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Networked multidimensional scaling

Multidimensional scaling is a method of converting distance data between two points into coordinate data.

You can also use it to convert high-dimensional distances to two-dimensional coordinates by regarding them as two-dimensional distances.

In multidimensional scaling, there are two types of data formats to start with. There are two types: distance matrix, which represents the data of the distance between all two points, and coordinate data. If you want to start the coordinate data, convert it to a distance matrix before using it.

Multidimensional scaling deals with "distance", so it has the property that "the larger the value, the farther it is". Therefore, when dealing with a coefficient of determination that has the property of "closer as the value is larger" in the multidimensional scaling method, subtract it from 1 and convert it so that it has the property of "farther as the value is larger". Use.

By the way, network analysis deals with data that has the property that "the larger the value, the closer it is". A network graph is a graph that shows the relationship between such data.

Therefore, as the opposite method to the case where the coefficient of determination is handled by the multidimensional scaling method, data having the property of "the larger the value is, the farther it is", such as distance, is converted into the property of "the larger the value, the closer" the network. There is also a way to use the graph .

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How to convert "the larger the value, the farther" to "the larger the value, the closer"

The way to convert "larger value is farther" to "larger value is closer" is

(max - x)

. Not only is the nature of the value reversed, but the value remains positive.

However, in the network graph , this value is directly converted to the line thickness data, so the value should be between 0 and 10.

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Software

Example of R is in the page,
Multidimensional scaling by R
.

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