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Info on the mapping class construction of PRTools

This is not a command, just an information file.

Mappings in PRTools are in the MATLAB language defined as objects of the  class MAPPING. In the text below, the words 'object' and 'class' are used  in the pattern recognition sense.

In the Pattern Recognition Toolbox PRTools, there are many commands to  define, train and use mappings between spaces of different (or equal)  dimensionalities. Mappings operate mainly on datasets, i.e. variables of  the type DATASET (see also DATASETS) and generate datasets and/or other  mappings. For example

    if    A  is a M x K dataset (M objects in  a K-dimensional space)
    and   W  is a K x N mapping (a map from K to N dimensions)
    then A*W is a M x N dataset (M objects in  a N-dimensional space)

This is enabled by overloading the *-operator for the MAPPING variables.  A*W is executed by MAP(A,W) and may also be called as such.

Mappings can be linear (e.g. a rotation) as well as nonlinear (e.g. a  neural network). Typically they are used to represent classifiers. In that  case, a K x C mapping maps a K-feature data vector on the output space of  a C-class classifier (an exception: some 2-class classifiers, like the  discriminant functions may be implemented by a mapping onto a 1-dimensional  space determined by the distance to the discriminant).

Mappings are of the data-type MAPPING (CLASS(W) is a MAPPING), have a size  of K x C if they map from K to C dimensions. Four types of mapping are  defined

untrained, V = A*W.

Trains the untrained mapping W, resulting in the trained mapping V. W has to be defined by W = MAPPING(MAPPING_FILE,{PAR1, PAR2}), in which  MAPPING_FILE is the name of the routine that executes the training and  PAR1, and PAR2 are two parameters that have to be included into the call  to MAPPING_FILE. Consequently, A*W is executed by PRTools as  MAPPING_FILE(A,PAR1,PAR2).

Example: train the 3-NN classifier on the generated data.

  W = knnc([],3);         % untrained classifier
  V = gendatd([50 50])*W; % trained classifier

trained, D = B*V

Maps the dataset B on the trained mapping or classifier V, e.g. as  trained above. The resulting dataset D has as many objects (rows) as A,  but its feature size is now C if V is a K x C mapping. Typically, C is  the number of classes in the training set A or a reduced number of  features determined by the the training of V. V is defined by  V = MAPPING(MAPPING_FILE,'trained',DATA,LABELS,SIZE_IN,SIZE_OUT),  in which the MAPPING_FILE is the name of the routine that executes the  mapping, DATA is a field in which the parameters are stored (e.g.  weights) for the mapping execution, LABELS are the feature labels to be  assigned to the resulting dataset D = B*V (e.g. the class names) and  SIZE_IN and SIZE_OUT are the dimensionalities of the input and output  spaces. They are used for error checking only. D = B*V is executed by  PRTools as MAPPING_FILE(B,W). Example:

  A = gendatd([50 50],10);  % generate random 10D datasets
  B = gendatd([50 50],10);
  W = klm([],0.9);          % untrained mapping, Karhunen-Loeve projection
  V = A*W;                  % trained mapping V
  D = B*V;                  % the result of the projection of B onto V

fixed, D = A*W

Maps the dataset A by the fixed mapping W, resulting into a transformed  dataset D. Examples are scaling and normalization, e.g. W = MAPPING('SIGM','fixed',S) defines a fixed mapping by the sigmoid function  SIGM a scaling parameter S. A*W is executed by PRTools as SIGM(A,S).

Example: normalize the distances of all objects in A such that their  city block distances to the origin are one.

  A = gendatb([50 50]);
  W = normm;
  D = A*W;

combiner, U = V*W

Combines two mappings. The mapping W is able to combine itself with V and produces a single mapping U. A combiner is defined by  W = MAPPING(MAPPING_FILE,'combiner',{PAR1,PAR2}) in which MAPPING_FILE is the name of the routine that executes the  combining and PAR1, and PAR2 are the parameters that have to be included  into the call to the MAPPING_FILE. Consequently, V*W is executed by  PRTools as MAPPING_FILE(V,PAR1,PAR2). In a call as D = A*V*W, first B = A*V is resolved and may result in a dataset B. Consequently, W should be  able to handle datasets, and MAPPING_FILE is now called by  MAPPING_FILE(B,PAR1,PAR2) Remark: the combiner construction is not  necessary, since PRTools stores U = V*W as a SEQUENTIAL mapping (see  below) if W is not a combiner. The construction of combiners, however,  may increase the transparency for the user and efficiency in  computations. Example:

  A = gendatd([50 50],10); % generate random 10D datasets
  B = gendatd([50 50],10);
  V = klm([],0.9);         % untrained Karhunen-Loeve (KL) projection
  W = ldc;                 % untrained linear classifier LDC
  U = V*W;                 % untrained combiner
  T = A*U;                 % trained combiner
  D = B*T;                 % apply the combiner (first KL projection, 
                           %       then LDC) to B

Differences between the four types of mappings are now summarized for  a dataset A and a mapping W

  • untrained : results in a mapping
  • trained : results in a dataset, size checking
  • fixed : results in a dataset, no size checking
  • combiner : treated as fixed

Suppose V is a fixed mapping, then for the various possibilities of  the mapping W, the following holds

  • untrained : evaluated as V*(A*V*W), resulting in a mapping
  • trained : evaluated as A*V*W, resulting in a dataset
  • fixed : evaluated as A*V*W, resulting in a dataset
  • combiner : evaluated as A*V*W, resulting in a dataset

Suppose V is an untrained mapping, then for the various possibilities of  the mapping W holds

  • untrained : evaluated as A*V*(A*(A*V)*W), resulting in a mapping
  • trained : evaluated as A*V*W, resulting in a mapping
  • fixed : evaluated as A*V*W, resulting in a mapping
  • combiner : evaluated as A*(V*W), resulting in a mapping

Suppose V is a trained mapping, then for the various possibilities of  the mapping W holds

  • untrained : evaluated as V*(A*V*W), resulting in a mapping
  • trained : evaluated as A*V*W, resulting in a dataset
  • fixed : evaluated as A*V*W, resulting in a dataset
  • combiner : evaluated as A*(V*W), resulting in a dataset

The data fields stored in the MAPPING W = A*QDC can be found by


which may display

     MAPPING_FILE: 'normal_map'
     MAPPING_TYPE: 'trained'
     DATA:          [1x1 struct]
     LABELS:        [2x1 double]
     SIZE_IN:       2
     SIZE_OUT:      2
     SCALE:         1
     COST:          []
     OUT_CONV:      0
     NAME:          []
     USER:          []
     VERSION:       {1x2 cell  }

These fields have the following meaning
MAPPING_FILE: Name of the m-file that executes the mapping.  MAPPING_TYPE: Type of mapping: 'untrained','trained','fixed' or 'combiner'.

 DATA: Parameters or data for handling or executing the mapping.
 LABELS: Label list used as FEATLAB for labeling the features of the  output DATASET.
 SIZE_IN: Expected input dimensionality of the data to be mapped.  If not set, it is neglected, otherwise it is used for the error  checking and display of the mapping size on the command line.
 SIZE_OUT: Dimensionality of the output space. It should correspond to the  size of LABLIST. SIZE_OUT may be size vector, e.g. describing  the size of an image. See also the FEATSIZE field of DATASET.
 SCALE: Output multiplication factor. If SCALE is a scalar all  multiplied by it. SCALE may also be a vector with size as  defined by SIZE_OUT to set separate scalings for each output.
 COST: Classification costs in case the mapping defines a classifier.
 OUT_CONV: Defines for trained and fixed mappings the output conversion:
  • 0 : no conversion (to be used for mappings that output  confidences or densities;
  • 1 : sigmoid (for discriminants that output distances);
  • 2 : normalisation (for converting densities and confidences  into posterior probability estimates;
  • 3 : for performing sigmoid as well as normalisation.
 NAME: Name of the mapping, used for informing the user on the  command line, as well as for annotating plots.
 USER: User field, not used by PRTools.
 VERSION: Some information related to the version of PRTools used for  the mapping definition.

The fields can be set by commands like SETMAPPING_FILE, SETDATA, SETLABELS SETSIZE, and may be retrieved by commands like GETMAPPING_FILE, GETDATA GETLABELS and SETSIZE. Information stored in a mapping can be found  as follows

Some standard MATLAB operations have been overloaded for variables of the  type MAPPING. They are defined as follows

 W' Defined for affine mappings only. It returns a transposed mapping.
 [W,V] Builds a combined classifier (see STACKED) operating in the same  feature space. aA * [W V] = [A*W A*V].
 [W;V] Builds a combined classifier (see PARALLEL) operating in different  feature spaces: [A B] * [W;V] = [A*W B*V]. W and V should be  mappings that correspond to the feature sizes of A and B.
 A*W Maps a DATASET A by the MAPPING W. This is executed by MAP(A,W).
 V*W Combines the mappings V and W sequentially. This is executed by  SEQUENTIAL(V,W).
 W+CON Adding a constant is defined for affine mappings only.
 W(:,K) Output selection. If W is a trained mapping, just the features  listed in K are returned.

See also

mapping, classc, cnormc, labeld,

nmc, knnc, udc, ldc, qdc, mogc, quadrc, fisherc, parzenc, parzendc, treec, loglc, naivebc, svc, rbsvc, nusvc, libsvc, treec, perlc, bpxnc, rbnc, lmnc, weakc, stumpc, subsc, adaboostc, baggingc, fdsc, vpc, drbmc,

Classifier Combiners
stacked, parallel, sequential, meanc, averagec, prodc, medianc, minc, maxc, votec, wvotec, modselc, dcsc, rsscc, mlrc, naivebcc, traincc,

Density Estimation
gaussm, parzenm, knnm,

Dimension Reduction
featsel, featselb, featself, featseli, featsellr, featselm, featselo, featselp, featselv, bhatm, fisherm, chernoffm, klm, klms, nlfisherm, pca, reducm,

scalem, cmapm, sigm, invsigm, normm,

Set commands
setbatch, setcost, setdata, setlabels, setmapping_file, setmapping_type, setname, setout_conv, setpostproc, setscale, setsize, setsize_in, setsize_out, setuser,

Get commands
getbatch, getcost, getdata, getlabels, getmapping_file, getmapping_type, getname, getout_conv, getscale, getsize, getsize_in, getsize_out, getuser,

isaffine, isclassifier, isempty, isparallel, isstacked, issequential, istrained, isuntrained, isfixed, iscombiner,

PRTools contents

PRTools manual