# 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 |

### 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)
``` |