function [x,sNorm] = som_norm_variable(x, method, operation)%SOM_NORM_VARIABLE Normalize or denormalize a scalar variable.%% [x,sNorm] = som_norm_variable(x, method, operation)%%   xnew = som_norm_variable(x,'var','do');%   [dummy,sN] = som_norm_variable(x,'log','init');%   [xnew,sN]  = som_norm_variable(x,sN,'do');%   xorig      = som_norm_variable(xnew,sN,'undo');%%  Input and output arguments: %   x         (vector) a set of values of a scalar variable for%                      which the (de)normalization is performed.%                      The processed values are returned.%   method    (string) identifier for a normalization method: 'var',%                      'range', 'log', 'logistic', 'histD', or 'histC'.%                      A normalization struct with default values is created.%             (struct) normalization struct, or an array of such%             (cellstr) first string gives normalization operation, and the%                      second gives denormalization operation, with x %                      representing the variable, for example: %                      {'x+2','x-2}, or {'exp(-x)','-log(x)'} or {'round(x)'}.%                      Note that in the last case, no denorm operation is %                      defined. %   operation (string) the operation to be performed: 'init', 'do' or 'undo'%                     %   sNorm     (struct) updated normalization struct/struct array%% For more help, try 'type som_norm_variable' or check out online documentation.% See also SOM_NORMALIZE, SOM_DENORMALIZE.%%%%%%%%%%%%% DETAILED DESCRIPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% som_norm_variable%% PURPOSE%% Initialize, apply and undo normalizations on a given vector of% scalar values.%% SYNTAX%%  xnew = som_norm_variable(x,method,operation)%  xnew = som_norm_variable(x,sNorm,operation)%  [xnew,sNorm] = som_norm_variable(...)%% DESCRIPTION%% This function is used to initialize, apply and undo normalizations% on scalar variables. It is the low-level function that upper-level% functions SOM_NORMALIZE and SOM_DENORMALIZE utilize to actually (un)do% the normalizations.%% Normalizations are typically performed to control the variance of % vector components. If some vector components have variance which is% significantly higher than the variance of other components, those% components will dominate the map organization. Normalization of % the variance of vector components (method 'var') is used to prevent % that. In addition to variance normalization, other methods have% been implemented as well (see list below). %% Usually normalizations convert the variable values so that they no % longer make any sense: the values are still ordered, but their range % may have changed so radically that interpreting the numbers in the % original context is very hard. For this reason all implemented methods% are (more or less) revertible. The normalizations are monotonic% and information is saved so that they can be undone. Also, the saved% information makes it possible to apply the EXACTLY SAME normalization% to another set of values. The normalization information is determined% with 'init' operation, while 'do' and 'undo' operations are used to% apply or revert the normalization. %% The normalization information is saved in a normalization struct, % which is returned as the second argument of this function. Note that % normalization operations may be stacked. In this case, normalization % structs are positioned in a struct array. When applied, the array is % gone through from start to end, and when undone, in reverse order.%%    method  description%%    'var'   Variance normalization. A linear transformation which %            scales the values such that their variance=1. This is%            convenient way to use Mahalanobis distance measure without%            actually changing the distance calculation procedure.%%    'range' Normalization of range of values. A linear transformation%            which scales the values between [0,1]. %%    'log'   Logarithmic normalization. In many cases the values of%            a vector component are exponentially distributed. This %            normalization is a good way to get more resolution to%            (the low end of) that vector component. What this %            actually does is a non-linear transformation: %               x_new = log(x_old - m + 1) %            where m=min(x_old) and log is the natural logarithm. %            Applying the transformation to a value which is lower %            than m-1 will give problems, as the result is then complex.%            If the minimum for values is known a priori, %            it might be a good idea to initialize the normalization with%              [dummy,sN] = som_norm_variable(minimum,'log','init');%            and normalize only after this: %              x_new = som_norm_variable(x,sN,'do');%%    'logistic' or softmax normalization. This normalization ensures%            that all values in the future, too, are within the range%            [0,1]. The transformation is more-or-less linear in the %            middle range (around mean value), and has a smooth %            nonlinearity at both ends which ensures that all values%            are within the range. The data is first scaled as in %            variance normalization: %               x_scaled = (x_old - mean(x_old))/std(x_old)%            and then transformed with the logistic function%               x_new = 1/(1+exp(-x_scaled))% %    'histD' Discrete histogram equalization. Non-linear. Orders the %            values and replaces each value by its ordinal number. %            Finally, scales the values such that they are between [0,1].%            Useful for both discrete and continuous variables, but as %            the saved normalization information consists of all %            unique values of the initialization data set, it may use%            considerable amounts of memory. If the variable can get%            more than a few values (say, 20), it might be better to%            use 'histC' method below. Another important note is that%            this method is not exactly revertible if it is applied%            to values which are not part of the original value set.%            %    'histC' Continuous histogram equalization. Actually, a partially%            linear transformation which tries to do something like %            histogram equalization. The value range is divided to %            a number of bins such that the number of values in each%            bin is (almost) the same. The values are transformed %            linearly in each bin. For example, values in bin number 3%            are scaled between [3,4[. Finally, all values are scaled%            between [0,1]. The number of bins is the square root%            of the number of unique values in the initialization set,%            rounded up. The resulting histogram equalization is not%            as good as the one that 'histD' makes, but the benefit%            is that it is exactly revertible - even outside the %            original value range (although the results may be funny).%%    'eval'  With this method, freeform normalization operations can be %            specified. The parameter field contains strings to be %            evaluated with 'eval' function, with variable name 'x'%            representing the variable itself. The first string is %            the normalization operation, and the second is a %            denormalization operation. If the denormalization operation%            is empty, it is ignored.% % INPUT ARGUMENTS%%   x          (vector) The scalar values to which the normalization      %                       operation is applied.%                     %   method              The normalization specification.%              (string) Identifier for a normalization method: 'var', %                       'range', 'log', 'logistic', 'histD' or 'histC'. %                       Corresponding default normalization struct is created.%              (struct) normalization struct %              (struct array) of normalization structs, applied to %                       x one after the other%              (cellstr) of length %              (cellstr array) first string gives normalization operation, and %                       the second gives denormalization operation, with x %                       representing the variable, for example: %                       {'x+2','x-2}, or {'exp(-x)','-log(x)'} or {'round(x)'}.%                       Note that in the last case, no denorm operation is %                       defined. %%               note: if the method is given as struct(s), it is%                     applied (done or undone, as specified by operation)%                     regardless of what the value of '.status' field%                     is in the struct(s). Only if the status is%                     'uninit', the undoing operation is halted.%                     Anyhow, the '.status' fields in the returned %                     normalization struct(s) is set to approriate value.%   %   operation  (string) The operation to perform: 'init' to initialize%                       the normalization struct, 'do' to perform the %                       normalization, 'undo' to undo the normalization, %                       if possible. If operation 'do' is given, but the%                       normalization struct has not yet been initialized,%                       it is initialized using the given data (x).%% OUTPUT ARGUMENTS% %   x        (vector) Appropriately processed values. %%   sNorm    (struct) Updated normalization struct/struct array. If any,%                     the '.status' and '.params' fields are updated.% % EXAMPLES%%  To initialize and apply a normalization on a set of scalar values: %%    [x_new,sN] = som_norm_variable(x_old,'var','do'); %%  To just initialize, use: % %    [dummy,sN] = som_norm_variable(x_old,'var','init'); % %  To undo the normalization(s): %%    x_orig = som_norm_variable(x_new,sN,'undo');%%  Typically, normalizations of data structs/sets are handled using%  functions SOM_NORMALIZE and SOM_DENORMALIZE. However, when only the%  values of a single variable are of interest, SOM_NORM_VARIABLE may %  be useful. For example, assume one wants to apply the normalization%  done on a component (i) of a data struct (sD) to a new set of values %  (x) of that component. With SOM_NORM_VARIABLE this can be done with: %%    x_new = som_norm_variable(x,sD.comp_norm{i},'do'); % %  Now, as the normalizations in sD.comp_norm{i} have already been %  initialized with the original data set (presumably sD.data), %  the EXACTLY SAME normalization(s) can be applied to the new values.%  The same thing can be done with SOM_NORMALIZE function, too: %%    x_new = som_normalize(x,sD.comp_norm{i}); %%  Or, if the new data set were in variable D - a matrix of same%  dimension as the original data set: %%    D_new = som_normalize(D,sD,i);%% SEE ALSO%  %  som_normalize    Add/apply/redo normalizations for a data struct/set.%  som_denormalize  Undo normalizations of a data struct/set.% Copyright (c) 1998-2000 by the SOM toolbox programming team.% http://www.cis.hut.fi/projects/somtoolbox/% Version 2.0beta juuso 151199 170400 150500%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% check argumentserror(nargchk(3, 3, nargin));  % check no. of input arguments is correct% methodsNorm = []; if ischar(method)   if any(strcmp(method,{'var','range','log','logistic','histD','histC'})),     sNorm = som_set('som_norm','method',method);  else     method = cellstr(method);   endendif iscell(method),   if length(method)==1 & isstruct(method{1}), sNorm = method{1};   else    if length(method)==1 | isempty(method{2}), method{2} = 'x'; end    sNorm = som_set('som_norm','method','eval','params',method);  endelse   sNorm = method; end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% actionorder = [1:length(sNorm)]; if length(order)>1 & strcmp(operation,'undo'), order = order(end:-1:1); endfor i=order,