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.

• 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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Case I

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

Case II

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

Case III