impplot.asv

Jackknife PARAFAC, 用在多维线性分解.

All=zeros(I,I+2);
All(1:I,3:I+2)=B1;
All(1:I,1:I)=All(1:I,1:I)+BI;
All=All(:,2:I+1);
Allmin=All;
Allmax=All;
% All(:,i) holds the ULSR solution for modloc = i, disregarding x(i),


iii=find(x>=max(All)');
b=All(:,iii(1));
b(iii(1))=x(iii(1));
Bestfit=sum((b-x).^2);
MaxML=iii(1);
for ii=2:length(iii)
  this=All(:,iii(ii));
  this(iii(ii))=x(iii(ii));
  thisfit=sum((this-x).^2);
  if thisfit<Bestfit
    b=this;
    Bestfit=thisfit;
    MaxML=iii(ii);
  end
end

if xmin<0
  b=b+xmin;
end


% Impose nonnegativity
if NonNeg==1
  if any(b<0)
    id=find(b<0);
    % Note that changing the negative values to zero does not affect the
    % solution with respect to nonnegative parameters and position of the
    % maximum.
    b(id)=zeros(size(id))+0;
  end
end

function [b,B,AllBs]=monreg(x);

%MONREG monotone regression
%
% See also:
% 'unimodal' 'monreg' 'fastnnls'
%
%
% MONTONE REGRESSION
% according to J. B. Kruskal 64
%
% b     = min|x-b| subject to monotonic increase
% B     = b, but condensed
% AllBs = All monotonic regressions, i.e. AllBs(1:i,i) is the 
%         monotonic regression of x(1:i)
%
%	Copyright
%	Rasmus Bro 1997
%	Denmark
%	E-mail [e-mail]
%
% Reference
% Bro and Sidiropoulos, "Journal of Chemometrics", 1998, 12, 223-247. 
%
% [b,B,AllBs]=monreg(x);

% Copyright, 1998 - 
% This M-file and the code in it belongs to the holder of the
% copyrights and is made public under the following constraints:
% It must not be changed or modified and code cannot be added.
% The file must be regarded as read-only. Furthermore, the
% code can not be made part of anything but the 'N-way Toolbox'.
% In case of doubt, contact the holder of the copyrights.
%
% Rasmus Bro
% Chemometrics Group, Food Technology
% Department of Food and Dairy Science
% Royal Veterinary and Agricultutal University
% Rolighedsvej 30, DK-1958 Frederiksberg, Denmark
% Phone  [phone]
% Fax    [phone]
% E-mail [e-mail]
%

I=length(x);
if size(x,2)==2
   B=x;
else
   B=[x(:) ones(I,1)];
end

   AllBs=zeros(I,I);
   AllBs(1,1)=x(1);
   i=1;
   while i<size(B,1)
      if B(i,1)>B(min(I,i+1),1)
          summ=B(i,2)+B(i+1,2);
          B=[B(1:i-1,:);[(B(i,1)*B(i,2)+B(i+1,1)*B(i+1,2))/(summ) summ];B(i+2:size(B,1),:)];
          OK=1;
          while OK
             if B(i,1)<B(max(1,i-1),1)
                summ=B(i,2)+B(i-1,2);
                B=[B(1:i-2,:);[(B(i,1)*B(i,2)+B(i-1,1)*B(i-1,2))/(summ) summ];B(i+1:size(B,1),:)];
                i=max(1,i-1);
             else
                OK=0;
             end
          end
          bInterim=[];
          for i2=1:i
             bInterim=[bInterim;zeros(B(i2,2),1)+B(i2,1)];
          end
          No=sum(B(1:i,2));
          AllBs(1:No,No)=bInterim;
      else
          i=i+1;
          bInterim=[];
          for i2=1:i
             bInterim=[bInterim;zeros(B(i2,2),1)+B(i2,1)];
          end
          No=sum(B(1:i,2));
          AllBs(1:No,No)=bInterim;
      end
  end

  b=[];
  for i=1:size(B,1)
    b=[b;zeros(B(i,2),1)+B(i,1)];
  end
  
  function [x,w] = fastnnls(XtX,Xty,tol)

%FASTNNLS Fast version of built-in NNLS
%	b = fastnnls(XtX,Xty) returns the vector b that solves X*b = y
%	in a least squares sense, subject to b >= 0, given the inputs
%       XtX = X'*X and Xty = X'*y.
%
%	A default tolerance of TOL = MAX(SIZE(X)) * NORM(X,1) * EPS
%	is used for deciding when elements of b are less than zero.
%	This can be overridden with b = fastnnls(X,y,TOL).
%
%	[b,w] = fastnnls(XtX,Xty) also returns dual vector w where
%	w(i) < 0 where b(i) = 0 and w(i) = 0 where b(i) > 0.
%
%
%	L. Shure 5-8-87 Copyright (c) 1984-94 by The MathWorks, Inc.
%
%  Revised by:
%	Copyright
%	Rasmus Bro 1995
%	Denmark
%	E-mail [e-mail]
%  According to Bro & de Jong, J. Chemom, 1997, 11, 393-401

% initialize variables


if nargin < 3
    tol = 10*eps*norm(XtX,1)*max(size(XtX));
end
[m,n] = size(XtX);
P = zeros(1,n);
Z = 1:n;
x = P';
ZZ=Z;
w = Xty-XtX*x;

% set up iteration criterion
iter = 0;
itmax = 30*n;

% outer loop to put variables into set to hold positive coefficients
while any(Z) & any(w(ZZ) > tol)
    [wt,t] = max(w(ZZ));
    t = ZZ(t);
    P(1,t) = t;
    Z(t) = 0;
    PP = find(P);
    ZZ = find(Z);
    nzz = size(ZZ);
    z(PP')=(Xty(PP)'/XtX(PP,PP)');
    z(ZZ) = zeros(nzz(2),nzz(1))';
    z=z(:);
% inner loop to remove elements from the positive set which no longer belong

    while any((z(PP) <= tol)) & iter < itmax

        iter = iter + 1;
        QQ = find((z <= tol) & P');
        alpha = min(x(QQ)./(x(QQ) - z(QQ)));
        x = x + alpha*(z - x);
        ij = find(abs(x) < tol & P' ~= 0);
        Z(ij)=ij';
        P(ij)=zeros(1,length(ij));
        PP = find(P);
        ZZ = find(Z);
        nzz = size(ZZ);
        z(PP)=(Xty(PP)'/XtX(PP,PP)');
        z(ZZ) = zeros(nzz(2),nzz(1));
        z=z(:);
    end
    x = z;
    w = Xty-XtX*x;
end

x=x(:);


function AB=ppp(A,B);

% $ Version 1.02 $ Date 28. July 1998 $ Not compiled $
%
% Copyright, 1998 - 
% This M-file and the code in it belongs to the holder of the
% copyrights and is made public under the following constraints:
% It must not be changed or modified and code cannot be added.
% The file must be regarded as read-only. Furthermore, the
% code can not be made part of anything but the 'N-way Toolbox'.
% In case of doubt, contact the holder of the copyrights.
%
% Rasmus Bro
% Chemometrics Group, Food Technology
% Department of Food and Dairy Science
% Royal Veterinary and Agricultutal University
% Rolighedsvej 30, DK-1958 Frederiksberg, Denmark
% Phone  [phone]
% Fax    [phone]
% E-mail [e-mail]
%
% The parallel proportional profiles product - triple-P product
% For two matrices with similar column dimension the triple-P product
% is ppp(A,B) = [kron(B(:,1),A(:,1) .... kron(B(:,F),A(:,F)]
% 
% AB = ppp(A,B);
%
% NB. This file is obsolete. Use kr.m instead but not that it takes
% inputs oppositely

%
% Copyright 1998
% Rasmus Bro
% KVL,DK
% [e-mail]


disp('PPP.M is obsolete and will be removed in future versions. ')
disp('use KR.M instead. Note that kr(B,A) = ppp(A,B)')

[I,F]=size(A);
[J,F1]=size(B);

if F~=F1
   error(' Error in ppp.m - The matrices must have the same number of columns')
end

AB=zeros(I*J,F);
for f=1:F
   ab=A(:,f)*B(:,f).';
   AB(:,f)=ab(:);
end

function [A,B,C,fit]=dtld(X,F,SmallMode);

%DTLD direct trilinear decomposition
%
% See also:
% 'gram', 'parafac'
%
% Copyright, 1998 - 
% This M-file and the code in it belongs to the holder of the
% copyrights and is made public under the following constraints:
% It must not be changed or modified and code cannot be added.
% The file must be regarded as read-only. Furthermore, the
% code can not be made part of anything but the 'N-way Toolbox'.
% In case of doubt, contact the holder of the copyrights.
%
% Rasmus Bro
% Chemometrics Group, Food Technology
% Department of Food and Dairy Science
% Royal Veterinary and Agricultutal University
% Rolighedsvej 30, DK-1958 Frederiksberg, Denmark
% Phone  [phone]
% Fax    [phone]
% E-mail [e-mail]
%
%
% DIRECT TRILINEAR DECOMPOSITION
%
% calculate the parameters of the three-
% way PARAFAC model directly. The model
% is not the least-squares but will be close
% to for precise data with little model-error
%
% This implementation works with an optimal
% compression using least-squares Tucker3 fitting
% to generate two pseudo-observation matrices that
% maximally span the variation of all samples. per
% default the mode of smallest dimension is compressed
% to two samples, while the remaining modes are 
% compressed to dimension F.
% 
% For large arrays it is fastest to have the smallest
% dimension in the first mode
%
% INPUT
% [A,B,C]=dtld(X,F);
% X is the I x J x K array
% F is the number of factors to fit
% An optional parameter may be given to enforce which
% mode is to be compressed to dimension two
%
% Copyright 1998
% Rasmus Bro, KVL
% [e-mail]

% $ Version 2.00 $ May 2001 $ Changed to array notation $ RB $ Not compiled $
% $ Version 1.02 $ Date 28. July 1998 $ Not compiled $
% $ Version 1.03 $ Date 25. April 1999 $ Not compiled $

DimX = size(X);
X = reshape(X,DimX(1),prod(DimX(2:end)));

DontShowOutput = 1;

%rearrange X so smallest dimension is in first mode


if nargin<4
  [a,SmallMode] = min(DimX);
  X = nshape(reshape(X,DimX),SmallMode);
  DimX = DimX([SmallMode 1:SmallMode-1 SmallMode+1:3]);
  Fac   = [2 F F];
else
  X = nshape(reshape(X,DimX),SmallMode);
  DimX = DimX([SmallMode 1:SmallMode-1 SmallMode+1:3]);
  Fac   = [2 F F];
end
f=F;
if F==1;
  Fac   = [2 2 2];
  f=2;
end 


if DimX(1) < 2
  error(' The smallest dimension must be > 1')
end

if any(DimX(2:3)-Fac(2:3)<0)
  error(' This algorithm requires that two modes are of dimension not less the number of components')
end



% Compress data into a 2 x F x F array. Only 10 iterations are used since exact SL fit is insignificant; only obtaining good truncated bases is important
[Factors,Gt]=tucker(reshape(X,DimX),Fac,[0 0 0 0 NaN 10]);
% Convert to old format
Gt = reshape(Gt,size(Gt,1),prod(size(Gt))/size(Gt,1));

[At,Bt,Ct]=fac2let(Factors);

% Fit GRAM to compressed data
[Bg,Cg,Ag]=gram(reshape(Gt(1,:),f,f),reshape(Gt(2,:),f,f),F);

% De-compress data and find A


BB = Bt*Bg;
CC = Ct*Cg;
AA = X*pinv(kr(CC,BB)).';

if SmallMode == 1
  A=AA;
  B=BB;
  C=CC;
elseif SmallMode == 2 
  A=BB;
  B=AA;
  C=CC;
elseif SmallMode == 3
  A=BB;
  B=CC;
  C=AA;
end

fit = sum(sum(abs(X - AA*kr(CC,BB).').^2));
if ~DontShowOutput
  disp([' DTLD fitted raw data with a sum-squared error of ',num2str(fit)])
end


function [Factors]=ini(X,Fac,MthFl,IgnFl)
%INI initialization of loadings
%
% function [Factors]=ini(X,Fac,MthFl,IgnFl)
%
% This algorithm requires access to:
% 'gsm' 'fnipals' 'missmult'
%
% Copyright
% Claus A. Andersson 1995-1999
% Chemometrics Group, Food Technology
% Department of Food and Dairy Science
% Royal Veterinary and Agricultutal University
% Rolighedsvej 30, T254
% DK-1958 Frederiksberg
% Denmark
% Phone  [phone]
% Fax    [phone]
% E-mail [e-mail]
%
% ---------------------------------------------------------
%                    Initialize Factors 
% ---------------------------------------------------------
%
% [Factors]=ini(X,Fac,MthFl,IgnFl);
% [Factors]=ini(X,Fac,MthFl);
%
% X        : The multi-way data.
% Fac      : Vector describing the number of factors
%            in each of the N modes.
% MthFl    : Method flag indicating what kind of
%            factors you want to initiate Factors with:
%            '1' : Random values, orthogonal
%            '2' : Normalized singular vectors, orthogonal
% IgnFl    : This feature is only valid with MthFl==2.
%            If specified, these mode(s) will be ignored,
%            e.g. IgnFl=[1 5] or IgnFl=[3] will
%            respectively not initialize modes one and 
%            five, and mode three.
% Factors  : Contains, no matter what method, orthonormal
%            factors. This is the best general approach to
%            avoid correlated, hence ill-posed, problems.
%
% Note that it IS possible to initialize the factors to have
% more columns than rows, since this may be required by some
% PARAFAC models. If this is required, the 'superfluos' 
% columns will be random and orthogonal columns.
% This algorithm automatically arranges the sequence of the
% initialization to minimize time and memory consumption.
% Note, if you get a warning from NIPALS about convergence has
% not been reached, you can simply ignore this. With regards 
% to initialization this is not important as long as the
% factors being returned are in the range of the eigensolutions.

% $ Version 1.02 $ Date 30 Aug 1999 $ Not compiled $
% $ Version 1.0201 $ Date 21 Jan 2000 $ Not compiled $ RB removed orth of additional columns
% $ Version 2.00 $ May 2