Labs and Project are NOT here.All course materials (homework/labs/tests/etc.) are on Canvas.

  • Lecture Notes

Section 0 Introduction Math4570Sec0Introduction
Section 1 is group, ring, and fields. (This is a generalization of real number field R.) Math4570Sec1Fields
Section 2 is about all matrix operations. Math4570Sec2MatrixAlgebra
Section 3 is the general vector spaces over a field. (This is a generalization of subspaces of R^n) Math4570Sec3LinearSpacesOverField
Section 4 is independence and basis (of any vector spaces) Math4570Sec4Bases
Section 5 is inner product spaces (this is a generalization on dot products.) Math4570Sec5InnerProductSpaces
Section 6 General Least squares problems, data fitting and polynomial approximation. Math4570Sec6GeneralLeastSquares
Section 7. Linear Regression and Matrix Calculus Math4570Sec7LinearReg_MatrixCalculus
Section 8. Weighted Linear Regression, Ridge and Lasso regressions Math4570Sec8RidgeLasso
Section 9. Gradient Descents, Newton’s methods, Descent with momentum, ADAM Math4570Sec9GrdientDescent
Section 10. Probability Review Math4570Sec10Probability
Section 11. Logistics Regression, SoftMax Math4570Sec11LogReg
Section 12. Bias and Variance Tradeoff, Cross Validations Math4570Sec12CrossValidation
Section 13. Perceptron, Neural Network, Backpropagation Math4570Sec13ANN
Section 14. Convolutional Neural Network Math4570Sec14CNN
Section 15. Support Vector Machine and Kernel methods Math4570Sec16SVM
Section 16. Perron-Frobenius Theorem, Dynamical system, Malkov chains, etc.Math4570Sec17DynamicalSystem and Math4570Sec17DynamicalSystemEx
Section 17. Singular value decompositions(SVD) and Principal component analysis(PCA) Math4570Sec19PCA and Math4570Sec19SVD_picture
Section 18. Summary and Future Math4570Sec20Summury_Future

There are a few assignments and computer labs in Python or Matlab.

There are industry Experimental Network (XN) final projects for the course

XN project 1: Brain CT image hemorrhage segmentation 

  • XN project with Merck Research Laboratories: 

XN project 2: Find Novel Intrinsic Oncology Targets and Biology

  • References:

  1. Finite-dimensional linear algebra, Mark S. Gockenbach, CRC Press.
  2. Linear Algebra and Learning from Data., Gilbert Strang, Wellesley-Cambridge Press
  3.  Hands-On Machine Learning with Scikit-Learn and TensorFlow: Concepts, Tools, and Tech- niques to Build Intelligent Systems – by Aur elien G eron (Good for machine learning by Python)
  4. An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics) by Daniela Witten, Trevor Hastie, Robert Tibshirani, Gareth M. James
  5. The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Trevor Hastie, Robert Tibshirani, Jerome Friedman (Much more advanced on statistical learning for future study)
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