Daniel@0: 
Daniel@0: %SOM_DEMO1 Basic properties and behaviour of the Self-Organizing Map.
Daniel@0: 
Daniel@0: % Contributed to SOM Toolbox 2.0, February 11th, 2000 by Juha Vesanto
Daniel@0: % http://www.cis.hut.fi/projects/somtoolbox/
Daniel@0: 
Daniel@0: % Version 1.0beta juuso 071197
Daniel@0: % Version 2.0beta juuso 030200 
Daniel@0: 
Daniel@0: clf reset;
Daniel@0: figure(gcf)
Daniel@0: echo on
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: clc
Daniel@0: %    ==========================================================
Daniel@0: %    SOM_DEMO1 - BEHAVIOUR AND PROPERTIES OF SOM
Daniel@0: %    ==========================================================
Daniel@0: 
Daniel@0: %    som_make        - Create, initialize and train a SOM.
Daniel@0: %     som_randinit   - Create and initialize a SOM.
Daniel@0: %     som_lininit    - Create and initialize a SOM.
Daniel@0: %     som_seqtrain   - Train a SOM.
Daniel@0: %     som_batchtrain - Train a SOM.
Daniel@0: %    som_bmus        - Find best-matching units (BMUs).
Daniel@0: %    som_quality     - Measure quality of SOM.
Daniel@0: 
Daniel@0: %    SELF-ORGANIZING MAP (SOM):
Daniel@0: 
Daniel@0: %    A self-organized map (SOM) is a "map" of the training data, 
Daniel@0: %    dense where there is a lot of data and thin where the data 
Daniel@0: %    density is low. 
Daniel@0: 
Daniel@0: %    The map constitutes of neurons located on a regular map grid. 
Daniel@0: %    The lattice of the grid can be either hexagonal or rectangular.
Daniel@0: 
Daniel@0: subplot(1,2,1)
Daniel@0: som_cplane('hexa',[10 15],'none')
Daniel@0: title('Hexagonal SOM grid')
Daniel@0: 
Daniel@0: subplot(1,2,2)
Daniel@0: som_cplane('rect',[10 15],'none')
Daniel@0: title('Rectangular SOM grid')
Daniel@0: 
Daniel@0: %    Each neuron (hexagon on the left, rectangle on the right) has an
Daniel@0: %    associated prototype vector. After training, neighboring neurons
Daniel@0: %    have similar prototype vectors.
Daniel@0: 
Daniel@0: %    The SOM can be used for data visualization, clustering (or 
Daniel@0: %    classification), estimation and a variety of other purposes.
Daniel@0: 
Daniel@0: pause % Strike any key to continue...
Daniel@0: 
Daniel@0: clf
Daniel@0: clc
Daniel@0: %    INITIALIZE AND TRAIN THE SELF-ORGANIZING MAP
Daniel@0: %    ============================================
Daniel@0: 
Daniel@0: %    Here are 300 data points sampled from the unit square:
Daniel@0: 
Daniel@0: D = rand(300,2);
Daniel@0: 
Daniel@0: %    The map will be a 2-dimensional grid of size 10 x 10.
Daniel@0: 
Daniel@0: msize = [10 10];
Daniel@0: 
Daniel@0: %    SOM_RANDINIT and SOM_LININIT can be used to initialize the
Daniel@0: %    prototype vectors in the map. The map size is actually an
Daniel@0: %    optional argument. If omitted, it is determined automatically
Daniel@0: %    based on the amount of data vectors and the principal
Daniel@0: %    eigenvectors of the data set. Below, the random initialization
Daniel@0: %    algorithm is used.
Daniel@0: 
Daniel@0: sMap  = som_randinit(D, 'msize', msize);
Daniel@0: 
Daniel@0: %    Actually, each map unit can be thought as having two sets
Daniel@0: %    of coordinates: 
Daniel@0: %      (1) in the input space:  the prototype vectors
Daniel@0: %      (2) in the output space: the position on the map
Daniel@0: %    In the two spaces, the map looks like this: 
Daniel@0: 
Daniel@0: subplot(1,3,1) 
Daniel@0: som_grid(sMap)
Daniel@0: axis([0 11 0 11]), view(0,-90), title('Map in output space')
Daniel@0: 
Daniel@0: subplot(1,3,2) 
Daniel@0: plot(D(:,1),D(:,2),'+r'), hold on
Daniel@0: som_grid(sMap,'Coord',sMap.codebook)
Daniel@0: title('Map in input space')
Daniel@0: 
Daniel@0: %    The black dots show positions of map units, and the gray lines
Daniel@0: %    show connections between neighboring map units.  Since the map
Daniel@0: %    was initialized randomly, the positions in in the input space are
Daniel@0: %    completely disorganized. The red crosses are training data.
Daniel@0: 
Daniel@0: pause % Strike any key to train the SOM...
Daniel@0: 
Daniel@0: %    During training, the map organizes and folds to the training
Daniel@0: %    data. Here, the sequential training algorithm is used:
Daniel@0: 
Daniel@0: sMap  = som_seqtrain(sMap,D,'radius',[5 1],'trainlen',10);
Daniel@0: 
Daniel@0: subplot(1,3,3)
Daniel@0: som_grid(sMap,'Coord',sMap.codebook)
Daniel@0: hold on, plot(D(:,1),D(:,2),'+r')
Daniel@0: title('Trained map')
Daniel@0: 
Daniel@0: pause % Strike any key to view more closely the training process...
Daniel@0: 
Daniel@0: 
Daniel@0: clf
Daniel@0: 
Daniel@0: clc
Daniel@0: %    TRAINING THE SELF-ORGANIZING MAP
Daniel@0: %    ================================
Daniel@0: 
Daniel@0: %    To get a better idea of what happens during training, let's look
Daniel@0: %    at how the map gradually unfolds and organizes itself. To make it
Daniel@0: %    even more clear, the map is now initialized so that it is away
Daniel@0: %    from the data.
Daniel@0: 
Daniel@0: sMap = som_randinit(D,'msize',msize);
Daniel@0: sMap.codebook = sMap.codebook + 1;
Daniel@0: 
Daniel@0: subplot(1,2,1)
Daniel@0: som_grid(sMap,'Coord',sMap.codebook)
Daniel@0: hold on, plot(D(:,1),D(:,2),'+r'), hold off
Daniel@0: title('Data and original map')
Daniel@0: 
Daniel@0: %    The training is based on two principles: 
Daniel@0: %     
Daniel@0: %      Competitive learning: the prototype vector most similar to a
Daniel@0: %      data vector is modified so that it it is even more similar to
Daniel@0: %      it. This way the map learns the position of the data cloud.
Daniel@0: %
Daniel@0: %      Cooperative learning: not only the most similar prototype
Daniel@0: %      vector, but also its neighbors on the map are moved towards the
Daniel@0: %      data vector. This way the map self-organizes.
Daniel@0: 
Daniel@0: pause % Strike any key to train the map...
Daniel@0: 
Daniel@0: echo off
Daniel@0: subplot(1,2,2)
Daniel@0: o = ones(5,1);
Daniel@0: r = (1-[1:60]/60);
Daniel@0: for i=1:60,
Daniel@0:   sMap = som_seqtrain(sMap,D,'tracking',0,...
Daniel@0: 		      'trainlen',5,'samples',...
Daniel@0: 		      'alpha',0.1*o,'radius',(4*r(i)+1)*o);
Daniel@0:   som_grid(sMap,'Coord',sMap.codebook)
Daniel@0:   hold on, plot(D(:,1),D(:,2),'+r'), hold off
Daniel@0:   title(sprintf('%d/300 training steps',5*i))
Daniel@0:   drawnow
Daniel@0: end
Daniel@0: title('Sequential training after 300 steps')
Daniel@0: echo on
Daniel@0: 
Daniel@0: pause % Strike any key to continue with 3D data...
Daniel@0: 
Daniel@0: clf
Daniel@0: 
Daniel@0: clc
Daniel@0: %    TRAINING DATA: THE UNIT CUBE
Daniel@0: %    ============================
Daniel@0: 
Daniel@0: %    Above, the map dimension was equal to input space dimension: both
Daniel@0: %    were 2-dimensional. Typically, the input space dimension is much
Daniel@0: %    higher than the 2-dimensional map. In this case the map cannot
Daniel@0: %    follow perfectly the data set any more but must find a balance
Daniel@0: %    between two goals:
Daniel@0: 
Daniel@0: %      - data representation accuracy
Daniel@0: %      - data set topology representation accuracy    
Daniel@0: 
Daniel@0: %    Here are 500 data points sampled from the unit cube:
Daniel@0: 
Daniel@0: D = rand(500,3);
Daniel@0: 
Daniel@0: subplot(1,3,1), plot3(D(:,1),D(:,2),D(:,3),'+r')
Daniel@0: view(3), axis on, rotate3d on
Daniel@0: title('Data')
Daniel@0: 
Daniel@0: %    The ROTATE3D command enables you to rotate the picture by
Daniel@0: %    dragging the pointer above the picture with the leftmost mouse
Daniel@0: %    button pressed down.
Daniel@0: 
Daniel@0: pause % Strike any key to train the SOM...
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: clc
Daniel@0: %    DEFAULT TRAINING PROCEDURE
Daniel@0: %    ==========================
Daniel@0: 
Daniel@0: %    Above, the initialization was done randomly and training was done
Daniel@0: %    with sequential training function (SOM_SEQTRAIN). By default, the
Daniel@0: %    initialization is linear, and batch training algorithm is
Daniel@0: %    used. In addition, the training is done in two phases: first with
Daniel@0: %    large neighborhood radius, and then finetuning with small radius.
Daniel@0: 
Daniel@0: %    The function SOM_MAKE can be used to both initialize and train
Daniel@0: %    the map using default parameters:
Daniel@0: 
Daniel@0: pause % Strike any key to use SOM_MAKE...
Daniel@0: 
Daniel@0: sMap = som_make(D);
Daniel@0: 
Daniel@0: %    Here, the linear initialization is done again, so that 
Daniel@0: %    the results can be compared.
Daniel@0: 
Daniel@0: sMap0 = som_lininit(D); 
Daniel@0: 
Daniel@0: subplot(1,3,2)
Daniel@0: som_grid(sMap0,'Coord',sMap0.codebook,...
Daniel@0: 	 'Markersize',2,'Linecolor','k','Surf',sMap0.codebook(:,3)) 
Daniel@0: axis([0 1 0 1 0 1]), view(-120,-25), title('After initialization')
Daniel@0: 
Daniel@0: subplot(1,3,3)
Daniel@0: som_grid(sMap,'Coord',sMap.codebook,...
Daniel@0: 	 'Markersize',2,'Linecolor','k','Surf',sMap.codebook(:,3)) 
Daniel@0: axis([0 1 0 1 0 1]), view(3), title('After training'), hold on
Daniel@0: 
Daniel@0: %    Here you can see that the 2-dimensional map has folded into the
Daniel@0: %    3-dimensional space in order to be able to capture the whole data
Daniel@0: %    space. 
Daniel@0: 
Daniel@0: pause % Strike any key to evaluate the quality of maps...
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: clc
Daniel@0: %    BEST-MATCHING UNITS (BMU)
Daniel@0: %    =========================
Daniel@0: 
Daniel@0: %    Before going to the quality, an important concept needs to be
Daniel@0: %    introduced: the Best-Matching Unit (BMU). The BMU of a data
Daniel@0: %    vector is the unit on the map whose model vector best resembles
Daniel@0: %    the data vector. In practise the similarity is measured as the
Daniel@0: %    minimum distance between data vector and each model vector on the
Daniel@0: %    map. The BMUs can be calculated using function SOM_BMUS. This
Daniel@0: %    function gives the index of the unit.
Daniel@0: 
Daniel@0: %    Here the BMU is searched for the origin point (from the
Daniel@0: %    trained map):
Daniel@0: 
Daniel@0: bmu = som_bmus(sMap,[0 0 0]);
Daniel@0: 
Daniel@0: %    Here the corresponding unit is shown in the figure. You can
Daniel@0: %    rotate the figure to see better where the BMU is.
Daniel@0: 
Daniel@0: co = sMap.codebook(bmu,:);
Daniel@0: text(co(1),co(2),co(3),'BMU','Fontsize',20)
Daniel@0: plot3([0 co(1)],[0 co(2)],[0 co(3)],'ro-')
Daniel@0: 
Daniel@0: pause % Strike any key to analyze map quality...
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0: clc
Daniel@0: %    SELF-ORGANIZING MAP QUALITY
Daniel@0: %    ===========================
Daniel@0: 
Daniel@0: %    The maps have two primary quality properties:
Daniel@0: %      - data representation accuracy
Daniel@0: %      - data set topology representation accuracy
Daniel@0: 
Daniel@0: %    The former is usually measured using average quantization error
Daniel@0: %    between data vectors and their BMUs on the map.  For the latter
Daniel@0: %    several measures have been proposed, e.g. the topographic error
Daniel@0: %    measure: percentage of data vectors for which the first- and
Daniel@0: %    second-BMUs are not adjacent units.
Daniel@0: 
Daniel@0: %    Both measures have been implemented in the SOM_QUALITY function.
Daniel@0: %    Here are the quality measures for the trained map: 
Daniel@0: 
Daniel@0: [q,t] = som_quality(sMap,D)
Daniel@0: 
Daniel@0: %    And here for the initial map:
Daniel@0: 
Daniel@0: [q0,t0] = som_quality(sMap0,D)
Daniel@0: 
Daniel@0: %    As can be seen, by folding the SOM has reduced the average
Daniel@0: %    quantization error, but on the other hand the topology
Daniel@0: %    representation capability has suffered.  By using a larger final
Daniel@0: %    neighborhood radius in the training, the map becomes stiffer and
Daniel@0: %    preserves the topology of the data set better.
Daniel@0: 
Daniel@0: 
Daniel@0: echo off
Daniel@0: 
Daniel@0: