DIAV 2.0 User Manual: Specification and Guide through the
Contents
1. Naan 773 po v Poo fuam N lt gt lt E o0 5 4 I H ors E S Ta lt Att NN vot o8 lt T 5 a4 I lt E uS gt S SES X gi 5 zd i gt X a lt pE san 2 e eX 24 Co T SI lt gt o 5 gt d ph RN gt Ji 555 XX E Sid Lal 0 e en ENN Sx N am I S 9 c Youn il SSO 2222 3 AA at SiT d 50 gt lt x 27 lt 6 5 wo LII N et _ a om lt ma gt lt 3 cd gt gt c S 5 2 9 _ E 2 9 o gt orr 8 2 gt lt 9 gt lt oo lt ato E A e m Nc KE Oa Mw Oe un i Unn AHS 88 cat T t gt O O gt O N o 5 eee Ue ee uod 4e a 5 32 Before generating the 4th STAR Cover 1 x120 2 x2 0 x4 0 1 x5 2 3 x6 1 t 5 2 1 0 x4 1 2 x5 1 x6 1 t 5 3 x2 1 x3 0 x4 0 1 x5 12. ambiguous example ambiguous example Figure 3 Visualization of multi class and binary class training examples 4 2 Visualization of Target and Learned Concepts In DIAV concepts are expressed using a modified version of variable valued logic VL 11 language A concept can be described using either rules or examples Figures 4 amp 5 The rules consist of conjunctive conditions enclosed in brackets The rules are separated by semicolons The conditions relate attribute with their possible values If the concept 15 specified using examples a list of attribute names should appear before the examples to define order of attribute values in the table The concept representation in the form of rules is useful for symbolic learning systems that produce output of this kind e g AQIS Michalski et al 1986 C4 5 Quinlan 1993 For nonsymbolic learning systems such as neural networks genetic algorithms the concept representation in the form of examples facilitates visualization of results from those systems Wnek et al 1989 concept rule rule listOfAttributeNames example example rule condition condition condition expression expression attributeName REL attributeValue attributeValue attributeName interval REL Ex de P interval attributeValue attributeValue listOfAttributeNames attributeName attributeName example attributeValue
3. x1 0 x2 0 6 1 Selected examples for the next specialization step 1 x120 x2 0 x3 1 x4 1 x5 3 x6 1 6 1 0 x2 0 x3 1 x4 2 x5 0 x6 1 As result of the specialization of the STAR from step E three rules are generated 1 x120 2 2 0 1 x4 0 1 x6 1 612 2 1 0 x2 0 x6 1 2 3 1 0 x2 0 1 x4 0 1 x6 1 63 Since rule 3 is subsumed by rule 1 rule 3 is removed from the cover This way there are only two rules in the partial cover and therefore there is no need to trim the cover as required by the MAXSTAR parameter MONK2 B Ed BORO Seo ea SOOO Bee ee eee ee eee EEC ERS E dm rr ES ri RGR ODE ee z H PEHEHHAEHHHERISHIT E Current cover Partial STAR Training examples 30 G Generating the Ist STAR before the last specialization STAR 1 x1 0 2 x2 0 x4 0 1 x5 1 2 3 x6 1 2 x120 2 x2 0 1 4 0 1 x5 3 x6 1 Selected examples for the next specialization step 1 1 0 x2 0 x3 1 x4 1 x5 3 6 1 x120 x2 0 x3 0 x4 0 x5 1 x6 1 Some steps uncovering consecutive negative examples were skipped When we resume this demonstration there is one negative example left to uncover This negative example differs from the seed positive example on three attributes x3 x4 and xS H
4. x1 x2 x3 0 1 0 1 n 0000 0 1 1 0 n 001 1 1 0 0 1 n 0101 1 0 1 0 n 0110 1 1 0 0 n 1001 1 1 1 1 n 1010 1100 111 1 The next example Figure 9 shows symmetry of the Monk2 concept Diagram A shows a symmetrical concept constructed by performing operation on all first attribute values Therefore the diagram shows concept odd FirstValue Attribute Diagram B shows the Monk2 concept Diagram C shows the odd FirstValue Attribute concept in light gray shading and the Monk2 concept in gray shading There is no intersection between the two Diagram D shows the negated concept odd FirstV alue Attribute and the Monk2 concept The black area intersection of 19 the two concepts is exactly Monk2 concept The negation of odd FirstValue Attribute is even FirstValue Attribute Monk2 is a subconcept of even FirstValue Attribute Robots fti he Ee C odd FirstValue Attribute or Monk2 D even FirstValue Attribute or Monk2 Figure 9 Constructing concept images the symmetry of the Monk2 concept 20 5 Changing the Representation Space The representation space transformations may involve contraction expansion or exchange operations In the context of the attribute value concept representation contraction is done by removing attributes or combining attribute values into larger units Expansion is done by adding new attributes or
5. 5 1 2 x6 1 t 4 u 3 10 x220 x3 1 x5 1 x6 0 t 3 u 3 11 x120 1 x222 x422 x520 1 t 4 u 2 11 x2 1 x3 0 4 0 5 1 2 3 x6 1 t 3 u 3 12 x2 0 x3 1 x5 1 x620 t 3 3 112 x2 1 2 x3 1 x5 0 x6 1 t 3 u 2 13 x2 1 2 x3 1 x5 0 x6 1 t 3 u 2 13 xl 1 2 x3 1 x5 0 x6 1 t 3 u 2 14 1 21 x3 1 x5 0 x6 1 t 3 u 2 14 1 0 x4 2 x5 1 x6 1 t 3 u 1 15 1 2 2 1 2 x4 1 x5 0 3 t 3 u 1 15 1 1 2 2 2 x4 0 x5 2 x6 1 t 2 u 2 16 1 1 2 x2 2 x4 0 5 1 2 x6 1 t 2 u 2 16 1 2 x2 1 x4 1 x5 0 t 2 u 1 Specific cover 1 x120 x2 1 2 x3 0 4 1 2 5 1 2 3 x6 1 t 9 1 98 GD 7 1 0 x4 1 2 xS 1 1 65 2 1 1 2 2 1 2 x3 0 x4 1 2 x5 1 2 3 6 0 49 u 8 MD 14 x1 0 4 2 x5 1 6 1 t 3 u 1 3 x1 1 2 x2 0 x3 0 x4 1 2 x5 1 2 3 x6 1 t 8 8 SD 16 x1 0 x2 0 x3 1 x4 2 5 1 6 1 t 1 u 1 4 1 1 2 x2 1 2 x3 1 x4 1 2 x5 0 x6 0 t 7 u 7 5 x120 x2 1 x3 1 x4 1 2 x522 3 x6 0 t 4 u 4 is 6 1 1 2 x2 1 2 x3 1 x4 0 x5 1 2 3 x6 0 t 4 u 4 The above comparison of the three descriptions details 7 x2 0 2 x3 1 x4 0 x5 1 2 114 0 3 differences between the cover types in terms of numbers of g x1 0 1 x2 2 x4 2 x5 0 1 t 4 0 2 conditions and condition values T
6. indexOf 1 offset i l ofs xx ofs xx where n number of attributes Ai i th attribute in the event vector Avi value of i th attribute indexOf gives index serial number of an attribute value in array aV offset gives an attribute offset in the diagram gives the integer reminder after dividing ofs by xx gives integer quotient after dividing 8 by xx For example the event hs square bs round sm yes ho flag jc 1 ti n has the following coordinates ofs 1 48 0 144 0 24 2 2 0 6 1 1 53 59 24 5 53 24 2 References Arciszewski T Bloedorn E Michalski R S Mustafa M and Wnek J Machine Learning of Design Rules Methodology and Case Study ASCE Journal of Computing Civil Engineering Vol 8 No 3 pp 286 308 July 1994 Arciszewski T Michalski R S and Wnek J Constructive Induction the Key to Design Creativity Proceedings of the Third International Round Table Conference on Computational Models of Creative Design Heron Island Queensland Australia December 3 7 1995 Digitalk Inc Smalltalk V Object Oriented Programming System OOPS Tutorial and Programming Handbook Digitalk Inc Los Angeles CA 1986 Guillen L E Jr and Wnek J Investigation of Hypothesis driven Constructive Induction in 17 Reports of Machine Learning and Inference Laboratory 93 13 George Mason Univers
7. Selecting the best rule from the first STAR STAR 1 x1 0 2 x2 0 x4 0 1 x5 2 3 x6 1 1 5 2 x120 2 2 0 x4 1 5 1 2 3 x6 1 t 4 The rules in the star do not cover any negative examples The best rule 1 is selected light gray area and the overlapping with rule 2 area also as black area in the next Figure The rule covers 5 positive examples versus 4 examples covered by the second rule The best rule is saved in the current cover I Before generating the 2nd STAR Cover 1 1 0 2 x2 0 x4 0 1 x5 2 3 x6 1 STAR Selected examples for the next specialization step 2 1 0 x2 0 x3 1 x4 2 x5 1 x6 1 1 1 1 2 0 x3 1 x4 2 x5 1 x6 1 t 5 The best rule black area covers 5 positive examples The rule is saved in the current cover There are still positive examples not covered by the Cover AQ selects a seed example for the second STAR and the first negative example for STAR specialization based on its proximity to the new seed 31 m on S HE xS ad wa wa gt e 5 I Ii B 25 5 poo N m E N amp ash NO c gt lt a c 5 A A gt 5 gt 9 BB ANN a e zu 1 Ox x 5 aim 9 2 gt 2
8. Start DIAV system by clicking twice on the icon 2 Create a new file with the domain description 2 1 Select New command from File menu 2 2 Type in the domain description e g Robots 3 3 2 3 4 2 hs round square octagonal bs round square octagonal sm yes no ho sword balloon flag jc red green blue yellow ti yes no 35 2 3 Save the domain description by chosing Save as from the File menu Type in the file name e g robotsDomain and click on Save button 3 Create a file with a target concept description 3 1 Select New command from File menu 3 2 Type in the target concept description e g hs round red hs square ho balloon 3 3 Save the target concept description by chosing Save as file name e g targetConcept and click on Save button 4 Create a file with a learned concept description 4 1 Select New command from File menu 4 2 Type in the learned concept description e g hs round square ho sword balloon jc red green from the File menu Type in the 4 3 Save the learned concept description by chosing Save as from the File menu Type in the file name e g learnedConcept and click on Save button 5 Create a file with training examples 5 1 Select New command from File menu 5 2 Type in the positive and negative examples descriptions e g Positive hs bs sm ho ti round round yes sword red no round
9. 2 x5 0 1 t 4 9 x2 0 x3 0 x4 1 2 x5 1 2 3 x6 1 t 8 10 x2 0 x3 1 x5 1 x6 0 t 3 11 xl 1 2 x3 1 x5 0 x6 1 t 3 12 xl 1 2 x2 1 2 x3 0 x4 1 2 x5 1 2 3 x6 0 t 9 13 1 1 2 x2 1 2 x3 1 x4 0 x5 1 2 3 x6 0 t 4 14 1 1 2 x2 1 2 x3 1 x4 1 2 x5 0 t 7 15 xl1z1 2 2 2 x4 0 x5 1 2 x6 1 t 2 16 1 2 x2 1 2 x4 1 x5 0 3 t 3 33 Description cover optimization After all positive examples are covered AQ optimizes the cover according to the trim parameter For general discriminant descriptions with the trim parameter set to gen the cover remains unchanged The following figures illustrate the differences between the general description and two additional description types specific characteristic and minimal complexity All description types are consistent and complete with regard to the training set of examples 1 none of the negative examples is covered and all of the positive examples are covered Since each condition applies a further constraint on the examples that satisfy the rule the removal of conditions will generalize the rule Since each value in a condition loosens the constraint given by that condition the removal of values a condition will specialize the rule Hence the covers can be described as follows General discriminant description GD consists of rules as general as possible 1 involving the minimum number of condition
10. 41 identifier number interval attrbiuteName attributeName l expression attributeName REL attributeValue attributeValue attributeName interval lt gt gt attributeValue attributeValue letter letter digit digit digit capitalLetter a b e d e f g h i j k s t u A B C D E E G J K L N O P YE o 1 1 2 19 qoem 9 Ww x y 7 Below is the syntax of files requested when executing respective commands from DIAV menus representationSpaceFile trainingExamplesFile positiveExamplesFile negativeExamplesFile targetConceptFile learnedConceptFile projectToFile ruleFromTranscript multiConceptExamplesFile multiConceptRulesFile constructConceptFile andFile orFile diffFile xorFile domainDescription trainingExamples positiveExamples negativeExamples positiveExamples negativeExamples targetConcept learnedConcept domainDescription ruleSet highlight the ruleSet in System Transcript window conceptExamples conceptSet concept concept starMethodDemoFile partialStar star seedPositiveExample selectedNegativeExample 42 domainDescription positiveExamples negativeExamples partialStar seedPositiveExample selectedNegativeExample sta
11. diagram in which each cell represents a unique combination of attribute values Each attribute partitions the diagram into areas corresponding to individual values of the attribute Conjunctive rules correspond to certain regular arrangements of cells that can be easily recognized visually The diagram can represent examples rules and rulesets DNF in the form of concept images The main goal of the diagrammatic visualization system DIAV is to provide a tool for a visual interpretation of various aspects of concept learning These include visualization of knowledge representation spaces and relationships between training examples and target and learned concepts Wnek et al 1990 visual comparison of generalization performed by various learning systems Wnek et al 1990 Wnek and Michalski 1994a visualization of changes in the representation space done by constructive induction Wnek 1993 Wnek amp Michalski 19945 An important feature of the diagrammatic visualization is that it permits one to display steps in learning processes as well as the errors in concept learning The set of cells representing the target concept the concept to be learned is called target concept image T The set of cells representing the learned concept is called learned concept image L The areas of the target concept not covered by the learned concept represent errors of omission T L while the areas of the learned concept not covered by the target conc
12. element representation space was compressed into 5 element representation space The presented operations do not cause ambiguity or impossible areas in the new representation spaces This 1s due to the symmetry in the original representation space and proper operators used in changing the representation space The changes in the representation space presented here are related to the problem of detecting symmetries in the representation spaces and constructing counting attributes Wnek and Michalski 1994 28 6 Demo STAR generation L EEE 0 2 A Generating the Ist STAR Ld bol i dc d 1 l1 1l i is STAR Selected examples for the next specialization step 1 1 0 x2 0 x3 1 x4 1 x523 x6 1 1 1 1 x2 0 x3 1 x4 1 x5 3 x6 1 AQ starts with the most general cover 1 the whole representation space is covered light gray area The first positive example seed 1 is selected for STAR generation Since the current STAR also covers negative examples AQ selects its first negative example 1 for uncovering The selected negative example is as close as possible in terms of different attribute values to the seed positive example In this case the two examples differ only olifolifolifolifol ijoli fo in the x1 attribute boldfaced descriptions ol liliz2l foli iB ESSET Negative example ISelected negative example STAR 1 B Generating the Is
13. images Eel cR Deui ERE a eee E Figure 7 cont Constructing concept images using the XOR shows construction of symmetrical concepts operator Wnek and Michalski 1994 In the 4 dimensional representation space represented by 4 The following example Figure 8 are created by Consecutive concepts 0 0 x3 the initial concept is xO X3 x2 executing the operation with 1 x1 binary attributes 0 rules respectively The resulting 2 0 concept D is symmetrical with respect to all four attributes odd the parity concept It represents number of attributes have value 1 A A 0 0 B A xor 1 0 C B xor 2 0 D xor 3 0 Figure 8 Constructing concept images symmetrical concepts A concept can be saved in the form of training examples in two formats one 1 AQ type format and second 1 C4 5 ID3 type format The following commands allow saving the constructed concept Save Concept AQ and Save Concept 4 5 The examples below show descriptions created for the concept D Example 5 Examples defining the constructed concept as saved in AQ and C4 5 formats 5a AQ format 5b C4 5 format p events x0 x1 x2 x3 x1 x2 x3 0 0 0 1 0001 0 0 1 0 0010 0 1 0 0 0100 0 1 1 1 0111 1 0 0 0 1000 1 0 1 1 1011 1 1 0 1 1101 1 1 1 0 1110 0 0 0 0 n n events 0 0 1 1
14. representation of this domain after reading the description from the file The name of the representation space is placed as the window title The diagram is partitioned into cells by horizontal and vertical lines Horizontal lines correspond to attributes described on the side of the diagram hs bs sm Vertical lines correspond to attributes described below the diagram ho jc ti The most outside attributes hs and bs generate the largest grid in the diagram marked by thickest lines The most inside attributes sm and ti generate the smallest grid and are marked by thinnest lines The attributes can be rearranged in the diagram by changing their sequence in the file describing the representation space Each example in the representation space has its unique representation in the diagram Example 2 Robots 3 3 2 3 4 2 Given this domain description the system will generate the diagram shown in Figure 2b Please note default attribute names and values lo e E 2 Default attribute names and values A Attribute names and values defined by a user Figure 2 Diagrammatic representations of the ROBOTS domain 4 Diagrammatic Representation of Concepts DIAV provides a visual interpretation of various aspects of concept learning These include visualization of knowledge representatio
15. some attribute values by more general values Representation space contraction can lead to interesting observations like finding strong relationships between attributes or on the other hand finding irrelevant attributes The example below illustrates the two ways of contrac ng the representation space We begin with the Robots representation space and four positive and one negative example Figure 10a square square yes flag yellow no Robots PT TT ie Positive mum hs bs sm ho ti octagonal round balloon red yes octagonal round balloon green yes square round no sword yes H round square yes flag red no T Negative TT Negative hs bs sm ho ic ti ane Min Figure 10a Original representation space with 5 training examples Figure 10b illustrates the representation space contraction by removing the attribute jc The new domain description file was created by simply changing the domain name and by removing jc attribute description In the abstracted representation space some examples from one class may end up having the same description and therefore be placed in the same diagram cell This operation combined two different examples of the positive class into two equivalent examples Positive hs bs sm ho je ti octagonal round no balloon red yes octagonal round no balloon green yes Robot
16. square yes sword red yes round octagonal yes balloon red yes square square yes balloon red yes square square no balloon green yes Negative hs bs sm ho ti round octagonal yes sword yellow square octagonal yes sword yellow no octagonal square no sword green no octagonal round yes sword blue yes octagonal octagonal no balloon green no octagonal round no balloon blue no octagonal square yes flag red no octagonal round no flag green no round octagonal no flag blue yes round octagonal no flag green yes square round yes flag yellow yes 36 5 3 Save the exmaples description by chosing Save from the File menu Type in the file name e g trainingExamples and click on Save button 6 Display a diagram representing the domain 6 1 Select Representation Space from DIAV 1 menu 6 2 Open robotsDomain file 7 Display the target concept 7 1 Select Target Concept from DIAV 1 menu 7 2 Open the targetConcept file 8 Display the learned concept 8 1 Select Learned Concept from DIAV 1 menu 8 2 Open learned Concept file 9 Display the positive examples 9 1 Select Positive Examples from DIAV 1 menu 9 2 Open trainingExamples file 10 Display the negative examples 10 1 Select Negative examples from DIAV 1 menu 10 2 Open trainingExamples file 11 Display errors of commission 11 1 Select Errors of commission from DIAV 1 menu 12 Display errors of omission 12 1 Select Errors of omission from D
17. sword sword sword sword sword flag flag flag flag flag flag jc red green blue yellow red green blue yellow red green blue yellow red green ti yes yes yes yes no no no no yes yes yes yes no no round round octagonal octagonal octagonal octagonal octagonal octagonal octagonal octagonal square square square square square square square square square square no no no no yes yes no no yes yes flag flag balloon balloon balloon balloon balloon balloon balloon balloon blue yellow red green red green red green red green Example 5b The concept represented as a set of rules hs round bs2square sm no ho sword flag hs octagonal bs square ho balloon jc red green Robots 5 nd HY HY HY b rad Figure 5 Concept visualization from descriptions in the form of examples or rules Robots raed C Target and learned concept image D Error area image Figure 6 Target and learned concept images and their relationship 4 3 Concept Construction DIAV enables construction of arbitrary concept images A concept image is constructed either by direct selection of examples on the screen or by combining current concept image with other concept descriptions using predefined operators such as AND OR DIFF NOT and XOR The direct selection of examples is d
18. 1 x4 2 x5 3 x6 1 The STAR was further specialized by adding condition x6 1 The next uncovered negative example 4 differs with the seed on two attributes x1 and x4 gg JOLE EH II E Generating the Ist STAR after the 4th specialization STAR x120 x220 1 6 1 t 8 E ie ET E E x1 0 2 x2 0 1 x4 0 1 x6 1 t 12 Selected examples for the next specialization step 1 1 0 x2 0 x3 1 x4 1 x5 3 x6 1 5 x120 x2 1 x3 1 x4 2 x5 3 x6 1 The cover under consideration consists now of two rules This 1 result of two way specialization based on the two different values of attributes x1 and x4 In the next steps AQ will maintain at most 2 rules in the partial star because the maximum number of rules in the partial cover parameter MAXSTAR is set to 2 The rules maintained in the partial cover compete with each other according to the preference selection criteria For the current run the rule with the higher coverage of positive examples is assumed to be better The first rule covers 8 positive examples t8 the second rule covers 12 positive examples t 12 The two rules overlap over the area that covers the seed The area of overlap is described by 1 0 2 0 1 4 0 1 6 1 i 8 E iid E E E 5 8 iid E Eid F Generating the 1st STAR after the 5th specialization STAR 1 0 2 x220 1 x4 0 1 x6 1
19. 2 3 x6 1 t 4 Selected examples for the next specialization step 4 x120 x2 1 x3 0 x4 2 x5 2 x6 1 1 x120 x2 1 x3 1 x4 2 x5 2 x6 1 N Before generating the last STAR Cover 1 x120 2 x2 0 x420 1 x522 3 x6 1 t 5 2 x120 4 1 2 x5 1 x6 1 t 5 3 x2 1 x3 0 x4 0 1 5 1 2 3 x6 1 t 4 4 x120 x320 4 1 2 x5 1 2 3 x6 1 t 9 5 x120 2 x2 1 x3 1 x4 1 2 x5 2 3 x6 0 t 4 6 x2 1 2 x3 1 x5 0 x6 1 t 3 7 x220 2 x3 1 x4 0 x5 1 2 x6 1 t 4 8 x120 1 x222 x4 2 x5 0 1 t 4 9 x2 0 x3 0 x4 1 2 x5 1 2 3 x6 1 t 8 10 x2 0 x3 1 x5 1 x6 0 t 3 11 xl 1 2 x3 1 x5 0 x6 1 t 3 12 xl 1 2 x2 1 2 x3 0 x4 1 2 5 1 2 3 x6 0 t 9 13 x1 1 2 x2 1 2 x3 1 x4 0 x5 1 2 3 x6 0 t 4 14 1 1 2 x2 1 2 x3 1 x4 1 2 x5 0 t 7 15 1 1 2 x222 x4 0 x5 1 2 x6 1 t 2 Selected examples for the next specialization step n x122 x2 1 x320 x4 1 5 0 x6 1 1 x122 x2 0 x3 0 x4 1 x5 0 x6 1 O After generating the last STAR Cover 1 x120 2 x2 0 x420 1 x522 3 x6 1 t 5 2 x120 x4 1 2 x5 1 x6 1 t 5 3 x2 1 x3 0 x4 0 1 x5 1 2 3 x6 1 t 4 4 x1 0 x3 0 x4 1 2 x5 1 2 3 x6 1 t 9 5 x120 2 x2 1 x3 1 x4 1 2 x5 2 3 x6 0 t 4 6 x2 1 2 x3 1 x5 0 x6 1 t 3 7 x220 2 x3 1 x4 0 5 1 2 x6 1 t 4 8 x120 1 x222 x4
20. DIA V 2 0 User Manual Specification and Guide through the Diagrammatic Visualization System Janusz Wnek Machine Learning and Inference Laboratory George Mason Univesity 4400 University Dr Fairfax VA 22030 jwnek aic gmu edu Tue Nov 21 1995 Table of Contents be INTRODUCTION 3 2 GETTING SIARLED e CAO ED 4 2 4 SYSTEM REQOUIBEMENIDS 5 5 ZA UEXT cerai atout ua cen ER Se Qu 6 2 5 lAKINCEASNAPSHOTOETHEDIAV SCREEN Su pP US RU udi 6 ING DIA Tc 6 3 VISUALIZATION OF THE KNOWLEDGE REPRESENTATION SPACE 7 4 DIAGRAMMATIC REPRESENTATION OF 5 9 VISUALIZATION OF TRAINING EXAMPLES 9 4 2 VISUALIZATION OF TARGET AND LEARNED CONCEPTS a serene ted tee 10 a CONCEPT CONSTR GC HON 13 5 CHANGING THE REPRESENTATION 20 SCO NTR AG DION ohn M ata T 20 EXPANSION deside o Mer UBI eda Uma ceu olet cat odisse acco dN ewan 23 6 DEMO STAR GE
21. IAV 1 menu 13 Display total error area 13 1 Select Total error area from DIAV 1 menu 8 DIAV System Menus 27 amp File 0190 1 DIRU 2 Window DIAV 1 Representation Space Training Examples Positive Examples Negative Examples Target Concept Learned Concept Project to Display Rule from Transcript Errors of commission Errors of omission Total error area Hide Grid Clear Diagram Read domain and display its representation Display positive and negative examples Display positive examples Display negative examples Display a target concept in light gray shade Display a learned concept in dark gray shade Project current representation space on another domain Convert highlighted text to a graphical rule Show commission error image Showomission error image Show error image Define examples representing a concept Clear screen DIAV 2 Multiclass Examples Multiclass Rules Construct a Concept AND OR DIFF XOR NOT Save Concept in AQ Format Save Concept in C4 5 Format STAR Method step by step STAR Method animated Disp ex using consecutive numbers for each concept Display rules using different shades for each concept Construct a concept in a given representation space AND OR DIFF XOR operators combine currently displayed concept with a concept description read from a file Negate currently displayed concept save examples defining currently di
22. NERA TIONG BUE dE OO 26 75 SIMPLE SESSION WITH DIAY 72 0 33 9 SYSETEM CMENUS 35 9 DIAV SYNTAX van pius 38 19 DIAY DATA 41 REFERENCES ee 55596 42 Abstract The goal of the diagrammatic visualization system DIAV is to provide a tool for a visual interpretation of various aspects of concept learning These include visualization of knowledge representation spaces and relationships between training examples and target and learned concepts and visual comparison of knowledge transmutations performed by various learning systems e g visualization of changes in the representation space done by constructive induction The system employs a planar model of a multidimensional space spanned over a set of discrete attributes The model is in the form of a diagram in which each cell represents a unique combination of attribute values The diagram can represent examples rules and rulesets DNF in the form of concept images The system is very useful for analyzing behavior of existing learning algorithms and in every stage of development of a new learning system 1 Introduction The diagrammatic visualization system DIAV employs a planar model of a multidimensional space spanned over a set of discrete attributes The model is called General Logic Diagram GLD and was introduced by Michalski in 1978 The model is in the form of a
23. attributeValue Figure 4 Concept representation using rules or examples An important feature of DIAV 1 that it permits displaying steps in concept learning The set of cells representing the target concept the concept to be learned 1s called target concept image T The set of cells representing the learned concept 1 called learned concept image L Concept images are represented in the diagrams by shaded areas Target concept image is represented by light gray shade learned concept image is represented by dark gray shade If the target and learned concepts are both visualized in the same diagram then their overlap becomes black One of the three cases may occur If the learned concept totally matches the target concept then the whole image 1 black If there are some areas of the target concept not covered by the learned concept description then these areas reflect errors of omission light gray area If the learned area 1s larger than the target overgeneralization of the concept then the dark gray area represents errors of commission Figure 6 12 Example 5 concept represented as a set of examples hs bs round square round square round square round square round square round square round square round square round square round square round square round square round square round square sm ho sword sword sword
24. by a learning system e g 15 Output 1s directed to a graphical terminal with regards to visual effects and to data files for communication with a learning system or for a further use by DIAV The graphical terminal 1s able to display and control multiple windows Windows are furnished with standard control boxes for zooming in and out the window Scroll bars on sides of the panes enable to display larger then screen size images and to have an convenient character input output inherits all standard Smalltalk V features A user can take advantage of for instance built in text editor cut copy paste feature or font chooser see Appendix DIAV system menus 3 The DIAV 2 0 system enables Visualization of target and learned concepts Visualization of arbitrary rules either by specifying their description or by direct drawing Visualization of errors of commission omission and the complete error image Construction of complex concepts by using AND OR DIFF NOT and XOR operators Projection of a given representation space into another one by removing and or adding attributes 4 Future features of the DIAV system will include the following AQ specific operators operator refunion extension against EA square root the set of all maximal complexes inside the set star of event SR EA e NegEvents 2 Getting Started 2 1 System Requirements In order to use the DIAV visualization pro
25. by adding new attribute values to the value sets of existing attributes Exchange 1s done by replacing original attributes with new ones All transformations of the representation space are performed using the Project to command DIAV prompts for a new description file and creates an internal mapping between the representations A new window with a diagram is created for the new representation space The diagram is labeled with its predecessor s name followed by semicolon and new domain name read from the description file e g Original RS New RS Next by selecting commands such as Training Examples Target Concept etc DIAV will project examples or concepts from the previous representation space to the new one instead of reading them form a file The new representation space description file has similar syntax to the description file of the original representation space Additional components consist of definitions of new attribute values Those definitions use original attributes and are in the DNF form see the DIAV Syntax section 5 1 Contraction In some situations there is an interest displaying an image of a reduced abstracted representation space For example some constructive induction learning systems reduce knowledge representation spaces to remove redundancy or insignificant attributes Wnek 1993 Wnek amp Michalski 1994 The representation space can be reduced either by removing some attributes or by replacing
26. d E x E Ed 7H Oe EO E EO Ru 1 5 i L L i EG l Baki HERNED NE NN Ei BEERS 1 1 1 E il i o 111 34 General vs minimal description The general cover is equivalent to the cover obtained after the last STAR generation Figure O The minimal cover black area covers a smaller area of the representation space than the general cover gray and black The two covers differ in 21 locations B General vs specific characteristic description The specific cover black area covers a smaller area of the representation space than the general cover In this case the specific cover differs from the general cover in 53 locations C Minimal vs specific description The specific cover black area covers a smaller area of the representation space than the minimal cover In this case the specific cover differs from the minimal cover in 32 locations Note The term minimal description refers to the number of conditions and condition values used in the description Minimal description has usually larger coverage in terms of the number of instances covered than the specific description 7 Simple session with DIAV 2 1
27. ept represent errors of commission L T The union of both types of errors represents the error image The system can also display results of any operation on the concept such as generalization specification or any change of the description space such as adding or deleting attributes or their values Another interesting feature 1s that it can also visualize concepts acquired by non symbolic systems such as neural nets or genetic algorithms Using the diagram one can express the learned concepts in the form of decision rules Thus the diagram allows one to evaluate both the quality and the rule complexity of the results of symbolic and non symbolic learning The implemented 4 system DIAV can display description spaces up to 4M events 1 spaces spanned over up to 22 binary variables or correspondingly smaller number of multiple valued variables The system is very useful for analyzing behavior of existing learning algorithms and in every stage of development of a new learning system Following are the features implemented the current version of the system DIAV 2 0 1 The maximum event space ES size for a direct display is 4 events 22 binary attributes and for a virtual display is 32 M events 25 binary attributes on a workstation with 8 MB memory System is window and menu driven An input to the system comes from a graphical terminal and from data files generated within the system or generated
28. es sword yellow square octagonal yes sword yellow square square no sword yellow square square no sword yellow no square octagonal no sword yellow square octagonal no sword yellow no square round flag yellow yes square round yes flag yellow yes square round no flag yellow yes square round no flag yellow yes Class3 Negative hs bs sm jc ti hs bs sm ho jc ti round octagonal yes sword yelow yes round octagonal yes sword yelow yes octagonal octagonal yes sword yellow no octagonal octagonal yes sword yellow no round octagonal sword yellow yes round octagonal no sword yellow yes 554 Negative hs bs sm ho jc ti hs bs sm ho jc ti round octagonal yes flag yellow yes round octagonal yes flag yellow yes round octagonal yes flag yellow no round octagonal yes flag yellow no square octagonal yes flag yellow yes square octagonal yes yellow yes square octagonal yes flag yellow no square octagonal yes flag yellow no octagonal octagonal yes flag green yes octagonal octagonal yes flag green yes octagonal octagonal yes flag green no octagonal octagonal yes flag green octagonal octagonal no flag green yes octagonal octagonal no flag green yes octagonal octagonal no flag green no octagonal octagonal no flag green no Robots Robots HARES ENAA TE TE ea BREE ER Eee eee ENNIBEINSRE
29. esentation space representation space projected onto xor projected onto ca bin4 2 2 2 2 xor 3 3 ca 5 x0 0 1 0 0 1 2 ca 0 4 1 0 1 1 0 1 2 2 0 1 0 x3 0 1 1500 0 0 1 0 x020 1 0 1 50 1 0 0 s1 1 0 0 1 1 50 1 1 0 x021 1 0 2 1510 0 0 s1 2 x2 0 x3 0 0 1 s1 1 0 2 1 0 51 1 x2 0 x3 1 3 x2 1 x3 0 0 1 s1 2 0 2 1 1 Figure 12 Two exchanges of the representation spaces 27 In the first mapping from bin4 to xor attributes x0 and replaced by the sO attribute Symmetrically x2 and x3 are replaced by the 1 attribute Value 0 0 representing the top row in the bin4 xor diagram replaces the conjunction x020 amp x120 i e the top row in bin4 diagram Value 0 1 representing the middle row in the bin4 xor diagram replaces the disjunction 0 1 1 0 or 0 0 amp 1 1 i e two middle rows in the bin4 diagram The two rows can be merged without causing ambiguity because they are symmetrical Value 0 2 representing the bottom row in the bin4 xor diagram replaces the conjunction xO 1 amp 1 1 1 e the bottom row in the bin4 diagram Since this value complements other values it is not necessary to specify it in the attribute definition In the second mapping from xor to ca attributes 0 and 1 are replaced by the ca attribute As a result of the two transformations a 16
30. gonal Figure 10 Ambiguity caused by contraction it a a N E E E M 21121 1 seses 21 1 21121 121 MI 21 121 Robots jc hs s removed2 2 3 2 3 2 Hs round x bs round square octagonal sm yes no ho sword balloon flag ti yes no Hs round hs round Hs x hs square hs octagonal Figure 10d Alternative combination of attribute values 23 5 2 Expansion The representation space expansion operation is done by adding new attribute definitions or by adding new attribute vales to the value sets of existing attributes The changes have to be specified in the file defining the new representation space The new attribute values are defined using original attributes DNF expressions Expansion may remove ambiguity of examples in the representation space There may be however different side effect of this operation In the process some impossible areas may be created Wnek 1993 The impossible areas consist of impossible instances 1 e instances that do not have equivalent descriptions in the original representation space Figure 11a shows a five dimensional binary representation space In order to show how examples of a given concept are projected the complete set of examples is used Figure 11b shows the expanded representation space One binary attribute was added that separates most of the positive examples from negative examp
31. gram hereafter referred to as DIAV the following system requirements must be satisfied Macintosh System 7 or later Installed Smalltalk V Mac from Digitalk Inc At least 2M of free RAM 2 2 DIAV Distribution The complete DIAV distribution is provided on a single diskette entitled DIAV 2 0 which contains the following DIAV the DIAV application ReadMe the ReadMe text file Be sure to read this file as it may contain important information and instructions not provided in this manual Example the Example folder with an example knowledge representation space Robots rs target and learned concepts Robots tc1 Robots Ic1 2 3 Running DIAV To start DIAV double click on its icon to open the program You can use DIAV without any additional setting If you wish however you can change default font style from the Window menu DIAV 1 run under the control of Smalltalk V Mac This way DIAV inherits whole functionality of Smalltalk V allowing for file and string manipulation as well as window control It is easy to distinguish between Smalltalk V and DIAV environments by checking which set of menus is currently available Smalltalk V uses the following menus File Edit Smalltalk Window DIAV uses File DIAV 1 DIAV 2 Window After the start two windows are displayed Figure 1 One window Diagrammatic Visualization System DIAV 2 0 is used for visualization of knowledge representation spaces This window come
32. he GD7 rule has more x4 9 x1 1 2 x2 0 2 x3 1 x4 0 2 x5 0 x6 1 t 3 u 3 attribute values than the corresponding rules SD16 and EUN daa cm 1 2 XI 4 1 2 t 3 U MD14 from the other covers SD16 meanwhile has more x102 x2 0 x3 1 x4 0 1 5 23 1 t3 42 conditions than GD7 and MD14 namely conditions that x1 1 2 x2 2 x3 0 x4 0 x5 2 x6 1 t 2 u 2 specify the values of x2 and x3 14 1 0 x2 1 2 x3 1 x4 1 2 x5 0 x6 1 t 2 u 2 15 1 2 x2 1 x3 0 x4 1 x5 0 x6 1 t 1 u 1 16 x1 0 x2 0 x3 1 x4 2 x5 1 x6 1 u 1 The rules are presented in the 15 format Each rule is accompanied with two numbers t is the total number of positive examples covered by the rule 15 the number of positive examples uniquely covered by the rule Unique coverage means that none of the other rules in the description covers those examples The rules each of the descriptions are ordered according to the t and u weights since the trimming process may change a rule s coverage the rule may be placed in different positions of the cover lists For example rule 7 in the general cover becomes 14 in the minimal cover and 16 in the specific cover Note also changes the total and unique coverage values of this rule 1 7H Oe By E E
33. hm Methods Proceedings of the 5th International Symposium on Methodologies for Intelligent Systems ISMIS 90 Knoxville TN pp 428 437 October 1990 Wnmek J Hypothesis driven Constructive Induction Ph D dissertation School of Information Technology and Engineering Reports of Machine Learning and Inference Laboratory MLI 93 2 George Mason University also published by University Microfilms Int Ann Arbor MI March 1993 Wnek J and Michalski R S Comparing Symbolic and Subsymbolic Learning Three Studies in Machine Learning A Multistrategy Approach Vol 4 R S Michalski and Tecuci Eds Morgan Kaufmann San Mateo CA 1994 Wnek J and Michalski R S Hypothesis driven Constructive Induction in AQI7 HCI Method and Experiments Machine Learning Vol 14 No 2 pp 139 168 1994 Wnek J and Michalski R S Symbolic Learning of M of N Concepts Reports of Machine Learning and Inference Laboratory MLI 94 1 George Mason University Fairfax VA April 1994 Wnek J and Michalski R S Discovering Representation Space Transformations for Learning Concept Descriptions Combining DNF and M of N Rules Working Notes of the ML COLT 94 Workshop on Constructive Induction and Change of Representation New Brunswick NJ July 1994 Wnek J and Michalski R S Conceptual Transition from Logic to Arithmetic Reports of Machine Learning and Inference Laboratory MLI 94 7 George Mason Univers
34. ho balloon hs square B hs square ho balloon hs octagonal bs square D bs square F ho balloon hs square ho flag hs round octagonal bs round H jc red blue The following sequence of commands constructs the images shown in Figure 7 It starts with displaying the initial concept A This concept image is combined using operator AND with the concept B The resulting image concept C is combined with concept D using operator OR etc Construct a Concept Input A Output A AND Input A B Output C OR Input C D Output E DIFF Input Output G 15 Input G H Output I Input I Output J The following transcript is created in the System Transcript window Domain description read from file 2 CONSTLUCE LNG concepts Robots rs A concept read from file CONSLIEUCLING concepts AND concept from file cOlstrucblng conospts OR concept from file oss toonsbructing Concepts DIFF concept from file tconstr ctaadg concepuss XOR concept from file CONSEEUCEING concepts NOT ConsbtructconDcoept CONSE LUCLCCONCEDE AND pee Lt UNI NES HH Figure 7 Constructing concept
35. ibute partitions the diagram into areas corresponding to individual values of the attribute A representation space description is assumed to be a form of a text file This file has to begin with a domain name followed by a specification of a size of the domain for every attribute the number of values has to be specified If there 15 no attribute and value definition following system will assume default names for attributes and their values attributes can be then referred as xl x2 xn values will be default numerical numbers 0 1 2 Values of an attribute can be expressed as a list of nominal values e g red green blue yellow or an interval e g 10 17 The following 15 an EBNF syntax specification for domain description see Appendix A DIAV Syntax for detailed specification domainDescription domainName number number attributeName interval attributeName attributeValue attributeValue Example I The following description of the representation space is in the Robots rs file Robots 3 3 2 3 4 2 hs round square octagonal bs round square octagonal sm yes no ho sword balloon flag jc red green blue yellow ti yes The Robots domain consists of six attributes The header line defines the domain space 3 x 3 x 2 x 3x4x 2 The lines following the headline define names of attributes and their values Figure 2a shows the graphical
36. ity Fairfax VA December 1994 Wnek J Kaufman K Bloedorn E and Michalski R S Selective Induction Learning System AQI5c The Method and User s Guide Reports of Machine Learning and Inference Laboratory MLI 95 4 George Mason University Fairfax VA March 1995 References marked with include examples of General Logic Diagrams
37. ity Fairfax VA December 1993 45 Michalski R S Wnek J Constructive Induction An Automated Improvement of Knowledge Representation Spaces for Machine Learning Proceedings of the 2nd Conference on Practical Aspects of Artificial Intelligence pp 188 236 Augustow IPI PAN Warszawa Poland 1993 Michalski R S and Wnek J Learning Hybrid Descriptions Proceedings of the 4th International Symposium on Intelligent Information Systems Augustow Poland June 5 9 1995 Szczepanik W Arciszewski T and Wnek J Empirical Performance Comparison of Two Symbolic Learning Systems Based On Selective And Constructive Induction Proceedings of the IJCAI 95 Workshop on Machine Learning in Engineering Montreal Canada August 1995 Thrun S B Bala J Bloedorn E Bratko I Cestnik B Cheng J De Jong K A Dzeroski S Fahlman S E Hamann R Kaufman K Keller S Kononenko Kreuziger J Michalski R S Mitchell T Pachowicz P Vafaie H Van de Velde W Wenzel W Wnek J and Zhang J The MONK s problems A Performance Comparison of Different Learning Algorithms Computer Science Reports CMU CS 91 197 Carnegie Mellon University Revised version Pittsburgh PA December 1991 Wnek J Sarma J Wahab A and Michalski R S Comparing Learning Paradigms via Diagrammatic Visualization A Case Study in Concept Learning Using Symbolic Neural Net Genetic Algorit
38. les This operation caused however creation of impossible instances For an analysis of impossible areas and ways of informing learning systems about their existence see Wnek 1993 a FiveD_Space Concept lt 1 1 x2 1 Ic121 x321 x4 0 x5 1 x1 1 x2 1 lla The Concept in 5D representation space 11b The Concept in the expanded representation space Blank cells indicate impossible instances no instances from the original representation space were projected onto Figure 11 Expansion of the representation space 24 5 3 Exchange The representation space exchange operation occurs when some attributes are replaced new attributes In order to maintain projection capability between the two representation spaces there have to be a relationship between the original and the new attributes Similarly to the expansion operation the new attribute values are expressed using original attributes in DNF expressions Attributes that are being replaced have to be removed from the domain description Figure 12 presents two consecutive exchanges of the representation space The first exchange occurs between the bin4 four dimensional binary representation space and the xor two dimensional three valued representation space The second exchange occurs between the xor representation space and the ca one dimensional representation space 12a bin4 the original 12b bin4 representation space 12c xor repr
39. n spaces relationship between training examples target and learned concepts visualization of changes in the representation space done by constructive induction 4 1 Visualization of Training Examples There can be a number of ways to visualize preclassified examples of many classes In the context of concept learning we use the following two modes for visualizing training examples 1 Multi class mode Training examples of different classes are visualized using consecutive numbers This mode allows seeing distribution of examples in the representation space 2 Binary class mode Training examples are visualized using and to distinguish between positive and negative examples Examples of some classes can be marked as positive examples and the remaining classes as negative examples A special case of this type includes situation when one class is selected as positive and other classes as negative This is a typical strategy in multiple concept learning Example 3b A set of training examples for visualization 1 read from a text file The file can be created using the smalltalk s editor see Section 2 4 Editing Text Training examples are grouped into classes represented as relational tables Each class has to be identified by its name and followed by the line with attribute names defining their order in the table Training examples are listed in the following lines In order to display examples in multi clas
40. nt in the concept represented by the Form In order to visualize a concept represented by a Form the Form 1s magnified and displayed on the screen The Form 1 very useful data structure for storing concepts as diagrams It allows for direct mapping between a diagram as a Form This way many operations performed with concepts such as union product etc are easy to implement The example below refers to the ROBOTS domain description Robots 3 3 2 3 4 2 hs round square octagonal 6 round square octagonal sm yes no ho sword balloon flag jc 1 4 ti yes no DIAV represents this domain description in the form of following arrays and variables aA 3 1 48 2 144 bs 2 3 24 3 4 2 4 5 6 2 6 1 ti xA 4 5 6 3 2 2 6 1 ti 3 2 144 bs 3 1 48 2 3 24 44 square octagonal round square octagonal sword balloon flag 1 2 3 4 yes 24 18 thisDomainName Robots parentWindow nil Each cell in a planar diagram representing the domain has two coordinates a column coordinate x and a row coordinate y represented as a pair x y The range of the coordinate x is from 0 to xx 1 The range of y is from to yy 1 The coordinates of a cell x of an event vector Av1 Av2 are calculated according to the formulas n
41. one by clicking on selected cells in the diagram Clicking on an empty cell adds the cell into the concept image Clicking on an cell belonging to the concept image removes the cell from the concept image The concept image can be combined with another concept by selecting one of the predefined operators and the concept description stored in a file The concept description can be in the form of rules or examples 14 The constructed concept image can at any time be transformed into the concept description in the form of positive and negative examples and stored in a file It can later be used as an input for a learning system In order to construct a concept image display a new Representation Space or select Clear Diagram clear the current one Next select Construct a Concept initialize the concept image by either direct input or visualization of the concept description stored in a file Next combine the image with other concept descriptions using the AND OR DIFF NOT and operators from the DIAV menu At any time the concept image can be changed by directly switching on off concept examples Figure 7 illustrates application of various operators used in constructing concept images in the Robots representation space The descriptions of the initial concept A and other concepts B D F and H used as operands were stored in separate files Below are the concept descriptions in the form of rules A ho sword flag
42. r ruleSet rule condition condition conditions for all attributes condition condition 43 10 DIAV Data Structures This section describes the data structures used in DIAV system It also gives an example of a domain in DIAV s internal representation aA array describing attributes of a domain size aA nr of attributes Each attribute is described by four numbers of values levels serial number defines the serial number of a column in the data table offset in the diagram filled out by crArr name XA array describing attributes placed on x axes of a diagram yA array describing attributes placed on y axes of a diagram aV array describing possible values for each attribute size aA size aV Serial number of an attribute indexes appropriate values XX number of columns of a diagram yy number of rows of a diagram thisDomainName domain name of the current window parentWindow reference to the parent window from projected window Concepts sets of examples and other graphical images are represented as Forms A Form 1s characterized by its width height and content Bitmap The width of a Form 1 related to the number of columns in a diagram the height of a Form 15 related to the number of rows Each bit of the Form is related to the concept stored in the Form Bit 1 in the Form indicates that related event is present in the concept bit 0 indicates that the event is not prese
43. s each condition with a maximum number of values Minimal description MD consists of rules as simple as possible 1 involving the minimum number of conditions each condition with a minimum number of values Specific characteristic description SD consists of rules as specific as possible i e involving the maximum number of conditions each condition with a minimum of values General cover Minimal cover 1 xl 1 2 x2 1 2 x3 0 4 1 2 x5 1 2 3 x6 0 t9 u 8 1 xl 1 2 2 1 2 x3 0 4 1 2 x5 1 2 3 x6 0 t 9 u 8 2 x120 x320 4 1 2 x5 1 2 3 x6 1 t9 4 2 x120 x320 4 1 2 x5 1 2 3 x6 1 t 9 u 7 3 x2 0 x3 0 x4 1 2 x5 1 2 3 x6 1 t8 6 3 x2 0 x3 0 4 1 2 x5 1 2 3 x6 1 t 8 u 6 4 x1z1 2 x2 1 2 x3 1 x4 1 2 x5 0 t 7 5 4 1 1 2 x2 1 2 x3 1 x4 1 2 x5 0 t 7 u 6 5 x2 1 x3 0 x4 0 1 x5 1 2 3 x6 1 t5 u 3 5 x120 2 2 0 x4 0 1 x5 2 3 x6 1 t 5 u 2 6 1 0 2 2 0 x4 0 1 x5 2 3 x6 1 t5 2 6 x120 x2 1 x3 1 x4 1 2 x5 2 3 x6 0 t 4 u 4 7 1 0 x4 1 2 5 1 x6 1 t5 u 1 7 1 1 2 x2 1 2 x3 1 x4 0 x5 1 2 3 x6 0 t 4 u 4 8 x120 2 x2 1 x3 1 x4 1 2 x5 2 3 x6 0 t4 4 8 x2 0 2 x3 1 x4 0 5 1 2 x6 1 t 4 u 3 9 xl 1 2 2 1 2 x3 1 4 0 x5 1 2 3 x6 0 t4 4 9 x120 1 x222 x4 2 x5 0 1 t 4 u 2 10 x220 2 x3 1 x4 0
44. s jc removed 3 3 2 3 2 hs round square octagonal 6 round square octagonal sm yes no ho sword balloon flag ti yes no Figure 10b Contracted representation space by removing an attribute 22 Figures 10 10d illustrate the contraction operation by both removing the attribute jc and the attribute value hszsquare In order to remove attribute values they have to be combined into larger units with other attribute values Figure 10c shows how the representation space changes when the hs square is combined with hs round into a larger unit Hs x Figure 10d shows hs square combined with hs octagonal into Hs x Note that the attribute with combined values has different name and attribute values The modified attribute 1 defined by specifying its attribute values in relation to the original values For example Hs x in Figure 10c is defined as hs round or hszsquare Hs octagonal is just a copy of hs octagonal Contraction operation may cause ambiguity of some of the training examples Figure 10 shows how two different examples of two different classes were combined into two ambiguous examples Positive Hs bs sm ho je ti X square yes flag no Negative Hs bs sm ho je ti X square yes flag no Robots jc hs s removed 2 3 2 3 2 Hs x octagonal 6 round square octagonal sm yes no ho sword balloon flag ti yes no hs round hszsquare Hs octagonal hszocta
45. s mode select Multiclass examples from DIAV 2 menu and than select the file with training examples as in Example 3a In order to dispaly the same training examples in the binary class mode change class labels to Positive and Negative as in Example 3b select Training Examples from DIAV 1 menu and identify the data file If you want to display Positive or Negative examples only select Positive Examples or Negative Examples respectively Ambiguous examples i e examples that have the same attribute values but different class labels are marked with the multi class mode and with in the binary class mode In Figure 3 the example hs square amp bs round amp sm no amp ho flag amp jc yellow amp tizyes belongs to both Classl and Class2 and therefore is ambiguous 10 Example 3a Multi class examples Example 3b Positive and negative examples Class1 Negative hs bs sm jc ti hs bs sm ho jc ti round round no sword red yes round round no sword red yes round square no sword red yes round square no sword red yes round square no sword red no round square no sword red no square round yes sword red yes square round yes sword red yes square round yes sword red no square round yes sword red no square round no flag yellow yes square round no flag yellow yes Class2 Positive hs bs sm ho jc ti hs bs sm jc ti square square yes sword yellow square square yes sword yellow square octagonal y
46. s with the DIAV menus Another window is System Transcript This 1s Smalltalk s window and when selected Smalltalk s menus will become available This window 1 used by DIAV to display textual information about various transformations performed on diagrams such as the number of commission errors which file the representation space description was read from etc Through this window you can also specify rules to be displayed by DIAV At the beginning of the System Transcript there is a command DIAV new open on nil to open more DIAV type windows In order to create an additional window select highlight the text of the command including brackets and select Do it from Smalltalk menu This way you can visualize many DIAV windows at the same time File 0180 1 0190 2 Window 7 5 95 2 Diagrammatic Visualization System 2 0 2 4 1 4 T poer POWERDrive Share 417 CH a Hello DIRU ver 2 0 7 5295 System Transcript CAE AES UAE LRL Janusz Wnek A AL AES George Mason Universi ty Pu Mur ror rre NC a Machine Learning and Inference Lab hoa he ME a 4400 University Dr Fairfax UR 22030 junek amp eaic dgmu edu 032 993 1717 Smalltalk compre
47. splayed concept Use C4 5 format Step by step demo of the STAR learning method Animated demo of the STAR learning method 38 File New Open File In Browse Classes Close Save Save as Revert to Saved Create new text file using text editor Open file window for editing Read and execute Smalltalk source code Open multi paned browser on available Smalltalk code Close file window Save the text contents of the currently active window Save the text contents in the specified file Replace with the last version saved on disk Page Setup Setup for page printing Print Print the contents of the active text window Save Image Save the state of environment to disk Quit Quit the system Edit Undo Undo a last operation Cut Cut a portion of text and copy it to clipboard Copy Copy text to clipboard Paste Paste from clipboard Clear Delete highlighted text Select All Select a contents of current pane window Find Find string in a text of current pane window Replace Find and replace text Search Again Repeat searching replacing text Smalltalk Show it Do it File it in Inspect It In Stop Evaluate Smalltalk expression Execute Smalltalk code File in execute Smalltalk code Inspect a Smalltalk object Interrupt process 39 Window Send To Back Collapse Expand Zoom In Out Change Text Font Change List Font Redraw Screen Stack Windows Pu
48. ssSources Smalltalk compressChanges JcDIRU new open on nil 2 4 Text Editing Text editing in DIAV is one of the features inherited from Smalltalk V It conforms to text editing conventions of the Macintosh such as moving the insertion point deleting inserting characters selecting words lines text deselecting text deleting selected text cutting coping pasting selected text The File menu contains all commands needed for text exditing and printing They include New Open Save Save As Revert to Saved Page Setup and Print 2 5 Taking a Snapshot of the DIAV Screen In order to make a snapshot of the current screen press the following keys Shift 3 A Picture file will be created in the main folder You can cut and paste a desired segment into your publication 2 6 Exiting DIAV To exit DIAV and return to the Macintosh OS select Quit from the File menu You will be prompted with a dialog box which asks whether or not to save your current environment a kind of snapshot of all existing objects on your DIAV desktop including window placement and contents This way when you restart DIAV program you will begin right where you left off 3 Visualization of the Knowledge Representation Space DIAV employs a planar model of a multidimensional space spanned over a set of discrete attributes The model is in the form of a diagram in which each cell represents a unique combination of attribute values Each attr
49. t STAR after the Ist specialization cz LI I5 1 02 Ss Iu x m Selected examples for the next specialization step eee 1 1 0 x2 0 x3 1 x4 1 x5 3 x6 1 NECCEN 2 x1 0 x2 2 x3 1 x4 1 x5 3 x6 1 de a at m As result of the first extend against operation the negative example 1 is no longer covered because 1 1 was removed from the coverage The current cover 15 equivalent to a simple rule 1 0 2 AQ continues building the STAR around the same seed positive example 1 The next negative example 2 is 54 selected The examples have different x2 attribute values Negative example L Uncovered Selected negative example Generating the Ist STAR after the 2nd specialization STAR 1 0 2 x2 0 1 Selected examples for the next specialization step 1 x120 2 0 x3 1 x4 1 x5 3 x6 1 3 x1 0 x2 0 x3 1 x4 1 x5 3 x6 0 The STAR was further specialized by adding condition x2 0 1 There are still uncovered negative examples e g 3 gg PERE Fi 29 L4 i MONK2 c ITF D Generating the Ist STAR after the 3rd specialization STAR 1 0 2 x2 0 1 x6 1 Selected examples for the next specialization step 1 x1 0 x2 0 x3 1 x4 1 x5 3 x6 1 4 1 2 2 0 x3
50. t this window below other opened ones Collapse expand current window Zoom in out current window Change font in text pane Change font in list pane Redraw screen in case anything 15 wrong Order opened windows so all headers are visible 9 DIAV Syntax 40 The following is EBNF syntax specification for DIAV syntax domainDescription constructedAttribute concept conceptSet targetConcept learnedConcept example exampleSet trainingExamples conceptExamples positiveExamples negativeExamples ruleSet rule domainName conceptName attributeName attributeSize domainName attributeSize attributeSize attributeName attributeRange attributeName attributeValue attributeValue constructedAttribute 1 attributeName attributeValue concept ruleSet exampleSet 1 concept concept concept attributeValue attributeValue attributeOrder example example conceptExamples positiveExamples negativeExamples 1 exampleSet Positive exampleSet Negative exampleSet rule rule condition condition identifier identifier identifier number attributeValue attributeRange attributeOrder condition expression REL interval identifier number letter capitalLetter digit
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