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4.7 INSTANCE-BASED LEARNING 133Figure 4.13 were any bigger, which it would be if the black instance were a littlefurther from the target, it would intersect the lower right-hand corner of therectangle at the top left and then that rectangle would have to be investigated,too—despite the fact that the training instances that define it are a long wayfrom the corner in question. The corners of rectangular regions are awkward.The solution? Use hyperspheres, not hyperrectangles. Neighboring spheresmay overlap whereas rectangles can abut, but this is not a problem because thenearest-neighbor algorithm for kD-trees described previously does not dependon the regions being disjoint. A data structure called a ball tree defines k-dimensional hyperspheres (“balls”) that cover the data points, and arrangesthem into a tree.Figure 4.14(a) shows 16 training instances in two-dimensional space, overlaidby a pattern of overlapping circles, and Figure 4.14(b) shows a tree formedfrom these circles. Circles at different levels of the tree are indicated by differentstyles of dash, and the smaller circles are drawn in shades of gray. Each nodeof the tree represents a ball, and the node is dashed or shaded according to thesame convention so that you can identify which level the balls are at. To helpyou understand the tree, numbers are placed on the nodes to show how manydata points are deemed to be inside that ball. But be careful: this is not necessarilythe same as the number of points falling within the spatial region that theball represents. The regions at each level sometimes overlap, but points that fallinto the overlap area are assigned to only one of the overlapping balls (thediagram does not show which one). Instead of the occupancy counts in Figure4.14(b) the nodes of actual ball trees store the center and radius of their ball;leaf nodes record the points they contain as well.To use a ball tree to find the nearest neighbor to a given target, start by traversingthe tree from the top down to locate the leaf that contains the target andfind the closest point to the target in that ball. This gives an upper bound forthe target’s distance from its nearest neighbor. Then, just as for the kD-tree,examine the sibling node. If the distance from the target to the sibling’s centerexceeds its radius plus the current upper bound, it cannot possibly contain acloser point; otherwise the sibling must be examined by descending the treefurther. In Figure 4.15 the target is marked with a star and the black dot is itsclosest currently known neighbor. The entire contents of the gray ball can beruled out: it cannot contain a closer point because its center is too far away.Proceed recursively back up the tree to its root, examining any ball that maypossibly contain a point nearer than the current upper bound.Ball trees are built from the top down, and as with kD-trees the basic problemis to find a good way of splitting a ball containing a set of data points into two.In practice you do not have to continue until the leaf balls contain justtwo points: you can stop earlier, once a predetermined minimum number isreached—and the same goes for kD-trees. Here is one possible splitting method.
134 CHAPTER 4 | ALGORITHMS: THE BASIC METHODS(a)166 1042642 2 4 2 2 2(b)2 2Figure 4.14 Ball tree for 16 training instances: (a) instances and balls and (b) the tree.
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Data MiningPractical Machine Learni
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Publisher:Publishing Services Manag
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viFOREWORDThis book presents this n
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CONTENTSix4 Algorithms: The basic m
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CONTENTSxiGenerating good rules 202
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CONTENTSxiii8 Moving on: Extensions
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CONTENTSxv13 The command-line inter
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xviiiLIST OF FIGURESFigure 4.10 The
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xxLIST OF FIGURESFigure 10.13 Worki
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xxiiLIST OF TABLESTable 5.2 Confide
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xxivPREFACEalchemy. Instead, there
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xxviPREFACEwho interprets them, and
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xxviiiPREFACEin Section 6.3. We hav
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xxxPREFACEration. All who have work
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partIMachine Learning Toolsand Tech
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4 CHAPTER 1 | WHAT’S IT ALL ABOUT
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10 CHAPTER 1 | WHAT’S IT ALL ABOU
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chapter 2Input:Concepts, Instances,
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2.1 WHAT’S A CONCEPT? 43increase
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2.2 WHAT’S IN AN EXAMPLE? 45data
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2.2 WHAT’S IN AN EXAMPLE? 47Table
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2.3 WHAT’S IN AN ATTRIBUTE? 49Tab
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2.3 WHAT’S IN AN ATTRIBUTE? 51Not
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2.4 PREPARING THE INPUT 53cleaned u
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missing values in this dataset). Th
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dividing by the range between the m
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2.4 PREPARING THE INPUT 59a record
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chapter 3Output:Knowledge Represent
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3.2 DECISION TREES 63Alternatively,
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3.3 CLASSIFICATION RULES 65nated by
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3.3 CLASSIFICATION RULES 671abx = 1
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3.4 ASSOCIATION RULES 69yes, then i
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3.5 RULES WITH EXCEPTIONS 71If peta
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3.6 RULES INVOLVING RELATIONS 73ica
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Standard relations include equality
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PRP =-56.1+0.049 MYCT+0.015 MMIN+0.
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3.8 INSTANCE-BASED REPRESENTATION 7
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3.9 Clusters3.9 CLUSTERS 81When clu
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Page 130 and 131: 4.3 DIVIDE-AND-CONQUER: CONSTRUCTIN
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Page 146 and 147: 4.5 MINING ASSOCIATION RULES 113acc
Page 148 and 149: 4.5 MINING ASSOCIATION RULES 115Tab
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Page 152 and 153: 4.6 LINEAR MODELS 119through the da
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Page 158 and 159: 4.6 LINEAR MODELS 125Set all weight
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Page 164 and 165: 4.7 INSTANCE-BASED LEARNING 131Figu
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Page 170 and 171: 4.8 CLUSTERING 137As we saw in Sect
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Page 176 and 177: chapter 5Credibility:Evaluating Wha
Page 178 and 179: 5.1 TRAINING AND TESTING 145of each
Page 180 and 181: ather than error rate, so this corr
Page 182 and 183: 5.3 CROSS-VALIDATION 149mediate con
Page 184 and 185: 5.4 OTHER ESTIMATES 151A single 10-
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Page 188 and 189: 5.5 COMPARING DATA MINING METHODS 1
Page 190 and 191: 5.6 PREDICTING PROBABILITIES 157In
Page 192 and 193: 5.6 PREDICTING PROBABILITIES 159whe
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Page 198 and 199: 5.7 COUNTING THE COST 165different
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5.10 APPLYING THE MDL PRINCIPLE TO
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5.11 FURTHER READING 185tion theory
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188 CHAPTER 6 | IMPLEMENTATIONS: RE
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chapter 7Transformations:Engineerin
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7.1 ATTRIBUTE SELECTION 287attribut
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7.1 ATTRIBUTE SELECTION 289and less
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tion—and it is much easier to und
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7.1 ATTRIBUTE SELECTION 293outlook
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7.1 ATTRIBUTE SELECTION 295the t-te
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7.2 DISCRETIZING NUMERIC ATTRIBUTES
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7.3 SOME USEFUL TRANSFORMATIONS 305
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7.4 AUTOMATIC DATA CLEANSING 313Int
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7.5 COMBINING MULTIPLE MODELS 315da
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7.5 COMBINING MULTIPLE MODELS 319mo
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7.5 COMBINING MULTIPLE MODELS 323Ho
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7.5 COMBINING MULTIPLE MODELS 325Th
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7.5 COMBINING MULTIPLE MODELS 327of
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7.5 COMBINING MULTIPLE MODELS 335Ta
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7.6 Using unlabeled data7.6 USING U
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7.6 USING UNLABELED DATA 339automat
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7.7 FURTHER READING 341deal with we
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7.7 FURTHER READING 343Domingos (19
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346 CHAPTER 8 | MOVING ON: EXTENSIO
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chapter 9Introduction to WekaExperi
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9.2 How do you use it?9.2 HOW DO YO
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chapter 10The ExplorerWeka’s main
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10.1 GETTING STARTED 371(a)(b)(c)Fi
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10.1 GETTING STARTED 373deviation.
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10.1 GETTING STARTED 375=== Run inf
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10.1 GETTING STARTED 377Doing it ag
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10.1 GETTING STARTED 379(a)(b)Figur
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10.2 EXPLORING THE EXPLORER 381(a)(
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10.2 EXPLORING THE EXPLORER 383(b)(
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10.2 EXPLORING THE EXPLORER 385(a)(
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10.2 EXPLORING THE EXPLORER 387+ 0.
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10.2 EXPLORING THE EXPLORER 389posi
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10.2 EXPLORING THE EXPLORER 391Figu
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10.3 FILTERING ALGORITHMS 393method
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10.3 FILTERING ALGORITHMS 395(b)Fig
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10.3 FILTERING ALGORITHMS 397or fir
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10.3 FILTERING ALGORITHMS 399attrib
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10.3 FILTERING ALGORITHMS 401it int
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10.4 LEARNING ALGORITHMS 403There i
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10.4 LEARNING ALGORITHMS 405Table 1
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10.4 LEARNING ALGORITHMS 407Figure
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10.4 LEARNING ALGORITHMS 409value (
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10.4 LEARNING ALGORITHMS 411Neural
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10.4 LEARNING ALGORITHMS 413there a
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10.5 METALEARNING ALGORITHMS 415Tab
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10.7 ASSOCIATION-RULE LEARNERS 419N
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10.8 ATTRIBUTE SELECTION 421Table 1
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10.8 ATTRIBUTE SELECTION 423tribute
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10.8 ATTRIBUTE SELECTION 425with on
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428 CHAPTER 11 | THE KNOWLEDGE FLOW
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chapter 12The ExperimenterThe Explo
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12.1 GETTING STARTED 439Dataset,Run
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12.2 SIMPLE SETUP 441cance test of
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12.4 THE ANALYZE PANEL 443advanced
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12.5 DISTRIBUTING PROCESSING OVER S
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12.5 DISTRIBUTING PROCESSING OVER S
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450 CHAPTER 13 | THE COMMAND-LINE I
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chapter 14Embedded Machine Learning
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14.2 GOING THROUGH THE CODE 463/***
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14.2 GOING THROUGH THE CODE 465// I
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14.2 GOING THROUGH THE CODE 467}//
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14.2 GOING THROUGH THE CODE 469filt
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472 CHAPTER 15 | WRITING NEW LEARNI
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ReferencesAdriaans, P., and D. Zant
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Bouckaert, R. R. 2004. Bayesian net
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REFERENCES 489Cypher, A., editor. 1
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REFERENCES 491Fix, E., and J. L. Ho
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REFERENCES 493Gennari, J. H., P. La
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Conference on Knowledge Discovery a
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REFERENCES 497Kushmerick, N., D. S.
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Moore, A. W., and M. S. Lee. 1994.
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REFERENCES 501editor, Proceedings o
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REFERENCES 503Webb, G. I., J. Bough
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506 INDEXanomaly detection systems,
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508 INDEXcausal relations, 350CfsSu
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510 INDEXCSVLoader, 381cumulative m
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512 INDEXExperimenter, 437-447advan
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514 INDEXimplementation—real-worl
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516 INDEXlistOptions(), 482literary
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518 INDEXnumeric prediction (contin
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520 INDEXrelational data, 49relatio
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522 INDEXsupport vector, 216support
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524 INDEXWinnow, 410Winnow algorith
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