tpower {EESPCA}

Implementation of the Yuan and Zhang TPower method.

Description

Implements the TPower method by Yuan and Zhang. Specifically, it computes the sparse principal eigenvector using power iteration method where the estimated eigenvector is truncated on each iteration to retain just the k eigenvector loadings with the largest absolute values with all other values set to 0.

Usage

    tpower(X, k, v1.init, max.iter=10, lambda.diff.threshold=1e-6, trace=FALSE)

Arguments

X

Matrix for which the largest eigenvector and eigenvalue will be computed.

k

Must be an integer between 1 and ncol(X). The estimated eigenvector is truncated on each iteration to retain only the k loadings with the largest absolute values, all other loadings are set to 0.

v1.init

If specified, the power iteration calculation will be initialized using this vector, otherwise, the calculation will be initialized using a unit vector with equal values.

max.iter

Maximum number of iterations for power iteration method.

lambda.diff.threshold

Threshold for exiting the power iteration calculation. If the absolute relative difference in computed eigenvalues is less than this threshold between subsequent iterations, the power iteration method is terminated.

trace

True if debugging messages should be displayed during execution.

Value

The estimated sparse principal eigenvector.

References

• Yuan, X.-T. and Zhang, T. (2013). Truncated power method for sparse eigenvalue problems. J. Mach. Learn. Res., 14(1), 899-925.

See Also

powerIteration,tpowerPCACV

Examples

    set.seed(1)
    # Simulate 10x5 MVN data matrix
    X=matrix(rnorm(50), nrow=10)
    # Compute first sparse PC loadings with 2 non-zero elements
    tpower(X=cov(X), k=2)