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

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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

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## 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)