Representing and learning Boolean functions of multivalued features
An analysis and empirical measurement of threshold linear functions of multivalued features is presented. The number of thresholded linear functions, maximum weight size, training speed, and the number of nodes necessary to represent arbitrary Boolean functions are all shown to increase polynomially...
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| Veröffentlicht in: | IEEE transactions on systems, man, and cybernetics man, and cybernetics, 1990-01, Vol.20 (1), p.67-80 |
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| container_title | IEEE transactions on systems, man, and cybernetics |
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| creator | Hampson, S.E. Volper, D.J. |
| description | An analysis and empirical measurement of threshold linear functions of multivalued features is presented. The number of thresholded linear functions, maximum weight size, training speed, and the number of nodes necessary to represent arbitrary Boolean functions are all shown to increase polynomially with the number of distinct values the input features can assume and exponentially with the number of features. Two network training algorithms, focusing and back propagation, are described. Empirically, they are capable of learning arbitrary Boolean functions of multivalued features in a two-level net. Focusing is proved to converge to a correct classification and permits some time-space complexity analysis. Training time for this algorithm is polynomial in the number of values of a feature can assume, and exponential in the number of features. Back propagation is not necessarily convergent, but for randomly generated Boolean functions, the empirical behavior of the implementation is similar to that of the focusing algorithm.< > |
| doi_str_mv | 10.1109/21.47810 |
| format | Article |
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The number of thresholded linear functions, maximum weight size, training speed, and the number of nodes necessary to represent arbitrary Boolean functions are all shown to increase polynomially with the number of distinct values the input features can assume and exponentially with the number of features. Two network training algorithms, focusing and back propagation, are described. Empirically, they are capable of learning arbitrary Boolean functions of multivalued features in a two-level net. Focusing is proved to converge to a correct classification and permits some time-space complexity analysis. Training time for this algorithm is polynomial in the number of values of a feature can assume, and exponential in the number of features. Back propagation is not necessarily convergent, but for randomly generated Boolean functions, the empirical behavior of the implementation is similar to that of the focusing algorithm.< ></description><identifier>ISSN: 0018-9472</identifier><identifier>EISSN: 2168-2909</identifier><identifier>DOI: 10.1109/21.47810</identifier><identifier>CODEN: ISYMAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Acceleration ; Animals ; Applied sciences ; Artificial intelligence ; Boolean functions ; Computer science ; Computer science; control theory; systems ; Exact sciences and technology ; Instruments ; Learning and adaptive systems ; Logic ; Multidimensional systems ; Organisms ; Polynomials ; Shape</subject><ispartof>IEEE transactions on systems, man, and cybernetics, 1990-01, Vol.20 (1), p.67-80</ispartof><rights>1991 INIST-CNRS</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c339t-d6b5991a396cccb57f2d32a90868dcf540c0c94441cad262de6518992af693183</citedby><cites>FETCH-LOGICAL-c339t-d6b5991a396cccb57f2d32a90868dcf540c0c94441cad262de6518992af693183</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/47810$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,4024,27923,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/47810$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19722690$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Hampson, S.E.</creatorcontrib><creatorcontrib>Volper, D.J.</creatorcontrib><title>Representing and learning Boolean functions of multivalued features</title><title>IEEE transactions on systems, man, and cybernetics</title><addtitle>T-SMC</addtitle><description>An analysis and empirical measurement of threshold linear functions of multivalued features is presented. The number of thresholded linear functions, maximum weight size, training speed, and the number of nodes necessary to represent arbitrary Boolean functions are all shown to increase polynomially with the number of distinct values the input features can assume and exponentially with the number of features. Two network training algorithms, focusing and back propagation, are described. Empirically, they are capable of learning arbitrary Boolean functions of multivalued features in a two-level net. Focusing is proved to converge to a correct classification and permits some time-space complexity analysis. Training time for this algorithm is polynomial in the number of values of a feature can assume, and exponential in the number of features. Back propagation is not necessarily convergent, but for randomly generated Boolean functions, the empirical behavior of the implementation is similar to that of the focusing algorithm.< ></description><subject>Acceleration</subject><subject>Animals</subject><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Boolean functions</subject><subject>Computer science</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Instruments</subject><subject>Learning and adaptive systems</subject><subject>Logic</subject><subject>Multidimensional systems</subject><subject>Organisms</subject><subject>Polynomials</subject><subject>Shape</subject><issn>0018-9472</issn><issn>2168-2909</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1990</creationdate><recordtype>article</recordtype><recordid>eNpFj81LxDAQxYMouK6CV2-9CF66ZtI0zRx18QsWBNFzmc2HVLrpkrSC_72tFT29eczvPXiMnQNfAXC8FrCSlQZ-wBYClM4FcjxkC85B5ygrccxOUvoYrZRYLtj6xe2jSy70TXjPKNisdRTDZG67brxD5odg-qYLKet8thvavvmkdnA28476YQyfsiNPbXJnv7pkb_d3r-vHfPP88LS-2eSmKLDPrdqWiEAFKmPMtqy8sIUg5Fppa3wpueEGpZRgyAolrFMlaERBXmEBuliyq7nXxC6l6Hy9j82O4lcNvJ7G1wLqn_Ejejmje0qGWh8pmCb981gJoXDiLmaucc79veeObwxwYQw</recordid><startdate>199001</startdate><enddate>199001</enddate><creator>Hampson, S.E.</creator><creator>Volper, D.J.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>199001</creationdate><title>Representing and learning Boolean functions of multivalued features</title><author>Hampson, S.E. ; Volper, D.J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c339t-d6b5991a396cccb57f2d32a90868dcf540c0c94441cad262de6518992af693183</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1990</creationdate><topic>Acceleration</topic><topic>Animals</topic><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Boolean functions</topic><topic>Computer science</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Instruments</topic><topic>Learning and adaptive systems</topic><topic>Logic</topic><topic>Multidimensional systems</topic><topic>Organisms</topic><topic>Polynomials</topic><topic>Shape</topic><toplevel>online_resources</toplevel><creatorcontrib>Hampson, S.E.</creatorcontrib><creatorcontrib>Volper, D.J.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>IEEE transactions on systems, man, and cybernetics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Hampson, S.E.</au><au>Volper, D.J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Representing and learning Boolean functions of multivalued features</atitle><jtitle>IEEE transactions on systems, man, and cybernetics</jtitle><stitle>T-SMC</stitle><date>1990-01</date><risdate>1990</risdate><volume>20</volume><issue>1</issue><spage>67</spage><epage>80</epage><pages>67-80</pages><issn>0018-9472</issn><eissn>2168-2909</eissn><coden>ISYMAW</coden><abstract>An analysis and empirical measurement of threshold linear functions of multivalued features is presented. The number of thresholded linear functions, maximum weight size, training speed, and the number of nodes necessary to represent arbitrary Boolean functions are all shown to increase polynomially with the number of distinct values the input features can assume and exponentially with the number of features. Two network training algorithms, focusing and back propagation, are described. Empirically, they are capable of learning arbitrary Boolean functions of multivalued features in a two-level net. Focusing is proved to converge to a correct classification and permits some time-space complexity analysis. Training time for this algorithm is polynomial in the number of values of a feature can assume, and exponential in the number of features. 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| source | IEEE Electronic Library (IEL) |
| subjects | Acceleration Animals Applied sciences Artificial intelligence Boolean functions Computer science Computer science control theory systems Exact sciences and technology Instruments Learning and adaptive systems Logic Multidimensional systems Organisms Polynomials Shape |
| title | Representing and learning Boolean functions of multivalued features |
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