# AA type analysis

Type AA represents a one-to-one relationship between elements with respect to the view of A. This is the simplest of many-to-many analysis . Matrix representation of relationships

AA type can be classified according to whether it is a symmetric matrix (numbers are lined up symmetrically across a diagonal line).

## For symmetric matrix

Covariance and correlation matrices are symmetric matrices.

In addition, the distance matrix, in which the number of each element is "distance" (the larger the value, the farther the relationship is ), is also a symmetric matrix.

By the way, the larger the absolute value of the correlation, the stronger the relationship, but the larger the value of the distance, the farther it is, so it has the opposite property.

Multidimensional scaling is a way to start the analysis with the distance matrix . Principal component analysis is a way to start the analysis with the correlation matrix . In addition, there are methods such as self-organizing map and cluster analysis that start the analysis with AB type but include an algorithm that calculates the data corresponding to the symmetric matrix inside the software.

## For asymmetric matrices

The AA type of asymmetric matrix is called "adjacency matrix" in the field of networks . You can make a graph by writing and drawing the network . For network data, the simplest form is 0s and 1s, which indicate whether each element is connected. When using numbers other than 0 and 1, the larger the value, the closer the relationship . For an asymmetric matrix, it is a directed graph with arrows.

Aggregating conditional probabilities like P (X | Y) and P (Y | X) in the form of a matrix is ??an asymmetric matrix.

## Processing from AB type

AA type can be made by processing AB type . A well-known processing method is to obtain the correlation coefficient for the combination of two AB type columns and arrange them in the form of a matrix. It is used in correlation analysis of multivariate data .

In addition, the calculation of principal component analysis includes a procedure to convert AB type data into a covariance matrix or a correlation matrix. Little is known, but principal component analysis can also be started with type AA.

Please note that it may not be possible to process from AA type to AB type. In other words, the information of B of AB type cannot be used in AA type.

## Software

R-EDA1 includes the analysis of AA type data.

Analysis by network graph using adjacency matrix, analysis by multidimensional scaling (MDS) using distance matrix, eigenvalues analysis using correlation matrix and paired evaluation data are available.

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