(A) Data processing
① interpolating fitting
Mainly used for completion of basic data and trend analysis
② wavelet analysis, cluster analysis (Gaussian mixture clustering, K- means clustering, etc.)
Mainly for diagnostic data and outliers removed
③ into the main component analysis, linear discriminant analysis, and other local retention projection
Mainly for reducing the dimension of multidimensional data, reduce data redundancy
④ mean, analysis of variance, analysis of covariance statistical method
The main feature for intercepting data or selection
(B) associated with the cause and effect
① (fewer number of sample points) Gray Correlation Analysis
② Superman or kendall rank correlation analysis
③ Person correlation (more number of sample points)
④ Copula correlation (more difficult, financial mathematics, probability density)
⑤ canonical correlation analysis (dependent variable Y1234, the arguments set X1234, each group of related variables relatively strong, which asked which one dependent variable and one independent variable relationship more closely?)
(Iii) Classification and identification
① distance clustering (hierarchical clustering) commonly
② relevance of clustering (used)
③ hierarchical clustering
④ density clustering
⑤ other clusters
⑥ Bayes discrimination (statistical identification method)
⑦ Fisher discrimination (the training sample is relatively small)
⑧ fuzzy recognition (the sorted data point less)
(D) the evaluation and decision-making
① fuzzy comprehensive evaluation: evaluation of an object excellent, good, fair, poor levels of evaluation, the evaluation of a school and so on, can not be sorted.
② as the main component analysis: Evaluation of a plurality of objects and sorting levels, strong correlation between the index.
AHP analysis ③: decision making, through indicators, considering the decision
④ data envelopment (DEA) analysis: optimization, development of provincial judge
⑤ RSR comprehensive evaluation: evaluate individual objects and sorting, is not strong correlation between indicators
⑥ neural network evaluation: for a clear evaluation of multi-index nonlinear relationship
⑦ pros and cons of Range Law (TOPSIS method)
⑧ Projection Pursuit Comprehensive Evaluation Method: blend a variety of algorithms, such as genetic algorithms, optimization theory
⑨ analysis of variance, analysis of covariance
ANOVA: see whether the difference between types of data, differences affect, for example: the presence or absence of elements influence the amount of wheat, much difference amount; (92 Fertilization crop growth)
Analysis of covariance: There are several factors, we consider only one factor affecting the problem, ignoring other factors, but pay attention to the initial situation and the dimension of the initial data. (2006, AIDS Therapy Evaluation and prediction problems)
(E) prediction and forecasting
① internal prediction small sample
② large sample internal forecast
③ small samples to predict the future
Forecasts random factors or cycle characteristics ④ large sample
⑤ predict future large sample
Gray forecast model (must master)
Available two conditions are met:
- A small number of data sample points, 6-15
- b Data exponential curve or form
Prediction Equations (standby)
Can not find a direct relationship between the original data, but can be found in the relationship between the rate of change in the raw data, the formula is derived by converting the relationship between the original data
Regression analysis to predict (must master)
Seeking a relationship between the dependent variable and several independent variables, then if the independent variable, ask how the dependent variable changes
The number of sample points required by
- Covariance between variables from a relatively small, preferably tends to zero, the relationship between small argument;
- B The number of sample points n> 3k + 1, k is the number of independent variables;
- c to be normally distributed dependent variable
(F) optimization and control
① linear programming, integer programming, 0-1 programming (constrained, the goals set)
② nonlinear programming with intelligent optimization algorithm
③ multi-objective planning and goal programming (flexible constraints, goals ambiguous, more than)
④ dynamic programming
⑤ graph theory, network optimization (multi-factor staggered complex)
⑥ queuing theory and computer simulation
⑦ fuzzy programming (range constraints)
⑧ gray Plan (difficult)