Sprint classes
Numerical treatment of the problem
Interpolating fitting
Mainly used for completion of the data and the basic trend analysis
Wavelet analysis, cluster analysis (Gaussian mixture polymerization, - K-means clustering and the like)
Mainly for diagnostic data and outliers removed
Principal component analysis, linear discriminant analysis, Locality Preserving Projection etc.
Mainly for reducing the dimension of multidimensional data , reduce data redundancy
Mean, analysis of variance, analysis of covariance statistical method
Mainly for intercepting data or feature selection
Associated with the cause and effect
Wherein: the multi-dimensional data, it is independent and dependent variables, input-output relationship
Note: 1,5 more used; fitting can do causal analysis
Classification and identification
1 from the cluster (cluster system: apart mean, Gaussian mixture ) used
2 cluster association ( common )
3 hierarchical clustering (data not standard)
4 density clustering (data not reference)
5 Other clusters
6 Bayes discrimination ( and statistical analysis )
7 Fisher discrimination ( the training sample is relatively small )
8 fuzzy recognition ( data points the sorted less )
9SOM neural network clustering
Evaluation and decision
Fuzzy Comprehensive Evaluation: Evaluation of poor quality in an object-level evaluation , the evaluation of a school and so on, can not be sorted ( data non-quantitative)
Analysis of Main Hierarchy Process: evaluation of the level and sort multiple objects, between a strong correlation index
AHP: making decisions, through indicators, considering the decision ( Low, subjective evaluation)
Data envelopment ( DEA) analysis: optimization, development of provincial judge
than the rank and comprehensive evaluation: evaluate individual objects and sorting, inter-correlation is not strong indicators
Neural network evaluation: for multi-index clearly non-linear relationship evaluation ( important, basically can be used, or apply to many situations that do not need to build a lot of their own indicators index )
The pros and cons of Range Law ( TOPSIS method)
Projection Pursuit Comprehensive Evaluation Method: integration of a variety of algorithms, such as genetic algorithms, optimization theory
Analysis of variance, analysis of covariance and so on:
Analysis of variance: to see whether the differences between types of data, differences in the impact, for example: the element has no effect on the yield of wheat, how much difference amount;
Analysis of covariance: There are several factors, we consider only one factor of the problem, ignoring other factors , but pay attention to the dimensionless initial situation and the initial data .
Prediction and forecasting problems ( five kinds, be sure to locate good questions)
Internal prediction small sample: interpolation, basically not test
Inside a large sample prediction: data processing problems, not test
Forecasts small sample: less than 50, it is easy to test
Forecasts random elements or features of a large sample period: a large amount of data, a lot of random factors
Forecasts large sample: amount of data, did not say random
1 gray prediction model ( must master the future prediction small sample )
Available two conditions are met:
data a less number of sample points , 6-15
b Data presented exponential curve or form
Prediction Equations ( alternate , less)
You can not find a direct relationship between the original data ,
But the relationship can be found between the rate of change in the raw data,
By the equation (differential, etc.) to derive the relationship between the conversion of the raw data
Regression analysis to predict ( must master the internal small and large-sample forecasts predict future small sample )
Seeking a relationship between the dependent variable and several independent variables, then if the independent variable, ask how changes in the dependent variable
The number of sample points required:
a covariance argument so far is relatively small, it is best to zero, little relationship between the independent variable (preferably between independent variables)
The number of points the number of samples n is greater than b 3k + 1, k as variables
c to be normally distributed dependent variable
Markov ( future prediction backup, random elements or features of a large sample period )
That is, DP, and now only about objective optimization
No transmission of information between a sequence , not linked to front and rear, and the strong random data between data, independently of each phase;
Today's temperature and yesterday, the day after tomorrow there is no contact, high temperature forecast day after tomorrow, medium or low probability, probability can only get
Time Series Prediction ( must master, periodic random )
And Markov complementary to at least two points need to transmit information , the ARMA model, cycle model , seasonal models
Wavelet analysis and forecasting ( large sample to predict the future )
Neural network forecasting ( large sample to predict the future )
Chaos series forecasting ( large sample to predict the future )
Optimization and Control
Examples: production line, transportation, location problem
Linear programming, integer programming, 0-1 programming (constrained, target)
Nonlinear programming with intelligent optimization algorithm
Multi-objective programming and goal programming (flexible constraints, goals ambiguous, more than)
Dynamic Programming
Graph theory, network optimization (multi-factor staggered complex)
Queuing theory and computer simulation
Fuzzy Programming (range constraints)
Gray Planning (difficult)
Intelligent algorithms (any questions about the maximum and minimum values, disguised optimization):
Genetic Algorithm 1: bp neural network can be used to correct loss of function;
2 Simulated Annealing: a bit like reinforcement learning, this is not the same as the probability
3 PSO algorithm:
Sprint
1. The United States and get to know the race issue, first inform themselves about matching questions (training on classification questions of understanding)
2. Algorithms form a system, know what those algorithms are able to solve the problem, the corresponding algorithm document finishing (algorithms related to the principles of the document) a good backup.
3. programming entry, the formation of the library program , understand how to use, when to change the parameters
4. look excellent paper, the Chinese , look for writing feeling.
5. in advance to find a good venue , warm water and electricity must be taken into account
6. The team tacit understanding, communicate well in advance Contact and division of labor, of three parts, modeling, writing, programming.
7. To achieve contact English Daniel, ask him or her translation summary
8. exercise, do not get sick
The game concluded: Organizer;
MCM requires mathematical ability is relatively high, ICM is interdisciplinary, F is a hot issue, no routine.
Common 3d modeling software
Big data processing (data cleansing, dimensionality reduction analysis, build relationships, etc.)
To find information is an important way to find ideas
Thinking look at the subject general idea
Selection, optimization
example:
The best utilization of water
And receiving heated oven best
Best baseball stress points
Best boarding program
Optimal line service system
Quantity optimal cutting
Generator optimal combination
Optimal transport Road King
element:
Decision variables; objective function; constraints;
concept:
Feasible solution, feasible region, the optimal solution
Evaluation, classification, sorting
Clothing style judge
Sudoku difficulty classification
National health system quality service ordering
Comprehensive evaluation of the ability to recruit staff
Student knowledge level evaluation
Prevention and treatment of certain diseases Evaluation
Financial system risk assessment
Personal Credit Evaluation
element:
Determining a plurality of evaluation indicators identified (evidence-based paper; exclude subjective; must not be forced)
Analytic Hierarchy subjectivity, strong nonlinear mapping ability of neural networks, fuzzy mean.
Evaluation of step
Targeting; evaluation index; determining weights; seek a single evaluation index value; seek comprehensive evaluation value
Three kinds of problem-solving ideas
1. Locate the keywords, positioning kinds of questions, after re-positioning algorithm.
2. find similar problems, weaken the problem, or to strengthen the problem, see if there is relevant research literature, learn from it.
3. mathematical derivation