Vernacular spatial statistics: spatial autocorrelation

Vernacular spatial statistics: spatial autocorrelation

Spatial autocorrelation, is certainly the space statistics inside the first stumbling block, a lot of people met this tall on the vocabulary, immediately found that these five words I seem to know, but in the end said what? I don't know.

If open all kinds of textbooks, from statistics to mathematics to physics, all kinds of explanations have put up a pair of "Lao Tzu is tall to go to school pa, Dick Silk learn slag do not Disturb" appearance, this thing really is so difficult? Shrimp God I don't believe it, so: I have a dream, is to write a most ground gas spatial statistical interpretation. (Great ambition, amitabha God bless, don't blow it up.) ）

First of all, to understand the spatial autocorrelation of this magical concept, we have to first say a magical character. He is a professor of Waldo Tobler, a "Newton of Modern Geography".

Waldo, who was born in Switzerland in 1930 and received his doctorate in Washington University in 1961, was also a year in a turbulent year, and the current American leader, Barack Obama, is a student in 1961.

It seems that the heavens see physics already has three laws, and geography is not, so in 1969 (also said 1970), when God waved, let Professor Waldo Light the geography of the Sky Bar. So that year, he published the history of "the First Law of geography" of "Tobler" (TfL), that is, "all attribute values on a geographic surface is related to each othe R, but closer values is more strongly related than is more distant ones "translated into plain English, that is: anything, there is a relationship, but the closer, the closer the relationship."

Just as Newton's three laws pioneered the classical mechanics system, the first law of geography also provided a theoretical basis for the measurement revolution, from which the law of spatial analysis and space statistics could no longer be separated.

As the Ming scholar Mao Wuiyi evaluation of the art of war "grandson of the former grandson, grandson, after the grandson, can not have grandchildren," TfL also in the geography of the former, the latter can not be left behind the realm.

According to the law, every transaction in the space is connected, and the connection between the near transaction is much higher than that of the distant transaction. The so-called connection tightness, naturally also can say, two affairs will be in a certain aspect, have similar place.

Then the concept of spatial autocorrelation is brought out.

What is spatial autocorrelation? First, let's take a look at the following example:

Time: During recess.

Location: School playground.

When the broadcast sounded, all the students ran all the way to the playground (late to fined), so the headmaster upstairs, see should be such a scene:

How is a disorderly word, then this is called "random distribution", who do not know, which student is which class.

With the sports teacher's password, slowly to become the following this scene:

Students are neatly accounted for the queue, everyone around the distance is the same, this is the so-called "uniform distribution", in the case of uniform distribution, so there is no way to see the relationship between students.

After 5 minutes, the calisthenics ended, and as soon as the P.E. teacher's password was dissolved, the students became the following:

OK, now it is clear that the different students, themselves formed a small group of their own, which is called clustering.

Then you, as the headmaster, will naturally fill the brain, why these students will naturally gather together? Must be a common hobby or common purpose, as for this group, what common hobbies and common purpose, is a certain characteristic between students, such as learning good will automatically gather together, or like to play, will be together.

This, each student, and the students around him, generally have some kind of common characteristics. Theoretically, if a student with this trait appeared on the playground, there would be a great chance that he would have the same characteristics as him, and that they would have a potential dependency. For example, like to play the students, a person must not be able to play, so naturally need to have a common hobby of the small partners in the next.

The interdependence of this potential (because it is not clearly manifested, so it is certainly potentially) is called "Spatial autocorrelation".

The study of spatial autocorrelation is a very important concept to reveal the spatial data distribution, and the calculation of the degree of correlation in spatial autocorrelation is the main method to study spatial autocorrelation.

So, in the next issue, let's talk about one of the most important computational indicators of correlation for spatial autocorrelation: Moran's I (Mollance i) value.

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Vernacular spatial statistics: spatial autocorrelation