Pattern Classification

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11• A single “bias unit” is connected to each unit in addition tothe input units• Net activation:netdd∑ ∑tj= xiwji+ wj0= xiwji≡ wj.x,i= 1i=0where the subscript i indexes units in the input layer, j in thehidden layer; w ji denotes the input-to-hidden layer weights atthe hidden unit j. (In neurobiology, such weights orconnections are called “synapses”)• Each hidden unit emits an output that is a nonlinear functionof its activation, that is: y j = f(net j )Pattern Classification, Chapter 6
Figure 6.1 shows a simple threshold functionf ( net ) =1 if net ≥ 0sgn( net ) ≡⎩⎨⎧− 1 if net < 0• The function f(.) is also called the activationfunction or “nonlinearity” of a unit. There aremore general activation functions withdesirables properties12• Each output unit similarly computes its netactivation based on the hidden unit signals as:netnH nH=tk ∑ yjwkj+ wk0= ∑ yjwkj= wk.y,j= 1j=0where the subscript k indexes units in the ouputlayer and n H denotes the number of hidden unitsPattern Classification, Chapter 6
Page 1: PatternClassificationAll materials
Page 4 and 5: Natural Neural Net Models• Human
Page 6 and 7: Linear Discriminant Functions• A
Page 8 and 9: 7• There is no automatic method f
Page 10 and 11: 9Pattern Classification, Chapter 6
Page 14 and 15: 13• The output units are referred
Page 16 and 17: • General Feedforward Operation -
Page 18 and 19: 17• Eq (8) can be expressed in ne
Page 20 and 21: 19Pattern Classification, Chapter 6
Page 22 and 23: Backpropagation Algorithm21• Any
Page 24 and 25: • Network has two modes of operat
Page 26 and 27: Network Learning• Start with an u
Page 28 and 29: 27Since net k = w kt .y, therefore:
Page 30 and 31: Sensitivity at Hidden Node
Page 32 and 33: • Training protocols:• Stochast
Page 34 and 35: • Learning Curves33• Before tra
Page 36 and 37: Representation at the Hidden Layer
Page 38 and 39: Practical Techniques for ImprovingB
Page 40 and 41: Practical Considerations• Scaling
Page 42 and 43: Total no. of WeightsError per patte
Page 44 and 45: Practical Considerations• Momentu

Pattern Classification

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