/
2013-03-07-Clustering.html
771 lines (606 loc) · 20.4 KB
/
2013-03-07-Clustering.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<title>2013-03-07-Clustering</title>
<meta http-equiv="Content-Type" content="text/html;charset=utf-8"/>
<meta name="title" content="2013-03-07-Clustering"/>
<meta name="generator" content="Org-mode"/>
<meta name="generated" content="2013-03-08 08:57:18 PST"/>
<meta name="author" content="Jim Blomo"/>
<meta name="description" content=""/>
<meta name="keywords" content=""/>
<link rel="stylesheet" type="text/css" href="production/common.css" />
<link rel="stylesheet" type="text/css" href="production/screen.css" media="screen" />
<link rel="stylesheet" type="text/css" href="production/projection.css" media="projection" />
<link rel="stylesheet" type="text/css" href="production/color-blue.css" media="projection" />
<link rel="stylesheet" type="text/css" href="production/presenter.css" media="presenter" />
<link href='http://fonts.googleapis.com/css?family=Lobster+Two:700|Yanone+Kaffeesatz:700|Open+Sans' rel='stylesheet' type='text/css'>
</head>
<body>
<div id="preamble">
</div>
<div id="content">
<h1 class="title">2013-03-07-Clustering</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#sec-1">1 Clustering</a></li>
<li><a href="#sec-2">2 Types of Models</a>
<ul>
<li><a href="#sec-2-1">2.1 Details</a></li>
</ul>
</li>
<li><a href="#sec-3">3 Clustering</a>
<ul>
<li><a href="#sec-3-1">3.1 Perspectives</a></li>
</ul>
</li>
<li><a href="#sec-4">4 Machine Learning</a>
<ul>
<li><a href="#sec-4-1">4.1 Definitions</a></li>
</ul>
</li>
<li><a href="#sec-5">5 Clustering Applications</a>
<ul>
<li><a href="#sec-5-1">5.1 Apps</a></li>
</ul>
</li>
<li><a href="#sec-6">6 Yelp Examples</a>
<ul>
<li><a href="#sec-6-1">6.1 Examples</a></li>
</ul>
</li>
<li><a href="#sec-7">7 Intuition</a>
<ul>
<li><a href="#sec-7-1">7.1 Good Clusters</a></li>
</ul>
</li>
<li><a href="#sec-8">8 Methods</a>
<ul>
<li><a href="#sec-8-1">8.1 Algorithms</a></li>
</ul>
</li>
<li><a href="#sec-9">9 k-means</a>
<ul>
<li><a href="#sec-9-1">9.1 Iterative</a></li>
</ul>
</li>
<li><a href="#sec-10">10 Example</a>
<ul>
<li><a href="#sec-10-1">10.1 Process</a></li>
</ul>
</li>
<li><a href="#sec-11">11 Distance</a>
<ul>
<li><a href="#sec-11-1">11.1 You Can't</a></li>
</ul>
</li>
<li><a href="#sec-12">12 Normalization</a>
<ul>
<li><a href="#sec-12-1">12.1 Un-normalized</a></li>
</ul>
</li>
<li><a href="#sec-13">13 Normalization Techniques</a>
<ul>
<li><a href="#sec-13-1">13.1 Useful for?</a></li>
</ul>
</li>
<li><a href="#sec-14">14 Local Optima</a>
<ul>
<li><a href="#sec-14-1">14.1 No Guarantee</a></li>
</ul>
</li>
<li><a href="#sec-15">15 Uneven Groups</a>
<ul>
<li><a href="#sec-15-1">15.1 k-means</a></li>
</ul>
</li>
<li><a href="#sec-16">16 Medoids</a>
<ul>
<li><a href="#sec-16-1">16.1 Trade-offs</a></li>
</ul>
</li>
<li><a href="#sec-17">17 Example</a>
<ul>
<li><a href="#sec-17-1">17.1 Stability</a></li>
</ul>
</li>
<li><a href="#sec-18">18 <b>Break</b></a>
<ul>
<li><a href="#sec-18-1">18.1 Note</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-1" class="outline-2">
<h2 id="sec-1"><span class="section-number-2">1</span> Clustering <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-1">
</div>
</div>
<div id="outline-container-2" class="outline-2">
<h2 id="sec-2"><span class="section-number-2">2</span> Types of Models <span class="tag"><span class="slide">slide</span> <span class="animate">animate</span></span></h2>
<div class="outline-text-2" id="text-2">
<ul>
<li>Classifiers
</li>
<li>Regressions
</li>
<li>Clustering
</li>
<li>Outlier
</li>
</ul>
</div>
<div id="outline-container-2-1" class="outline-3">
<h3 id="sec-2-1"><span class="section-number-3">2.1</span> Details <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-2-1">
<dl>
<dt>Classifiers</dt><dd>describes and distinguishes cases. Yelp may want to find a
category for a business based on the reviews and business description
</dd>
<dt>Regressions</dt><dd>Predict a continuous value. Eg. predict a home's selling
price given sq footage, # of bedrooms
</dd>
<dt>Clustering</dt><dd>find "natural" groups of data <b>without labels</b>
</dd>
<dt>Outlier</dt><dd>find anomalous transactions, eg. finding fraud for credit cards
</dd>
</dl>
</div>
</div>
</div>
<div id="outline-container-3" class="outline-2">
<h2 id="sec-3"><span class="section-number-2">3</span> Clustering <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-3">
<ul>
<li>Group together similar items
</li>
<li>Separate dissimilar items
</li>
<li>Automatically discover groups without providing labels
</li>
</ul>
</div>
<div id="outline-container-3-1" class="outline-3">
<h3 id="sec-3-1"><span class="section-number-3">3.1</span> Perspectives <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-3-1">
<ul>
<li>Similar items: again, metrics of similarity critical in defining these
groups
</li>
<li>Marking boundaries between different classes
</li>
<li>Type of groups unknown before hand. Out of many attributes, what tend to be
shared?
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-4" class="outline-2">
<h2 id="sec-4"><span class="section-number-2">4</span> Machine Learning <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-4">
<ul>
<li>Supervised
</li>
<li>Unsupervised
</li>
<li>Semi-supervised
</li>
<li>Active
</li>
</ul>
</div>
<div id="outline-container-4-1" class="outline-3">
<h3 id="sec-4-1"><span class="section-number-3">4.1</span> Definitions <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-4-1">
<dl>
<dt>Supervised</dt><dd>Given data with a label, predict data without a
label
</dd>
<dt>Unsupervised</dt><dd>Given data without labels, group "similar" items
together
</dd>
<dt>Semi-supervised</dt><dd>Mix of the above: eg. unsupervised to find groups,
supervised to label and distinguish borderline cases
</dd>
<dt>Active</dt><dd>Starting with unlabeled data, select the most helpful cases for a
human to label
</dd>
</dl>
</div>
</div>
</div>
<div id="outline-container-5" class="outline-2">
<h2 id="sec-5"><span class="section-number-2">5</span> Clustering Applications <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-5">
<ul>
<li>Gain insight into how data is distributed
</li>
<li>Preprocessing step to bootstrap labeling
</li>
<li>Discover outliers
</li>
</ul>
</div>
<div id="outline-container-5-1" class="outline-3">
<h3 id="sec-5-1"><span class="section-number-3">5.1</span> Apps <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-5-1">
<ul>
<li>Closest we have to "magic box": put structured data in, see what groups may
exist
</li>
<li>You want labeled data, but where to start? How many classes? What to name
them?
<ul>
<li>Cluster data, investigate examples.
</li>
<li>Hand label exemplary cases
</li>
<li>Choose names that distinguish groups
</li>
<li>Run classifier on labeled data, compare with clustering, examine errors,
repeat
</li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-6" class="outline-2">
<h2 id="sec-6"><span class="section-number-2">6</span> Yelp Examples <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-6">
<ul>
<li>User groups based on usage, reviewing habits, feature adoption
</li>
<li>Businesses: when should a new category be created, what should it be called?
</li>
<li>Reviews: for a particular business, are there common themes. Show better
variety?
</li>
</ul>
</div>
<div id="outline-container-6-1" class="outline-3">
<h3 id="sec-6-1"><span class="section-number-3">6.1</span> Examples <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-6-1">
<ul>
<li>User groups may be trend spotters, "lurkers", travelers, early adopters
</li>
<li>Do we need a New American and American category? How similar are these
categories?
</li>
<li>Does a reviewer need to read 10 reviews about great food, so-so service?
Maybe providing different view points helps give a better picture
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-7" class="outline-2">
<h2 id="sec-7"><span class="section-number-2">7</span> Intuition <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-7">
<ul>
<li>Intuition => Mathematical Expression => Solution => Evaluation
</li>
<li>High intra-class similarity
</li>
<li>Low inter-class similarity
</li>
<li>Interpretable
</li>
</ul>
</div>
<div id="outline-container-7-1" class="outline-3">
<h3 id="sec-7-1"><span class="section-number-3">7.1</span> Good Clusters <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-7-1">
<ul>
<li>Just like all data mining, needs to be used to take action
</li>
<li>Can't take action if you don't understand the results
</li>
<li>Trade-offs: testing shows it works, but you don't understand it
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-8" class="outline-2">
<h2 id="sec-8"><span class="section-number-2">8</span> Methods <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-8">
<dl>
<dt>Partitioning</dt><dd>Construct <code>k</code> groups, evaluate fitness, improve groups
</dd>
<dt>Hierarchical</dt><dd>Agglomerate items into groups, creating "bottom-up" clusters; or divide set into ever smaller groups, creating "top-down" clusters
</dd>
<dt>Density</dt><dd>Find groups by examining continuous density within a potential
group
</dd>
<dt>Grid</dt><dd>Chunk space into units, cluster units instead of individual records
</dd>
</dl>
</div>
<div id="outline-container-8-1" class="outline-3">
<h3 id="sec-8-1"><span class="section-number-3">8.1</span> Algorithms <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-8-1">
<dl>
<dt>Partitioning</dt><dd>Method similar to gradient descent: find some grouping,
evaluate it, improve it somehow, repeat. k-means.
</dd>
<dt>Hierarchical</dt><dd>Build groups 1 "join" at a time, examining distance between
two things that can be joined together, if close, combine groups. Reverse:
divisive.
</dd>
<dt>Density</dt><dd>Many of the above methods just look for distance. This method
tries to find groups that might be strung out, but maintain a density. Think
about an asteroid belt. It is one group, but not clustered together in a way
you typically think.
</dd>
<dt>Grid</dt><dd>Can speed up clustering and provide similar results
</dd>
</dl>
</div>
</div>
</div>
<div id="outline-container-9" class="outline-2">
<h2 id="sec-9"><span class="section-number-2">9</span> k-means <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-9">
<ul>
<li>Start: Randomly pick <code>k</code> centers for clusters
</li>
<li>Repeat:
<ul>
<li>Assign all other points to their closest cluster
</li>
<li>Recalculate the center of the cluster
</li>
</ul>
</li>
</ul>
</div>
<div id="outline-container-9-1" class="outline-3">
<h3 id="sec-9-1"><span class="section-number-3">9.1</span> Iterative <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-9-1">
<ul>
<li>Start at a random point, find step in right direction, take step,
re-evaluate
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-10" class="outline-2">
<h2 id="sec-10"><span class="section-number-2">10</span> Example <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-10">
<p> <img src="img/kmeansclustering.jpg" alt="img/kmeansclustering.jpg" />
</p>
</div>
<div id="outline-container-10-1" class="outline-3">
<h3 id="sec-10-1"><span class="section-number-3">10.1</span> Process <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-10-1">
<ul>
<li>We pick some nodes at random, mark with a cross
</li>
<li>Find other points that are closest to the crosses
</li>
<li>Find new <b>centroid</b> based on the average of all points
</li>
<li>Start again
</li>
<li>img: <a href="http://apandre.wordpress.com/visible-data/cluster-analysis/">http://apandre.wordpress.com/visible-data/cluster-analysis/</a>
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-11" class="outline-2">
<h2 id="sec-11"><span class="section-number-2">11</span> Distance <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-11">
<ul>
<li><b>Centroid</b> is the average of all points in a cluster; the center
</li>
<li>Different distance metrics for real numbers
</li>
<li>But how to find "average" of binary or normative data?
</li>
</ul>
</div>
<div id="outline-container-11-1" class="outline-3">
<h3 id="sec-11-1"><span class="section-number-3">11.1</span> You Can't <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-11-1">
<ul>
<li>k-means is used for numerical data
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-12" class="outline-2">
<h2 id="sec-12"><span class="section-number-2">12</span> Normalization <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-12">
<ul>
<li>Cluster cities by average temperature and population attributes
</li>
<li><x,y> = <temp, pop>
</li>
<li>Using Euclidean distance, which attribute will affect similarity more?
</li>
</ul>
</div>
<div id="outline-container-12-1" class="outline-3">
<h3 id="sec-12-1"><span class="section-number-3">12.1</span> Un-normalized <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-12-1">
<ul>
<li>Population: it is a much bigger number, will contribute much more to
distance
</li>
<li>Artificially inflating importance just because units are different
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-13" class="outline-2">
<h2 id="sec-13"><span class="section-number-2">13</span> Normalization Techniques <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-13">
<dl>
<dt>Z-score</dt><dd><code>(v - mean) / stddev</code>
</dd>
<dt>Min-max</dt><dd><code>(v - min) / (max - min)</code>
</dd>
<dt>Decimal</dt><dd><code>* 10</code> <code>/ 10</code>
</dd>
<dt>Square</dt><dd><code>x**2</code>
</dd>
<dt>Log</dt><dd><code>log(x)</code>
</dd>
</dl>
</div>
<div id="outline-container-13-1" class="outline-3">
<h3 id="sec-13-1"><span class="section-number-3">13.1</span> Useful for? <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-13-1">
<dl>
<dt>Z-score</dt><dd>1-pass normalization, retaining information about stdev
</dd>
<dt>Min-max</dt><dd>keep within expected range, usually [0-1]
</dd>
<dt>Decimal</dt><dd>easy to apply
</dd>
<dt>Square</dt><dd>keep inputs positive
</dd>
<dt>Log</dt><dd>de-emphasize differences between large numbers
</dd>
</dl>
</div>
</div>
</div>
<div id="outline-container-14" class="outline-2">
<h2 id="sec-14"><span class="section-number-2">14</span> Local Optima <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-14">
<p> <img src="img/k-means-local.png" alt="img/k-means-local.png" />
</p>
</div>
<div id="outline-container-14-1" class="outline-3">
<h3 id="sec-14-1"><span class="section-number-3">14.1</span> No Guarantee <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-14-1">
<ul>
<li>Since there are many possible stable centers, we may not end up at the best
one
</li>
<li>How can we improve our odds of finding a good separation?
<ul>
<li>Why did we end up here? starting points
</li>
<li>Choose different starting points
</li>
<li>Compare results
</li>
</ul>
</li>
<li>Other problems? Mouse
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-15" class="outline-2">
<h2 id="sec-15"><span class="section-number-2">15</span> Uneven Groups <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-15">
<p> <img src="img/k-means-mouse.png" alt="img/k-means-mouse.png" />
</p>
</div>
<div id="outline-container-15-1" class="outline-3">
<h3 id="sec-15-1"><span class="section-number-3">15.1</span> k-means <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-15-1">
<ul>
<li>k-means is good for similarly sized groups, or at least groups that are
similar distance between other members
</li>
<li>Other problems that would pull the centroid away from the real groups?
</li>
<li>Outliers
</li>
<li>img: <a href="http://en.wikipedia.org/wiki/K-means_clustering">http://en.wikipedia.org/wiki/K-means_clustering</a>
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-16" class="outline-2">
<h2 id="sec-16"><span class="section-number-2">16</span> Medoids <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-16">
<ul>
<li>Instead of finding a <b>centroid</b> find a <b>medoid</b>
</li>
<li>Medoid: actual data point that represents median of the cluster
</li>
<li>PAM: Partitioning Around Medoids
</li>
</ul>
</div>
<div id="outline-container-16-1" class="outline-3">
<h3 id="sec-16-1"><span class="section-number-3">16.1</span> Trade-offs <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-16-1">
<ul>
<li>PAM more expensive to evaluate
</li>
<li>Scales poorly, since we need to evaluate many more medoids with many more
points
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-17" class="outline-2">
<h2 id="sec-17"><span class="section-number-2">17</span> Example <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-17">
<p> <img src="img/k-medoids.png" alt="img/k-medoids.png" />
</p>
</div>
<div id="outline-container-17-1" class="outline-3">
<h3 id="sec-17-1"><span class="section-number-3">17.1</span> Stability <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-17-1">
<ul>
<li>No stability between real clusters
</li>
<li>Outliers can't pull centroid far out of actual cluster
</li>
<li>img: <a href="http://en.wikipedia.org/wiki/K-medoids">http://en.wikipedia.org/wiki/K-medoids</a>
</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-18" class="outline-2">
<h2 id="sec-18"><span class="section-number-2">18</span> <b>Break</b> <span class="tag"><span class="slide">slide</span></span></h2>
<div class="outline-text-2" id="text-18">
<p><img src="img/screenshot_metroid2.jpg" alt="img/screenshot_metroid2.jpg" />
</p><ul>
<li>Do not confuse Medoid with Metroid
</li>
</ul>
</div>
<div id="outline-container-18-1" class="outline-3">
<h3 id="sec-18-1"><span class="section-number-3">18.1</span> Note <span class="tag"><span class="notes">notes</span></span></h3>
<div class="outline-text-3" id="text-18-1">
<ul>
<li>img: <a href="http://stealthboy.com/~msherman/metroid.html">http://stealthboy.com/~msherman/metroid.html</a>
</li>
</ul>
<script type="text/javascript" src="production/org-html-slideshow.js"></script>
</div>
</div>
</div>
</div>
<div id="postamble">
<p class="date">Date: 2013-03-08 08:57:18 PST</p>
<p class="author">Author: Jim Blomo</p>
<p class="creator">Org version 7.8.02 with Emacs version 23</p>
<a href="http://validator.w3.org/check?uri=referer">Validate XHTML 1.0</a>
</div>
</body>
</html>