%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 onclc%    ==========================================================%    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...clfclc%    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 onsom_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...clfclc%    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 offtitle('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 offsubplot(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))  drawnowendtitle('Sequential training after 300 steps')echo onpause % Strike any key to continue with 3D data...clfclc%    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 ontitle('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