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multiness (version 1.0.2)

ase: Adjacency Spectral Embedding (ASE)

Description

ase calculates the \(d\)-dimensional adjacency spectral embedding of a symmetric \(n \times n\) matrix \(M\).

Usage

ase(M,d)

Value

An \(n \times d\) matrix \(X\), defined as \(U |S|^{1/2}\)

where \(S\) is a diagonal matrix of the \(d\) leading (in absolute value) eigenvalues of \(M\), and \(U\) is a matrix of the corresponding eigenvectors.

\(X\) has an additional attribute "signs" which gives the sign of the eigenvalue corresponding to each column.

If \(d=0\), ase returns an \(n \times 1\)

matrix of zeros.

Arguments

M

A symmetric matrix.

d

A non-negative integer embedding dimension.