comparison toolboxes/MIRtoolbox1.3.2/somtoolbox/som_demo1.m @ 0:e9a9cd732c1e tip

first hg version after svn

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