f_df_sc

PURPOSE

Function value and derivative of second smallest eigenvalue of normalised Laplacian

SYNOPSIS

function [f, Df] = f_df_sc(v,X, pars)

DESCRIPTION

Function value and derivative of second smallest eigenvalue of normalised Laplacian
[F,DF] = F_DF_SC(V, X, PARS)

 Inputs:
     (V): Projection vector
    (X): N-by-D Data matrix
    (PARS): parameter struct containing 
        (sigma) Scaling parameter for Gaussian kernel
        (minsize): minimum cluster size
        (beta) (delta): parameters for similarity transformation

 Output: 
    (F): Second smallest eigenvalue of Normalised Laplacian
       (DF): derivative of (f) w.r.t. projection matrix (v)

CROSS-REFERENCE INFORMATION

This function calls:

dP_dv Derivative of transformed data projections along projection vector V
sim_transform Transformation of points to compute pairwise similarities of projected data Eqs.(17)-(18)

This function is called by:

scpp Spectral Clustering Projection Pursuit (SCPP) (divisive clustering is implemented in scppdc.m)