Home > NoiseTools > nt_pca_nodemean.m

# nt_pca_nodemean

## PURPOSE

[z,idx]=nt_pca_nodemean(x,shifts,keep,threshold,w) - time-shift pca

## SYNOPSIS

function [z,idx]=nt_pca_nodemean(x,shifts,keep,threshold,w)

## DESCRIPTION

    [z,idx]=nt_pca_nodemean(x,shifts,keep,threshold,w) - time-shift pca

      z: pcs
      idx: x(idx) maps to z

      x: data matrix
      shifts: array of shifts to apply
      keep: number of components shifted regressor PCs to keep (default: all)
      threshold: discard PCs with eigenvalues below this (default: 0)
      w: ignore samples with absolute value above this

     mean is NOT removed prior to processing

## CROSS-REFERENCE INFORMATION

This function calls:

- nt_cov [c,tw]=nt_cov(x,shifts,w) - time shift covariance
- nt_multishift z=nt_multishift(x,shifts,amplitudes) - apply multiple shifts to matrix
- nt_pcarot [topcs,eigenvalues]=pcarot(cov,nkeep,threshold,N) - PCA matrix from covariance

This function is called by:

- nt_tsr_nodemean [y,idx,w]=nt_tsr_nodemean(x,ref,shifts,wx,wref,keep,thresh) - time-shift regression (TSPCA)

## SOURCE CODE

    0001 function [z,idx]=nt_pca_nodemean(x,shifts,keep,threshold,w)
    0002 %[z,idx]=nt_pca_nodemean(x,shifts,keep,threshold,w) - time-shift pca
    0003 %
    0004 %  z: pcs
    0005 %  idx: x(idx) maps to z
    0006 %
    0007 %  x: data matrix
    0008 %  shifts: array of shifts to apply
    0009 %  keep: number of components shifted regressor PCs to keep (default: all)
    0010 %  threshold: discard PCs with eigenvalues below this (default: 0)
    0011 %  w: ignore samples with absolute value above this
    0012 %
    0013 % mean is NOT removed prior to processing
    0014
    0015 % TODO: reimplement using nt_pca0
    0016
    0017 if nargin<1; error('!'); end
    0018 if nargin<2||isempty(shifts); shifts=[0]; end
    0019 if nargin<3; keep=[]; end
    0020 if nargin<4; threshold=[]; end
    0021 if nargin<5; w=[]; end
    0022
    0023 [m,n,o]=size(x);
    0024
    0025 % offset of z relative to x
    0026 offset=max(0,-min(shifts));
    0027 shifts=shifts+offset;           % adjust shifts to make them nonnegative
    0028 idx=offset+(1:m-max(shifts));   % x(idx) maps to z
    0029
    0030 % remove mean
    0031 %x=nt_fold(nt_demean(nt_unfold(x),w),m);
    0032
    0033 % covariance
    0034 if isempty(w);
    0035     c=nt_cov(x,shifts);
    0036 else
    0037     if sum(w(:))==0; error('weights are all zero!'); end
    0038     c=nt_cov(x,shifts,w);
    0039 end
    0040
    0041 % PCA matrix
    0042 [topcs,evs]=nt_pcarot(c);
    0043
    0044 % truncate
    0045 if ~isempty(keep)
    0046     topcs=topcs(:,1:keep);
    0047     evs=evs(1:keep);
    0048 end
    0049 if ~isempty (threshold)
    0050     ii=find(evs/evs(1)>threshold);
    0051     topcs=topcs(:,ii);
    0052     evs=evs(ii);
    0053 end
    0054
    0055 %clf; plot(evs); set(gca,'yscale','log'); pause
    0056
    0057 % apply PCA matrix to time-shifted data
    0058 z=zeros(numel(idx),size(topcs,2),o);
    0059 for k=1:o
    0060     z(:,:,k)=nt_multishift(x(:,:,k),shifts)*topcs;
    0061 end
    0062
    0063