Title B of the certification cup of the pistar cluster in the Ibagu catalog

 

The certification cup of the binary star cluster in the Ibagu catalog B topic

Update content the next day , The two core models are shown in the figure on the right

1. A brief introduction to the topic ：

Stars observed using a satellite called Ibagu , A catalog made of their data . Now we have got a lot of star data from the Ibagu catalog , I hope you can find out who are the members of the Hyades . There are very few characteristics of the Pythagorean cluster given in the title , only one 22 Average parallax in milliseconds ……

2. Interpretation of important data ：

1. Vmag- Look at the stars ： The brightness of stars seen by the naked eye , The higher the value, the darker .
2. Plx- Angle difference and error ： Don't explain , The title is detailed
3. B-V- Color index ： A measure of surface temperature by color .

（4） Stellar self motion index ： The effect is unknown ..

（5） Right ascension and declination ： important ！ Star position

 

 

3. The title requires interpretation ：

（1） Confirm the members of bixingtuan

（2） Draw the Herod

A herogram is a graph of the spectral type and luminosity of a star , The vertical axis of the herogram is luminosity and absolute magnitude , The horizontal axis is the spectrum type and the surface temperature of the star , Decrease from left to right .

（ Baidu search , There are many more pictures ）

So drawing is very simple , Look at the stars 、 Color index （ Surface temperature ） There's data , After finding out the members of the bixingtuan, the painting will be finished .

 

 

 

Let me start by saying , The determination of star cluster membership is an important problem in astronomy , Many scholars have built many complex models to deal with （ For example, the Galactic gravitational potential orbital model , With very complex formulas and parameters ）, The model we established here is suitable for the small scientific research task of mathematical modeling , Large complex models are also possible , There are many references , But it is not suitable for mathematical modeling contest , All we have to do is learn and simplify others' models .

The following ideas are proposed for reference and modification only ！！！

 

 

4. Ideas ：

Identify cluster members in the catalog … This is an extremely arduous task . However, this is a mathematical modeling competition after all , Just be reasonable . But that's the data , What the judges hope to see is the novel interpretation and ingenious mining of the data . in addition , According to the experience of the landlord's two accompany training guidance certification cups , The title of the certification cup often needs to be supplemented with a lot of background knowledge to help solve the problem .

 

Such as the above ： Cluster 、 Star catalogue 、 Stellar characteristic nouns （ Look at the stars 、 Poor viewing angle 、 Color index 、 The stars themselves ）. these , It is mentioned in the title , Be sure to know for yourself . Here are some topics that are not mentioned but Vital information ：

 

1. First , To understand What is a star cluster ：

All members of the cluster should be a whole , It is different from other stars in many parameters , As mentioned in the title 、 parallax 、 Visual star 、 Color index, etc , Find... Through these features Exist together Some of the stars , Star clusters .

① Outlier detection The catalog data is scattered 、 It is normal to have noise and outliers , First do an outlier detection , Eliminate outliers , It can make the effect of subsequent models better , And enrich the content of the article .

You can also make pictures （ Is not very good , For reference only ） Here's the picture ：

② Descriptive statistics ：（ Must do ）

 

Can this kind of picture not exist ？ It has to be , Select a few features with good results , This task can be assigned to teammates who have nothing to do , This task has little to do with the main line . The creative type of drawing should come out , For example, the two vector orientations of a star's own motion , You can refer to relevant information to see how to draw vector diagram .

 

2. Build a multi-dimensional identification model of member stars ：（ It contains three contents ）

 

1. Select variable , It's a cliche , Remove irrelevant and redundant data , For this problem, the data redundancy is not high 、 A characteristic that is difficult to explain , Principal component analysis is not recommended （pca） And singular value decomposition （svd）, Still use omnipotent but not strong （ It's enough here ）r Type clustering , Keep one item in each category that is easy to explain （ Variable filtering is an important part of data analysis , Although the dimension of this question is small and important, it can not be sifted , But here you can enrich the content of the article , Write a few formulas , Make several cluster diagrams , Xiaobai is better to write . because r The clustering criterion is Euclidean distance , Pay attention to data standardization ）.

（ There is no need to enrich the article , Omit this section , There is no need to reduce dimension , If you have the ability, you can also use other dimensionality reduction methods , Or use Correlation coefficient method Redundancy of data sets 、 Correlation test ）

 

（ for example ： Cluster the indicators into 3 Types of data , Reasonable explanation , Is the brightness characteristic 、 Kinematic characteristics 、 Location features ）

It is reliable to say so , At present, the identification method of astronomical member stars mainly depends on optical and kinematic characteristics .

-------------------------（ The next day my view ：（1） not essential , Not much ）--------

 

notes ： We built Model Two things need to be done ：

① determine \ Find the member stars .

② Depict the differences in member star recognition —-- Measure the reliability of the identification results of the model .（ This is very important ！！！）

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（2） be based on k Nearest neighbor distance analysis ........ Model of

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