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first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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wolffd@0 1
wolffd@0 2 %SOM_DEMO3 Self-organizing map visualization.
wolffd@0 3
wolffd@0 4 % Contributed to SOM Toolbox 2.0, February 11th, 2000 by Juha Vesanto
wolffd@0 5 % http://www.cis.hut.fi/projects/somtoolbox/
wolffd@0 6
wolffd@0 7 % Version 1.0beta juuso 071197
wolffd@0 8 % Version 2.0beta juuso 080200 070600
wolffd@0 9
wolffd@0 10 clf reset;
wolffd@0 11 figure(gcf)
wolffd@0 12 echo on
wolffd@0 13
wolffd@0 14
wolffd@0 15
wolffd@0 16
wolffd@0 17 clc
wolffd@0 18 % ==========================================================
wolffd@0 19 % SOM_DEMO3 - VISUALIZATION
wolffd@0 20 % ==========================================================
wolffd@0 21
wolffd@0 22 % som_show - Visualize map.
wolffd@0 23 % som_grid - Visualization with free coordinates.
wolffd@0 24 %
wolffd@0 25 % som_show_add - Add markers on som_show visualization.
wolffd@0 26 % som_show_clear - Remove markers from som_show visualization.
wolffd@0 27 % som_recolorbar - Refresh and rescale colorbars in som_show
wolffd@0 28 % visualization.
wolffd@0 29 %
wolffd@0 30 % som_cplane - Visualize component/color/U-matrix plane.
wolffd@0 31 % som_pieplane - Visualize prototype vectors as pie charts.
wolffd@0 32 % som_barplane - Visualize prototype vectors as bar charts.
wolffd@0 33 % som_plotplane - Visualize prototype vectors as line graphs.
wolffd@0 34 %
wolffd@0 35 % pcaproj - Projection to principal component space.
wolffd@0 36 % cca - Projection with Curvilinear Component Analysis.
wolffd@0 37 % sammon - Projection with Sammon's mapping.
wolffd@0 38 % som_umat - Calculate U-matrix.
wolffd@0 39 % som_colorcode - Color coding for the map.
wolffd@0 40 % som_normcolor - RGB values of indexed colors.
wolffd@0 41 % som_hits - Hit histograms for the map.
wolffd@0 42
wolffd@0 43 % The basic functions for SOM visualization are SOM_SHOW and
wolffd@0 44 % SOM_GRID. The SOM_SHOW has three auxiliary functions:
wolffd@0 45 % SOM_SHOW_ADD, SOM_SHOW_CLEAR and SOM_RECOLORBAR which are used
wolffd@0 46 % to add and remove markers and to control the colorbars.
wolffd@0 47 % SOM_SHOW actually uses SOM_CPLANE to make the visualizations.
wolffd@0 48 % Also SOM_{PIE,BAR,PLOT}PLANE can be used to visualize SOMs.
wolffd@0 49
wolffd@0 50 % The other functions listed above do not themselves visualize
wolffd@0 51 % anything, but their results are used in the visualizations.
wolffd@0 52
wolffd@0 53 % There's an important limitation that visualization functions have:
wolffd@0 54 % while the SOM Toolbox otherwise supports N-dimensional map grids,
wolffd@0 55 % visualization only works for 1- and 2-dimensional map grids!!!
wolffd@0 56
wolffd@0 57 pause % Strike any key to create demo data and map...
wolffd@0 58
wolffd@0 59
wolffd@0 60
wolffd@0 61
wolffd@0 62
wolffd@0 63 clc
wolffd@0 64 % DEMO DATA AND MAP
wolffd@0 65 % =================
wolffd@0 66
wolffd@0 67 % The data set contructed for this demo consists of random vectors
wolffd@0 68 % in three gaussian kernels the centers of which are at [0, 0, 0],
wolffd@0 69 % [3 3 3] and [9 0 0]. The map is trained using default parameters.
wolffd@0 70
wolffd@0 71 D1 = randn(100,3);
wolffd@0 72 D2 = randn(100,3) + 3;
wolffd@0 73 D3 = randn(100,3); D3(:,1) = D3(:,1) + 9;
wolffd@0 74
wolffd@0 75 sD = som_data_struct([D1; D2; D3],'name','Demo3 data',...
wolffd@0 76 'comp_names',{'X-coord','Y-coord','Z-coord'});
wolffd@0 77 sM = som_make(sD);
wolffd@0 78
wolffd@0 79 % Since the data (and thus the prototypes of the map) are
wolffd@0 80 % 3-dimensional, they can be directly plotted using PLOT3.
wolffd@0 81 % Below, the data is plotted using red 'o's and the map
wolffd@0 82 % prototype vectors with black '+'s.
wolffd@0 83
wolffd@0 84 plot3(sD.data(:,1),sD.data(:,2),sD.data(:,3),'ro',...
wolffd@0 85 sM.codebook(:,1),sM.codebook(:,2),sM.codebook(:,3),'k+')
wolffd@0 86 rotate3d on
wolffd@0 87
wolffd@0 88 % From the visualization it is pretty easy to see what the data is
wolffd@0 89 % like, and how the prototypes have been positioned. One can see
wolffd@0 90 % that there are three clusters, and that there are some prototype
wolffd@0 91 % vectors between the clusters, although there is actually no
wolffd@0 92 % data there. The map units corresponding to these prototypes
wolffd@0 93 % are called 'dead' or 'interpolative' map units.
wolffd@0 94
wolffd@0 95 pause % Strike any key to continue...
wolffd@0 96
wolffd@0 97
wolffd@0 98
wolffd@0 99 clc
wolffd@0 100 % VISUALIZATION OF MULTIDIMENSIONAL DATA
wolffd@0 101 % ======================================
wolffd@0 102
wolffd@0 103 % Usually visualization of data sets is not this straightforward,
wolffd@0 104 % since the dimensionality is much higher than three. In principle,
wolffd@0 105 % one can embed additional information to the visualization by
wolffd@0 106 % using properties other than position, for example color, size or
wolffd@0 107 % shape.
wolffd@0 108
wolffd@0 109 % Here the data set and map prototypes are plotted again, but
wolffd@0 110 % information of the cluster is shown using color: red for the
wolffd@0 111 % first cluster, green for the second and blue for the last.
wolffd@0 112
wolffd@0 113 plot3(sD.data(1:100,1),sD.data(1:100,2),sD.data(1:100,3),'ro',...
wolffd@0 114 sD.data(101:200,1),sD.data(101:200,2),sD.data(101:200,3),'go',...
wolffd@0 115 sD.data(201:300,1),sD.data(201:300,2),sD.data(201:300,3),'bo',...
wolffd@0 116 sM.codebook(:,1),sM.codebook(:,2),sM.codebook(:,3),'k+')
wolffd@0 117 rotate3d on
wolffd@0 118
wolffd@0 119 % However, this works only for relatively small dimensionality, say
wolffd@0 120 % less than 10. When the information is added this way, the
wolffd@0 121 % visualization becomes harder and harder to understand. Also, not
wolffd@0 122 % all properties are equal: the human visual system perceives
wolffd@0 123 % colors differently from position, not to mention the complex
wolffd@0 124 % rules governing perception of shape.
wolffd@0 125
wolffd@0 126 pause % Strike any key to learn about linking...
wolffd@0 127
wolffd@0 128
wolffd@0 129
wolffd@0 130
wolffd@0 131
wolffd@0 132 clc
wolffd@0 133 % LINKING MULTIPLE VISUALIZATIONS
wolffd@0 134 % ===============================
wolffd@0 135
wolffd@0 136 % The other option is to use *multiple visualizations*, so called
wolffd@0 137 % small multiples, instead of only one. The problem is then how to
wolffd@0 138 % link these visualizations together: one should be able to idetify
wolffd@0 139 % the same object from the different visualizations.
wolffd@0 140
wolffd@0 141 % This could be done using, for example, color: each object has
wolffd@0 142 % the same color in each visualization. Another option is to use
wolffd@0 143 % similar position: each object has the same position in each
wolffd@0 144 % small multiple.
wolffd@0 145
wolffd@0 146 % For example, here are four subplots, one for each component and
wolffd@0 147 % one for cluster information, where color denotes the value and
wolffd@0 148 % position is used for linking. The 2D-position is derived by
wolffd@0 149 % projecting the data into the space spanned by its two greatest
wolffd@0 150 % eigenvectors.
wolffd@0 151
wolffd@0 152 [Pd,V,me] = pcaproj(sD.data,2); % project the data
wolffd@0 153 Pm = pcaproj(sM.codebook,V,me); % project the prototypes
wolffd@0 154 colormap(hot); % colormap used for values
wolffd@0 155
wolffd@0 156 echo off
wolffd@0 157 for c=1:3,
wolffd@0 158 subplot(2,2,c), cla, hold on
wolffd@0 159 som_grid('rect',[300 1],'coord',Pd,'Line','none',...
wolffd@0 160 'MarkerColor',som_normcolor(sD.data(:,c)));
wolffd@0 161 som_grid(sM,'Coord',Pm,'Line','none','marker','+');
wolffd@0 162 hold off, title(sD.comp_names{c}), xlabel('PC 1'), ylabel('PC 2');
wolffd@0 163 end
wolffd@0 164
wolffd@0 165 subplot(2,2,4), cla
wolffd@0 166 plot(Pd(1:100,1),Pd(1:100,2),'ro',...
wolffd@0 167 Pd(101:200,1),Pd(101:200,2),'go',...
wolffd@0 168 Pd(201:300,1),Pd(201:300,2),'bo',...
wolffd@0 169 Pm(:,1),Pm(:,2),'k+')
wolffd@0 170 title('Cluster')
wolffd@0 171 echo on
wolffd@0 172
wolffd@0 173 pause % Strike any key to use color for linking...
wolffd@0 174
wolffd@0 175 % Here is another example, where color is used for linking. On the
wolffd@0 176 % top right triangle are the scatter plots of each variable without
wolffd@0 177 % color coding, and on the bottom left triangle with the color
wolffd@0 178 % coding. In the colored figures, each data sample can be
wolffd@0 179 % identified by a unique color. Well, almost identified: there are
wolffd@0 180 % quite a lot of samples with almost the same color. Color is not as
wolffd@0 181 % precise linking method as position.
wolffd@0 182
wolffd@0 183 echo off
wolffd@0 184 Col = som_normcolor([1:300]',jet(300));
wolffd@0 185 k=1;
wolffd@0 186 for i=1:3,
wolffd@0 187 for j=1:3,
wolffd@0 188 if i<j, i1=i; i2=j; else i1=j; i2=i; end
wolffd@0 189 if i<j,
wolffd@0 190 subplot(3,3,k); cla
wolffd@0 191 plot(sD.data(:,i1),sD.data(:,i2),'ko')
wolffd@0 192 xlabel(sD.comp_names{i1}), ylabel(sD.comp_names{i2})
wolffd@0 193 elseif i>j,
wolffd@0 194 subplot(3,3,k); cla
wolffd@0 195 som_grid('rect',[300 1],'coord',sD.data(:,[i1 i2]),...
wolffd@0 196 'Line','none','MarkerColor',Col);
wolffd@0 197 xlabel(sD.comp_names{i1}), ylabel(sD.comp_names{i2})
wolffd@0 198 end
wolffd@0 199 k=k+1;
wolffd@0 200 end
wolffd@0 201 end
wolffd@0 202 echo on
wolffd@0 203
wolffd@0 204 pause % Strike any key to learn about data visualization using SOM...
wolffd@0 205
wolffd@0 206
wolffd@0 207 clc
wolffd@0 208 % DATA VISUALIZATION USING SOM
wolffd@0 209 % ============================
wolffd@0 210
wolffd@0 211 % The basic visualization functions and their usage have already
wolffd@0 212 % been introduced in SOM_DEMO2. In this demo, a more structured
wolffd@0 213 % presentation is given.
wolffd@0 214
wolffd@0 215 % Data visualization techniques using the SOM can be divided to
wolffd@0 216 % three categories based on their goal:
wolffd@0 217
wolffd@0 218 % 1. visualization of clusters and shape of the data:
wolffd@0 219 % projections, U-matrices and other distance matrices
wolffd@0 220 %
wolffd@0 221 % 2. visualization of components / variables:
wolffd@0 222 % component planes, scatter plots
wolffd@0 223 %
wolffd@0 224 % 3. visualization of data projections:
wolffd@0 225 % hit histograms, response surfaces
wolffd@0 226
wolffd@0 227 pause % Strike any key to visualize clusters with distance matrices...
wolffd@0 228
wolffd@0 229
wolffd@0 230
wolffd@0 231 clf
wolffd@0 232 clc
wolffd@0 233 % 1. VISUALIZATION OF CLUSTERS: DISTANCE MATRICES
wolffd@0 234 % ===============================================
wolffd@0 235
wolffd@0 236 % Distance matrices are typically used to show the cluster
wolffd@0 237 % structure of the SOM. They show distances between neighboring
wolffd@0 238 % units, and are thus closely related to single linkage clustering
wolffd@0 239 % techniques. The most widely used distance matrix technique is
wolffd@0 240 % the U-matrix.
wolffd@0 241
wolffd@0 242 % Here, the U-matrix of the map is shown (using all three
wolffd@0 243 % components in the distance calculation):
wolffd@0 244
wolffd@0 245 colormap(1-gray)
wolffd@0 246 som_show(sM,'umat','all');
wolffd@0 247
wolffd@0 248 pause % Strike any key to see more examples of distance matrices...
wolffd@0 249
wolffd@0 250 % The function SOM_UMAT can be used to calculate U-matrix. The
wolffd@0 251 % resulting matrix holds distances between neighboring map units,
wolffd@0 252 % as well as the median distance from each map unit to its
wolffd@0 253 % neighbors. These median distances corresponding to each map unit
wolffd@0 254 % can be easily extracted. The result is a distance matrix using
wolffd@0 255 % median distance.
wolffd@0 256
wolffd@0 257 U = som_umat(sM);
wolffd@0 258 Um = U(1:2:size(U,1),1:2:size(U,2));
wolffd@0 259
wolffd@0 260 % A related technique is to assign colors to the map units such
wolffd@0 261 % that similar map units get similar colors.
wolffd@0 262
wolffd@0 263 % Here, four clustering figures are shown:
wolffd@0 264 % - U-matrix
wolffd@0 265 % - median distance matrix (with grayscale)
wolffd@0 266 % - median distance matrix (with map unit size)
wolffd@0 267 % - similarity coloring, made by spreading a colormap
wolffd@0 268 % on top of the principal component projection of the
wolffd@0 269 % prototype vectors
wolffd@0 270
wolffd@0 271 subplot(2,2,1)
wolffd@0 272 h=som_cplane([sM.topol.lattice,'U'],sM.topol.msize, U(:));
wolffd@0 273 set(h,'Edgecolor','none'); title('U-matrix')
wolffd@0 274
wolffd@0 275 subplot(2,2,2)
wolffd@0 276 h=som_cplane(sM, Um(:));
wolffd@0 277 set(h,'Edgecolor','none'); title('D-matrix (grayscale)')
wolffd@0 278
wolffd@0 279 subplot(2,2,3)
wolffd@0 280 som_cplane(sM,'none',1-Um(:)/max(Um(:)))
wolffd@0 281 title('D-matrix (marker size)')
wolffd@0 282
wolffd@0 283 subplot(2,2,4)
wolffd@0 284 C = som_colorcode(Pm); % Pm is the PC-projection calculated earlier
wolffd@0 285 som_cplane(sM,C)
wolffd@0 286 title('Similarity coloring')
wolffd@0 287
wolffd@0 288 pause % Strike any key to visualize shape and clusters with projections...
wolffd@0 289
wolffd@0 290
wolffd@0 291
wolffd@0 292 clf
wolffd@0 293 clc
wolffd@0 294 % 1. VISUALIZATION OF CLUSTERS AND SHAPE: PROJECTIONS
wolffd@0 295 % ===================================================
wolffd@0 296
wolffd@0 297 % In vector projection, a set of high-dimensional data samples is
wolffd@0 298 % projected to a lower dimensional such that the distances between
wolffd@0 299 % data sample pairs are preserved as well as possible. Depending
wolffd@0 300 % on the technique, the projection may be either linear or
wolffd@0 301 % non-linear, and it may place special emphasis on preserving
wolffd@0 302 % local distances.
wolffd@0 303
wolffd@0 304 % For example SOM is a projection technique, since the prototypes
wolffd@0 305 % have well-defined positions on the 2-dimensional map grid. SOM as
wolffd@0 306 % a projection is however a very crude one. Other projection
wolffd@0 307 % techniques include the principal component projection used
wolffd@0 308 % earlier, Sammon's mapping and Curvilinear Component Analysis
wolffd@0 309 % (to name a few). These have been implemented in functions
wolffd@0 310 % PCAPROJ, SAMMON and CCA.
wolffd@0 311
wolffd@0 312 % Projecting the map prototype vectors and joining neighboring map
wolffd@0 313 % units with lines gives the SOM its characteristic net-like look.
wolffd@0 314 % The projection figures can be linked to the map planes using
wolffd@0 315 % color coding.
wolffd@0 316
wolffd@0 317 % Here is the distance matrix, color coding, a projection without
wolffd@0 318 % coloring and a projection with one. In the last projection,
wolffd@0 319 % the size of interpolating map units has been set to zero.
wolffd@0 320
wolffd@0 321 subplot(2,2,1)
wolffd@0 322 som_cplane(sM,Um(:));
wolffd@0 323 title('Distance matrix')
wolffd@0 324
wolffd@0 325 subplot(2,2,2)
wolffd@0 326 C = som_colorcode(sM,'rgb4');
wolffd@0 327 som_cplane(sM,C);
wolffd@0 328 title('Color code')
wolffd@0 329
wolffd@0 330 subplot(2,2,3)
wolffd@0 331 som_grid(sM,'Coord',Pm,'Linecolor','k');
wolffd@0 332 title('PC-projection')
wolffd@0 333
wolffd@0 334 subplot(2,2,4)
wolffd@0 335 h = som_hits(sM,sD); s=6*(h>0);
wolffd@0 336 som_grid(sM,'Coord',Pm,'MarkerColor',C,'Linecolor','k','MarkerSize',s);
wolffd@0 337 title('Colored PC-projection')
wolffd@0 338
wolffd@0 339 pause % Strike any key to visualize component planes...
wolffd@0 340
wolffd@0 341
wolffd@0 342 clf
wolffd@0 343 clc
wolffd@0 344 % 2. VISUALIZATION OF COMPONENTS: COMPONENT PLANES
wolffd@0 345 % ================================================
wolffd@0 346
wolffd@0 347 % The component planes visualizations shows what kind of values the
wolffd@0 348 % prototype vectors of the map units have for different vector
wolffd@0 349 % components.
wolffd@0 350
wolffd@0 351 % Here is the U-matrix and the three component planes of the map.
wolffd@0 352
wolffd@0 353 som_show(sM)
wolffd@0 354
wolffd@0 355 pause % Strike any key to continue...
wolffd@0 356
wolffd@0 357 % Besides SOM_SHOW and SOM_CPLANE, there are three other
wolffd@0 358 % functions specifically designed for showing the values of the
wolffd@0 359 % component planes: SOM_PIEPLANE, SOM_BARPLANE, SOM_PLOTPLANE.
wolffd@0 360
wolffd@0 361 % SOM_PIEPLANE shows a single pie chart for each map unit. Each
wolffd@0 362 % pie shows the relative proportion of each component of the sum of
wolffd@0 363 % all components in that map unit. The component values must be
wolffd@0 364 % positive.
wolffd@0 365
wolffd@0 366 % SOM_BARPLANE shows a barchart in each map unit. The scaling of
wolffd@0 367 % bars can be made unit-wise or variable-wise. By default it is
wolffd@0 368 % determined variable-wise.
wolffd@0 369
wolffd@0 370 % SOM_PLOTPLANE shows a linegraph in each map unit.
wolffd@0 371
wolffd@0 372 M = som_normalize(sM.codebook,'range');
wolffd@0 373
wolffd@0 374 subplot(1,3,1)
wolffd@0 375 som_pieplane(sM, M);
wolffd@0 376 title('som\_pieplane')
wolffd@0 377
wolffd@0 378 subplot(1,3,2)
wolffd@0 379 som_barplane(sM, M, '', 'unitwise');
wolffd@0 380 title('som\_barplane')
wolffd@0 381
wolffd@0 382 subplot(1,3,3)
wolffd@0 383 som_plotplane(sM, M, 'b');
wolffd@0 384 title('som\_plotplane')
wolffd@0 385
wolffd@0 386 pause % Strike any key to visualize cluster properties...
wolffd@0 387
wolffd@0 388
wolffd@0 389
wolffd@0 390 clf
wolffd@0 391 clc
wolffd@0 392 % 2. VISUALIZATION OF COMPONENTS: CLUSTERS
wolffd@0 393 % ========================================
wolffd@0 394
wolffd@0 395 % An interesting question is of course how do the values of the
wolffd@0 396 % variables relate to the clusters: what are the values of the
wolffd@0 397 % components in the clusters, and which components are the ones
wolffd@0 398 % which *make* the clusters.
wolffd@0 399
wolffd@0 400 som_show(sM)
wolffd@0 401
wolffd@0 402 % From the U-matrix and component planes, one can easily see
wolffd@0 403 % what the typical values are in each cluster.
wolffd@0 404
wolffd@0 405 pause % Strike any key to continue...
wolffd@0 406
wolffd@0 407 % The significance of the components with respect to the clustering
wolffd@0 408 % is harder to visualize. One indication of importance is that on
wolffd@0 409 % the borders of the clusters, values of important variables change
wolffd@0 410 % very rabidly.
wolffd@0 411
wolffd@0 412 % Here, the distance matrix is calculated with respect to each
wolffd@0 413 % variable.
wolffd@0 414
wolffd@0 415 u1 = som_umat(sM,'mask',[1 0 0]'); u1=u1(1:2:size(u1,1),1:2:size(u1,2));
wolffd@0 416 u2 = som_umat(sM,'mask',[0 1 0]'); u2=u2(1:2:size(u2,1),1:2:size(u2,2));
wolffd@0 417 u3 = som_umat(sM,'mask',[0 0 1]'); u3=u3(1:2:size(u3,1),1:2:size(u3,2));
wolffd@0 418
wolffd@0 419 % Here, the distance matrices are shown, as well as a piechart
wolffd@0 420 % indicating the relative importance of each variable in each
wolffd@0 421 % map unit. The size of piecharts has been scaled by the
wolffd@0 422 % distance matrix calculated from all components.
wolffd@0 423
wolffd@0 424 subplot(2,2,1)
wolffd@0 425 som_cplane(sM,u1(:));
wolffd@0 426 title(sM.comp_names{1})
wolffd@0 427
wolffd@0 428 subplot(2,2,2)
wolffd@0 429 som_cplane(sM,u2(:));
wolffd@0 430 title(sM.comp_names{2})
wolffd@0 431
wolffd@0 432 subplot(2,2,3)
wolffd@0 433 som_cplane(sM,u3(:));
wolffd@0 434 title(sM.comp_names{3})
wolffd@0 435
wolffd@0 436 subplot(2,2,4)
wolffd@0 437 som_pieplane(sM, [u1(:), u2(:), u3(:)], hsv(3), Um(:)/max(Um(:)));
wolffd@0 438 title('Relative importance')
wolffd@0 439
wolffd@0 440 % From the last subplot, one can see that in the area where the
wolffd@0 441 % bigger cluster border is, the 'X-coord' component (red color)
wolffd@0 442 % has biggest effect, and thus is the main factor in separating
wolffd@0 443 % that cluster from the rest.
wolffd@0 444
wolffd@0 445 pause % Strike any key to learn about correlation hunting...
wolffd@0 446
wolffd@0 447
wolffd@0 448 clf
wolffd@0 449 clc
wolffd@0 450 % 2. VISUALIZATION OF COMPONENTS: CORRELATION HUNTING
wolffd@0 451 % ===================================================
wolffd@0 452
wolffd@0 453 % Finally, the component planes are often used for correlation
wolffd@0 454 % hunting. When the number of variables is high, the component
wolffd@0 455 % plane visualization offers a convenient way to visualize all
wolffd@0 456 % components at once and hunt for correlations (as opposed to
wolffd@0 457 % N*(N-1)/2 scatterplots).
wolffd@0 458
wolffd@0 459 % Hunting correlations this way is not very accurate. However, it
wolffd@0 460 % is easy to select interesting combinations for further
wolffd@0 461 % investigation.
wolffd@0 462
wolffd@0 463 % Here, the first and third components are shown with scatter
wolffd@0 464 % plot. As with projections, a color coding is used to link the
wolffd@0 465 % visualization to the map plane. In the color coding, size shows
wolffd@0 466 % the distance matrix information.
wolffd@0 467
wolffd@0 468 C = som_colorcode(sM);
wolffd@0 469 subplot(1,2,1)
wolffd@0 470 som_cplane(sM,C,1-Um(:)/max(Um(:)));
wolffd@0 471 title('Color coding + distance matrix')
wolffd@0 472
wolffd@0 473 subplot(1,2,2)
wolffd@0 474 som_grid(sM,'Coord',sM.codebook(:,[1 3]),'MarkerColor',C);
wolffd@0 475 title('Scatter plot'); xlabel(sM.comp_names{1}); ylabel(sM.comp_names{3})
wolffd@0 476 axis equal
wolffd@0 477
wolffd@0 478 pause % Strike any key to visualize data responses...
wolffd@0 479
wolffd@0 480
wolffd@0 481 clf
wolffd@0 482 clc
wolffd@0 483 % 3. DATA ON MAP
wolffd@0 484 % ==============
wolffd@0 485
wolffd@0 486 % The SOM is a map of the data manifold. An interesting question
wolffd@0 487 % then is where on the map a specific data sample is located, and
wolffd@0 488 % how accurate is that localization? One is interested in the
wolffd@0 489 % response of the map to the data sample.
wolffd@0 490
wolffd@0 491 % The simplest answer is to find the BMU of the data sample.
wolffd@0 492 % However, this gives no indication of the accuracy of the
wolffd@0 493 % match. Is the data sample close to the BMU, or is it actually
wolffd@0 494 % equally close to the neighboring map units (or even approximately
wolffd@0 495 % as close to all map units)? Sometimes accuracy doesn't really
wolffd@0 496 % matter, but if it does, it should be visualized somehow.
wolffd@0 497
wolffd@0 498 % Here are different kinds of response visualizations for two
wolffd@0 499 % vectors: [0 0 0] and [99 99 99].
wolffd@0 500 % - BMUs indicated with labels
wolffd@0 501 % - BMUs indicated with markers, relative quantization errors
wolffd@0 502 % (in this case, proportion between distances to BMU and
wolffd@0 503 % Worst-MU) with vertical lines
wolffd@0 504 % - quantization error between the samples and all map units
wolffd@0 505 % - fuzzy response (a non-linear function of quantization
wolffd@0 506 % error) of all map units
wolffd@0 507
wolffd@0 508 echo off
wolffd@0 509 [bm,qe] = som_bmus(sM,[0 0 0; 99 99 99],'all'); % distance to all map units
wolffd@0 510 [dummy,ind] = sort(bm(1,:)); d0 = qe(1,ind)';
wolffd@0 511 [dummy,ind] = sort(bm(2,:)); d9 = qe(2,ind)';
wolffd@0 512 bmu0 = bm(1,1); bmu9 = bm(2,1); % bmus
wolffd@0 513
wolffd@0 514 h0 = zeros(prod(sM.topol.msize),1); h0(bmu0) = 1; % crisp hits
wolffd@0 515 h9 = zeros(prod(sM.topol.msize),1); h9(bmu9) = 1;
wolffd@0 516
wolffd@0 517 lab = cell(prod(sM.topol.msize),1);
wolffd@0 518 lab{bmu0} = '[0,0,0]'; lab{bmu9} = '[99,99,99]';
wolffd@0 519
wolffd@0 520 hf0 = som_hits(sM,[0 0 0],'fuzzy'); % fuzzy response
wolffd@0 521 hf9 = som_hits(sM,[99 99 99],'fuzzy');
wolffd@0 522
wolffd@0 523 som_show(sM,'umat',{'all','BMU'},...
wolffd@0 524 'color',{d0,'Qerror 0'},'color',{hf0,'Fuzzy response 0'},...
wolffd@0 525 'empty','BMU+qerror',...
wolffd@0 526 'color',{d9,'Qerror 99'},'color',{hf9,'Fuzzy response 99'});
wolffd@0 527 som_show_add('label',lab,'Subplot',1,'Textcolor','r');
wolffd@0 528 som_show_add('hit',[h0, h9],'Subplot',4,'MarkerColor','r');
wolffd@0 529 hold on
wolffd@0 530 Co = som_vis_coords(sM.topol.lattice,sM.topol.msize);
wolffd@0 531 plot3(Co(bmu0,[1 1]),Co(bmu0,[2 2]),[0 10*qe(1,1)/qe(1,end)],'r-')
wolffd@0 532 plot3(Co(bmu9,[1 1]),Co(bmu9,[2 2]),[0 10*qe(2,1)/qe(2,end)],'r-')
wolffd@0 533 view(3), axis equal
wolffd@0 534 echo on
wolffd@0 535
wolffd@0 536 % Here are the distances to BMU, 2-BMU and WMU:
wolffd@0 537
wolffd@0 538 qe(1,[1,2,end]) % [0 0 0]
wolffd@0 539 qe(2,[1,2,end]) % [99 99 99]
wolffd@0 540
wolffd@0 541 % One can see that for [0 0 0] the accuracy is pretty good as the
wolffd@0 542 % quantization error of the BMU is much lower than that of the
wolffd@0 543 % WMU. On the other hand [99 99 99] is very far from the map:
wolffd@0 544 % distance to BMU is almost equal to distance to WMU.
wolffd@0 545
wolffd@0 546 pause % Strike any key to visualize responses of multiple samples...
wolffd@0 547
wolffd@0 548
wolffd@0 549
wolffd@0 550 clc
wolffd@0 551 clf
wolffd@0 552 % 3. DATA ON MAP: HIT HISTOGRAMS
wolffd@0 553 % ==============================
wolffd@0 554
wolffd@0 555 % One can also investigate whole data sets using the map. When the
wolffd@0 556 % BMUs of multiple data samples are aggregated, a hit histogram
wolffd@0 557 % results. Instead of BMUs, one can also aggregate for example
wolffd@0 558 % fuzzy responses.
wolffd@0 559
wolffd@0 560 % The hit histograms (or aggregated responses) can then be compared
wolffd@0 561 % with each other.
wolffd@0 562
wolffd@0 563 % Here are hit histograms of three data sets: one with 50 first
wolffd@0 564 % vectors of the data set, one with 150 samples from the data
wolffd@0 565 % set, and one with 50 randomly selected samples. In the last
wolffd@0 566 % subplot, the fuzzy response of the first data set.
wolffd@0 567
wolffd@0 568 dlen = size(sD.data,1);
wolffd@0 569 Dsample1 = sD.data(1:50,:); h1 = som_hits(sM,Dsample1);
wolffd@0 570 Dsample2 = sD.data(1:150,:); h2 = som_hits(sM,Dsample2);
wolffd@0 571 Dsample3 = sD.data(ceil(rand(50,1)*dlen),:); h3 = som_hits(sM,Dsample3);
wolffd@0 572 hf = som_hits(sM,Dsample1,'fuzzy');
wolffd@0 573
wolffd@0 574 som_show(sM,'umat','all','umat','all','umat','all','color',{hf,'Fuzzy'})
wolffd@0 575 som_show_add('hit',h1,'Subplot',1,'Markercolor','r')
wolffd@0 576 som_show_add('hit',h2,'Subplot',2,'Markercolor','r')
wolffd@0 577 som_show_add('hit',h3,'Subplot',3,'Markercolor','r')
wolffd@0 578
wolffd@0 579 pause % Strike any key to visualize trajectories...
wolffd@0 580
wolffd@0 581
wolffd@0 582
wolffd@0 583 clc
wolffd@0 584 clf
wolffd@0 585 % 3. DATA ON MAP: TRAJECTORIES
wolffd@0 586 % ============================
wolffd@0 587
wolffd@0 588 % A special data mapping technique is trajectory. If the samples
wolffd@0 589 % are ordered, forming a time-series for example, their response on
wolffd@0 590 % the map can be tracked. The function SOM_SHOW_ADD can be used to
wolffd@0 591 % show the trajectories in two different modes: 'traj' and 'comet'.
wolffd@0 592
wolffd@0 593 % Here, a series of data points is formed which go from [8,0,0]
wolffd@0 594 % to [2,2,2]. The trajectory is plotted using the two modes.
wolffd@0 595
wolffd@0 596 Dtraj = [linspace(9,2,20); linspace(0,2,20); linspace(0,2,20)]';
wolffd@0 597 T = som_bmus(sM,Dtraj);
wolffd@0 598
wolffd@0 599 som_show(sM,'comp',[1 1]);
wolffd@0 600 som_show_add('traj',T,'Markercolor','r','TrajColor','r','subplot',1);
wolffd@0 601 som_show_add('comet',T,'MarkerColor','r','subplot',2);
wolffd@0 602
wolffd@0 603 % There's also a function SOM_TRAJECTORY which lauches a GUI
wolffd@0 604 % specifically designed for displaying trajectories (in 'comet'
wolffd@0 605 % mode).
wolffd@0 606
wolffd@0 607 pause % Strike any key to learn about color handling...
wolffd@0 608
wolffd@0 609
wolffd@0 610
wolffd@0 611
wolffd@0 612 clc
wolffd@0 613 clf
wolffd@0 614 % COLOR HANDLING
wolffd@0 615 % ==============
wolffd@0 616
wolffd@0 617 % Matlab offers flexibility in the colormaps. Using the COLORMAP
wolffd@0 618 % function, the colormap may be changed. There are several useful
wolffd@0 619 % colormaps readily available, for example 'hot' and 'jet'. The
wolffd@0 620 % default number of colors in the colormaps is 64. However, it is
wolffd@0 621 % often advantageous to use less colors in the colormap. This way
wolffd@0 622 % the components planes visualization become easier to interpret.
wolffd@0 623
wolffd@0 624 % Here the three component planes are visualized using the 'hot'
wolffd@0 625 % colormap and only three colors.
wolffd@0 626
wolffd@0 627 som_show(sM,'comp',[1 2 3])
wolffd@0 628 colormap(hot(3));
wolffd@0 629 som_recolorbar
wolffd@0 630
wolffd@0 631 pause % Press any key to change the colorbar labels...
wolffd@0 632
wolffd@0 633 % The function SOM_RECOLORBAR can be used to reconfigure
wolffd@0 634 % the labels beside the colorbar.
wolffd@0 635
wolffd@0 636 % Here the colorbar of the first subplot is labeled using labels
wolffd@0 637 % 'small', 'medium' and 'big' at values 0, 1 and 2. For the
wolffd@0 638 % colorbar of the second subplot, values are calculated for the
wolffd@0 639 % borders between colors.
wolffd@0 640
wolffd@0 641 som_recolorbar(1,{[0 4 9]},'',{{'small','medium','big'}});
wolffd@0 642 som_recolorbar(2,'border','');
wolffd@0 643
wolffd@0 644 pause % Press any key to learn about SOM_NORMCOLOR...
wolffd@0 645
wolffd@0 646 % Some SOM Toolbox functions do not use indexed colors if the
wolffd@0 647 % underlying Matlab function (e.g. PLOT) do not use indexed
wolffd@0 648 % colors. SOM_NORMCOLOR is a convenient function to simulate
wolffd@0 649 % indexed colors: it calculates fixed RGB colors that
wolffd@0 650 % are similar to indexed colors with the specified colormap.
wolffd@0 651
wolffd@0 652 % Here, two SOM_GRID visualizations are created. One uses the
wolffd@0 653 % 'surf' mode to show the component colors in indexed color
wolffd@0 654 % mode, and the other uses SOM_NORMALIZE to do the same.
wolffd@0 655
wolffd@0 656 clf
wolffd@0 657 colormap(jet(64))
wolffd@0 658 subplot(1,2,1)
wolffd@0 659 som_grid(sM,'Surf',sM.codebook(:,3));
wolffd@0 660 title('Surf mode')
wolffd@0 661
wolffd@0 662 subplot(1,2,2)
wolffd@0 663 som_grid(sM,'Markercolor',som_normcolor(sM.codebook(:,3)));
wolffd@0 664 title('som\_normcolor')
wolffd@0 665
wolffd@0 666 pause % Press any key to visualize different map shapes...
wolffd@0 667
wolffd@0 668
wolffd@0 669
wolffd@0 670 clc
wolffd@0 671 clf
wolffd@0 672 % DIFFERENT MAP SHAPES
wolffd@0 673 % ====================
wolffd@0 674
wolffd@0 675 % There's no direct way to visualize cylinder or toroid maps. When
wolffd@0 676 % visualized, they are treated exactly as if they were sheet
wolffd@0 677 % shaped. However, if function SOM_UNIT_COORDS is used to provide
wolffd@0 678 % unit coordinates, then SOM_GRID can be used to visualize these
wolffd@0 679 % alternative map shapes.
wolffd@0 680
wolffd@0 681 % Here the grids of the three possible map shapes (sheet, cylinder
wolffd@0 682 % and toroid) are visualized. The last subplot shows a component
wolffd@0 683 % plane visualization of the toroid map.
wolffd@0 684
wolffd@0 685 Cor = som_unit_coords(sM.topol.msize,'hexa','sheet');
wolffd@0 686 Coc = som_unit_coords(sM.topol.msize,'hexa','cyl');
wolffd@0 687 Cot = som_unit_coords(sM.topol.msize,'hexa','toroid');
wolffd@0 688
wolffd@0 689 subplot(2,2,1)
wolffd@0 690 som_grid(sM,'Coord',Cor,'Markersize',3,'Linecolor','k');
wolffd@0 691 title('sheet'), view(0,-90), axis tight, axis equal
wolffd@0 692
wolffd@0 693 subplot(2,2,2)
wolffd@0 694 som_grid(sM,'Coord',Coc,'Markersize',3,'Linecolor','k');
wolffd@0 695 title('cylinder'), view(5,1), axis tight, axis equal
wolffd@0 696
wolffd@0 697 subplot(2,2,3)
wolffd@0 698 som_grid(sM,'Coord',Cot,'Markersize',3,'Linecolor','k');
wolffd@0 699 title('toroid'), view(-100,0), axis tight, axis equal
wolffd@0 700
wolffd@0 701 subplot(2,2,4)
wolffd@0 702 som_grid(sM,'Coord',Cot,'Surf',sM.codebook(:,3));
wolffd@0 703 colormap(jet), colorbar
wolffd@0 704 title('toroid'), view(-100,0), axis tight, axis equal
wolffd@0 705
wolffd@0 706 echo off