# The graph based penalty transformation matrix

### Description

Get the graph based penalty transformation matrix, i.e. D_p in p_{λ}(β) = λ\|D_pβ\|_1.

### Usage

 1 fused.trans(A) 

### Arguments

 A input matrix – adjacency matrix of an observed graph based on the non-isolated nodes, of dimension n.noniso x n.noniso, where n.noniso is the number of the non-isolated nodes.

### Value

the graph based penalty transformation matrix, of dimension |E| \times n, where |E| is the number of edges in the graph and n is the number of nodes.

### Author(s)

Yang Feng, Richard J. Samworth and Yi Yu

### References

Yang Feng, Richard J. Samworth and Yi Yu, Community Detection via Fused Principal Component Analysis, manuscript.

### Examples

 1 2 3 4 5 6 7 8 ## to generate an adjacency matrix A = matrix(c(0,1,1,1,0,0,1,0,0), byrow = TRUE, ncol = 3) ## have a look at A A ## the graph based transformation matrix fused.trans(A) 

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