EOSC 510 (Data Analysis in Atmospheric, Earth and Ocean Sciences)

Course description and outline

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Reading material from textbook

Week 1:

• Sect.1.1 Expectation and mean
  
• Sect.1.2 Variance and covariance
  
• Sect.1.3 Correlation
  
• Sect.1.4 Regression
  Lecture notes: Ch1_lec.pdf

Week 2:

• Sect.2.1.1-2.1.7 Principal component analysis (PCA)
  Homework #1 assigned (due Sept.27).
  Lectures notes: Ch2_lec_a.pdf, Ch2_lec_b.pdf
  

Week 3:

• Sect.2.1.8-2.1.12 (PCA continued)
  
• Sect.2.2 Rotated PCA
  
• Sect.2.3 PCA for vectors
  Lecture notes: Ch2_lec_c.pdf

Week 4:

• Sect.2.4 Canonical correlation analysis (CCA)
  Lecture notes: Ch3_lec.pdf
  Homework #2 assigned (due Oct.11).
  
• Sect.3.1-3.1.1 Autospectrum
  Lecture notes: Ch4_lec_a.pdf
  

Week 5:

• Sect.3.1.2 Cross-spectrum
  
• Sect 3.2 Windows
  Lecture notes: Ch4_lec_b.pdf
  
• Sect.3.3 Filters
  
• Sect.3.4 Singular spectrum analysis
  
• Sect.3.5 Multichannel singular spectrum analysis
  Lecture notes: Ch4_lec_c.pdf
  Homework #3 assigned (due Oct.20).
  

Week 6:

• Sect.4.1 McCulloch and Pitts model
  
• Sect.4.2 Perceptrons (skipping technical parts: Eqns. (4.6)-(4.15))
  
• Sect.4.3 Multi-layer perceptrons (MLP)
  
• Sect.4.4 Back-propagation (skipping Eqs. (4.26)-(4.40))
  Lecture notes: Ch5_lec_a.pdf
  

Week 7:

• Sect.4.5 Hidden neurons
  
• Sect.8.1 Multi-layer perceptron classifier (omit the pages in Chap.8 before Sect.8.1, and omit Sect.8.1.1);
  
• Sect.4.6 Radial basis functions
  
• Sect.4.7 Conditional probability distributions
  Lecture notes: Ch5_lec_b.pdf
  
• The beginning of Chap.5 (before Sect.5.1) nonlinear optimization;
  
• Sect.5.5. Evolutionary computation and genetic algorithms
  Lecture notes: Ch6_lec.pdf
  

Week 8: No reading assigned; Midterm exam.

Week 9: Instructor away. No classes.

Week 10:

• Sect.6.1 Mean squared error and maximum likelihood (rather theoretical)
• Sect.6.2 Objective functions and robustness (rather theoretical)
• Sect.6.3 Variance and bias errors
  
• Sect.6.5 Regularization
  
• Sect.6.6 Cross-validation
  
• Sect.6.7 Bayesian NN (just the first paragraph)
  
• Sect.6.8 Ensemble of models
  
• sect.6.10 Linearization from time-averaging
  Lecture notes: Ch7_lec.pdf
  Homework #4 assigned (due Thur., Dec.8).

Week 11:

• Sect.10.1.1-10.1.2 Auto-associative NN for Nonlinear PCA
• Sect.10.3 Self-organizing maps (SOM)
  Lecture notes: Ch8_lec.pdf
  

Week 12:

• Sect.11.1 (excluding Sect.11.1.2) Nonlinear CCA
  Lecture notes: Ch9_lec.pdf
  
• Sect.9.2 Classification and Regression Trees (CART)
  Lecture notes: Ch10_lec.pdf
  

Week 13:

• Sect.8.5 Forecast verification
  Lecture notes: Ch11_lec_a.pdf
  
• Sect.7.1 From neural networks to kernel methods
• Sect.7.5 Advantages and disadvantages of kernel methods.
• Sect.9.1 Support vector regression Lecture notes: Ch11_lec_b.pdf