-
Notifications
You must be signed in to change notification settings - Fork 7
/
nprocess.m
318 lines (289 loc) · 9.38 KB
/
nprocess.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
function [Xnew,mX,sX]=nprocess(X,Cent,Scal,mX,sX,reverse,show,usemse);
%NPROCESS pre and postprocessing of multiway arrays
%
%
% CENTERING AND SCALING OF N-WAY ARRAYS
%
% This m-file works in two ways
% I. Calculate center and scale parameters and preprocess data
% II. Use given center and scale parameters for preprocessing data
%
% %%% I. Calculate center and scale parameters %%%
%
% [Xnew,Means,Scales]=nprocess(X,Cent,Scal);
%
% INPUT
% X Data array
% Cent is binary row vector with as many elements as DimX.
% If Cent(i)=1 the centering across the i'th mode is performed
% I.e cnt = [1 0 1] means centering across mode one and three.
% Scal is defined likewise. Scal(i)=1, means scaling to standard
% deviation one within the i'th mode
%
% OUTPUT
% Xnew The preprocessed data
% mX Sparse vector holding the mean-values
% sX Sparse vector holding the scales
%
% %%% II. Use given center and scale parameters %%%
%
% Xnew=nprocess(X,Cent,Scal,mX,sX,reverse);
%
% INPUT
% X Data array
% Cent is binary row vector with as many elements as DimX.
% If Cent(i)=1 the centering across the i'th mode is performed
% I.e Cent = [1 0 1] means centering across mode one and three.
% Scal is defined likewise. Scal(i)=1, means scaling to standard
% deviation one within the i'th mode
% mX Sparse vector holding the mean-values
% sX Sparse vector holding the scales
% reverse Optional input
% if reverse = 1 normal preprocessing is performed (default)
% if reverse = -1 inverse (post-)processing is performed
%
% OUTPUT
% Xnew The preprocessed data
%
% For convenience this m-file does not use iterative
% preprocessing, which is necessary for some combinations of scaling
% and centering. Instead the algorithm first standardizes the modes
% successively and afterwards centers. The prior standardization ensures
% that the individual variables are on similar scale (this might be slightly
% disturbed upon centering - unlike for two-way data).
%
% The full I/O for nprocess is
% [Xnew,mX,sX]=nprocess(X,Cent,Scal,mX,sX,reverse,show,usemse);
% where show set to zero avoids screen output and where usemse set
% to one uses RMSE instead of STD for scaling (more appropriate
% in some settings)
% Copyright, 1998 -
%
% Rasmus Bro
% Chemometrics Group, Food Technology
% Department of Food and Dairy Science
% Royal Veterinary and Agricultutal University
% Rolighedsvej 30, DK-1958 Frederiksberg, Denmark
% Phone +45 35283296
% Fax +45 35283245
% E-mail rb@kvl.dk
% $ Version 1.03 $ Date 6. May 1998 $ Drastic error in finding scale parameters corrected $ Not compiled $
% $ Version 1.031 $ Date 25. January 2000 $ Error in scaling part $ Not compiled $
% $ Version 1.032 $ Date 28. January 2000 $ Minor bug$ Not compiled $
% $ Version 1.033 $ Date 14. April 2001 $ Incorrect backscaling fixed.
% $ Version 2.00 $ May 2001 $ Changed to array notation $ RB $ Not compiled $
% $ Version 2.00 $ May 2001 $ rewritten by Giorgio Tomasi $ RB $ Not compiled $
% $ Version 2.01 $ Feb 2002 $ Fixed errors occuring with one-slab inputs $ RB $ Not compiled $
% $ Version 2.02 $ Oct 2003 $ Added possibility for sclaing with RMSE $ RB $ Not compiled $
% $ Version 1.03 $ Date 6. May 1998 $ Drastic error in finding scale parameters corrected $ Not compiled $
% Copyright (C) 1995-2006 Rasmus Bro & Claus Andersson
% Copenhagen University, DK-1958 Frederiksberg, Denmark, rb@life.ku.dk
%
%
% CENTERING AND SCALING OF N-WAY ARRAYS
%
% This m-file works in two ways
% I. Calculate center and scale parameters and preprocess data
% II. Use given center and scale parameters for preprocessing data
%
% %%% I. Calculate center and scale parameters %%%
%
% [Xnew,Means,Scales]=nprocess(X,DimX,Cent,Scal);
%
% INPUT
% X Data array
% DimX Size of X
% Cent is binary row vector with as many elements as DimX.
% If Cent(i)=1 the centering across the i'th mode is performed
% I.e cnt = [1 0 1] means centering across mode one and three.
% Scal is defined likewise. Scal(i)=1, means scaling to standard
% deviation one within the i'th mode
%
% OUTPUT
% Xnew The preprocessed data
% mX Sparse vector holding the mean-values
% sX Sparse vector holding the scales
%
% %%% II. Use given center and scale parameters %%%
%
% Xnew=nprocess(X,DimX,Cent,Scal,mX,sX);
%
% INPUT
% X Data array
% DimX Size of X
% Cent is binary row vector with as many elements as DimX.
% If Cent(i)=1 the centering across the i'th mode is performed
% I.e Cent = [1 0 1] means centering across mode one and three.
% Scal is defined likewise. Scal(i)=1, means scaling to standard
% deviation one within the i'th mode
% mX Sparse vector holding the mean-values
% sX Sparse vector holding the scales
% reverse Optional input
% if reverse = 1 normal preprocessing is performed (default)
% if reverse = -1 inverse (post-)processing is performed
%
% OUTPUT
% Xnew The preprocessed data
%
% For convenience this m-file does not use iterative
% preprocessing, which is necessary for some combinations of scaling
% and centering. Instead the algorithm first standardizes the modes
% successively and afterwards centers. The prior standardization ensures
% that the individual variables are on similar scale (this might be slightly
% disturbed upon centering - unlike for two-way data).
%
% Copyright
% Rasmus Bro 1997
% Denmark
% E-mail rb@kvl.dk
ord = ndims(X);
DimX = size(X);
Xnew = X;
if nargin<3
error(' Three input arguments must be given')
end
if nargin==4
error(' You must input both mX and sX even if you are only doing centering')
end
if nargin<8
usemse=0;
end
if ~exist('mX','var')
mX = [];
end
if ~exist('sX','var')
sX = [];
end
MODE = isa(mX,'cell')&isa(sX,'cell');
if ~(exist('show')==1)
show=1;
end
if ~exist('reverse')==1
reverse=1;
end
if ~any([1 -1]==reverse)
error( 'The input <<reverse>> must be one or minus one')
end
if show~=-1
if ~MODE
disp(' Calculating mean and scale and processing data')
else
if reverse==1
disp(' Using given mean and scale values for preprocessing data')
elseif reverse==-1
disp(' Using given mean and scale values for postprocessing data')
end
end
end
for i=1:ndims(X)
Inds{i} = ones(size(Xnew,i),1);
end
Indm = repmat({':'},ndims(Xnew) - 1,1);
out=0;
if ~MODE
mX = cell(ord,1);
sX = cell(ord,1);
end
Ord2Patch = [2,1;1,2];
if reverse == 1
%Standardize
for j = ord:-1:1
o = [j 1:j-1 j+1:ord];
if Scal(j)
if show~=-1
disp([' Scaling mode ',num2str(j)])
end
if ~MODE
if ~usemse
sX{j} = (stdnan(nshape(Xnew,j)')').^-1;
else
sX{j} = (rmsenan(nshape(Xnew,j)')').^-1;
end
end
Xnew = Xnew.*ipermute(sX{j}(:,Inds{o(2:end)}),o);
end
end
%Center
for j = ord:-1:1
o = [1:j-1 j+1:ord,j];
if Cent(j)
if show~=-1
if ~MODE
disp([' Centering mode ',num2str(j)])
else
disp([' Subtracting off-sets in mode ',num2str(j)])
end
end
if ~MODE
if ord ~= 2
mmm = nshape(Xnew,j);
if min(size(mmm))==1
mmm = mmm;
else
mmm = missmean(mmm);
end
mX{j} = reshape(mmm,DimX(o(1:end-1)));
else
mX{j} = reshape(missmean(nshape(Xnew,j)),DimX(o(1)),1);
end
end
size(Xnew)
size(ipermute(mX{j}(Indm{:},Inds{j}),o))
Xnew = Xnew - ipermute(mX{j}(Indm{:},Inds{j}),o);
end
end
else
%Center
for j = 1:ord
if Cent(j)
if show~=-1
disp([' Adding off-sets in mode ',num2str(j)])
end
Xnew = Xnew + ipermute(mX{j}(Indm{:},Inds{j}),[1:j-1 j+1:ord,j]);
end
end
%Standardize
for j = 1:ord
o = [1:j-1 j+1:ord];
if Scal(j)
if show~=-1
disp([' Rescaling back to original domain in mode ',num2str(j)])
end
Xnew = Xnew ./ ipermute(sX{j}(:,Inds{o}),[j o]);
end
end
end
function st=rmsenan(X);
%RMSENAN estimate RMSE with NaN's
%
% Estimates the RMSE of each column of X
% when there are NaN's in X.
%
% Columns with only NaN's get a standard deviation of zero
% $ 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
% E-mail: rb@kvl.dk
[I,J]=size(X);
st=[];
for j=1:J
id=find(~isnan(X(:,j)));
if length(id)
st=[st sqrt(mean(X(id,j).^2))];
else
st=[st 0];
end
end