4. Supplementary

4.1. Nomenclature

Collection of mathematical notations and abbreviations in this documentation.

• 4.1.1. Math symbols and abbreviations
  • 4.1.1.1. Math symbols
  • 4.1.1.2. Acronyms

4.2. Data science essentials

Essentials of multivariate statistics and analysis. Basic concepts of analytics used for statistical algorithm, data mining, decision theory, automation, as well as AI-support systems [MacCrimmon1968, Slovic1977, Nelder1990].

• 4.2.1. High dimensional data
  • 4.2.1.1. Design matrix
  • 4.2.1.2. Distance matrix
  • 4.2.1.3. Pattern in high dimensional data
  • 4.2.1.4. Correlation on high dimensional data
• 4.2.2. About matrix
  • 4.2.2.1. Rank and trace
• 4.2.3. Factor analysis
  • 4.2.3.1. Factor and level
  • 4.2.3.2. Factorize indexing
  • 4.2.3.3. Rearranged pseudo-tensor
  • 4.2.3.4. Priori scoring
• 4.2.4. Mathematical statistics
  • 4.2.4.1. Probability distribution
  • 4.2.4.2. Hypothesis testing
• 4.2.5. Monte Carlo method
• 4.2.6. Bayesian statistics
  • 4.2.6.1. The basic theories
  • 4.2.6.2. Discrete distribution family
  • 4.2.6.3. Continuous distribution family

4.3. Scientific calculation essentials

Essentials of scientific calculation from principle to implementation. Basic technical foundations to construct functions for data pre- and post-processing, modality transition, applying statistics, and etc.

• 4.3.1. Feature capturing
  • 4.3.1.1. How we define features
  • 4.3.1.2. Spatial filtering
  • 4.3.1.3. Curvature of image
• 4.3.2. Anomaly and change
  • 4.3.2.1. Anomaly detection
    • 4.3.2.1.1. Hotelling T-squared
    • 4.3.2.1.2. Empirical distribution and neighbors
    • 4.3.2.1.3. Bayesian and mixture Gaussian
    • 4.3.2.1.4. Directional data

4.4. Informatics essentials

Essentials of functional programming and computing flow control in informatics. The indispensable concepts for building functional units and pipelines via informatics.

• 4.4.1. Functional programming primer
  • 4.4.1.1. Abstraction for behaviors
  • 4.4.1.2. Using functions
• 4.4.2. Basic concepts in informatics
  • 4.4.2.1. Informatics function
  • 4.4.2.2. Unit and pipeline

---

Authors:

Chen Zhang

Version:

0.0.5

Created on:

Apr 26, 2023