Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes...
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![Page 1: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/1.jpg)
Multi-class Classification
Mu-Chun Su
![Page 2: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/2.jpg)
Case I
• Each pattern class is separable from the other classes by a single hyperplane.
• M classes need M Perceptrons.
• A decision can not be made if • (1) more than one perceptron have positive outputs; • (2) none of the perceptron has positiveb output.
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jj cxif
cxify
0
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![Page 3: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/3.jpg)
Case I
![Page 4: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/4.jpg)
Case II• Each pattern is separable from every other individual class by a distinct hyperpl
ane.• M classes need M(M-1)/2 perceptrons.• If x belongs to wi then
• These hyperplanes have the property that ijforyij 0
jiij yy
![Page 5: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/5.jpg)
Case II
![Page 6: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/6.jpg)
Case III• There exist M hyperplanes with the property that if
a pattern x belongs to the class wi.
• If the classes are separable under case 3 condition, they are automatically separable under Case 2.
• There exists no indeterminate region.
ijallforji yy
![Page 7: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/7.jpg)
Case III
![Page 8: Multi-class Classification Mu-Chun Su. Case I Each pattern class is separable from the other classes by a single hyperplane. M classes need M Perceptrons.](https://reader036.fdocuments.net/reader036/viewer/2022062518/56649d6c5503460f94a4bed3/html5/thumbnails/8.jpg)