drsc_linesearch
PURPOSE
Line search subroutine to determine stepsize for gradient ascent performed by DRSC
SYNOPSIS
function step = drsc_linesearch(Data, W, max_step, f, grad, sigma, U, degs)
DESCRIPTION
Line search subroutine to determine stepsize for gradient ascent performed by DRSC
STEP = DRSC_LINESEARCH(DATA, W, MAX_STEP, F, GRAD, SIGMA, U, DEGS)
Line-search for gradient ascent within DRSC satisfying only first Wolfe condition
(using both takes excessively long)
Inputs:
(DATA): N-by-D data matris
(W): Projection matrix (ascent is performed w.r.t. last column of W)
(MAX_STEP): Maximum stepszie
(F): Function value at current poit
(GRAD): Gradient at current point
(SIGMA): Scale parameter for Gaussian kernel (used to estimate similarity matrix)
(U): Top K eigenvectors of D^{-1/2} *K*D^{-1/2}
(DEGS): Vector of degrees of each vertex: D = diag(degs)
Output:
(STEP): Stepsize satisfying 1st Wolfe condition
(Returns 0 if no such stepsize is found)CROSS-REFERENCE INFORMATION
This function calls:- f_df_drsc Function value and derivative with respect to last projection vector (column) of W
- gram_schmidt Gram-Schmidt orthonormalisation of vector (V) with respect to columns of (W)
- drsc Dimensionality Reduction for Spectral Clustering
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