# PPt3 - Derivation of Delta Rules

Chia sẻ: Pham Thanh Hai | Ngày: | Loại File: PPT | Số trang:6

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## PPt3 - Derivation of Delta Rules

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Tài liệu tham khảo về thuật toán tính Derivation of Delta Rules

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## Nội dung Text: PPt3 - Derivation of Delta Rules

1. Derivation of Delta Rule  Nguồn gốc của Delta rule cho mạng sau 1 w0 w1 y = ϕ ( net ) = ϕ ( w0 + w1 x1 + w2 x2 ) x1 w2 x2 1 1 E ( w0 , w1 , w2 ) = ( y − d ) = (( w0 + w1 x1 + w2 x2 ) − d ) 2 2 2 2 ∂E ∆wi = −η cho i ∈{0,1,2} ∂wi ∂E ∂E ∂E  Cần tìm , , ∂w0 ∂w1 ∂w2 NN Faculty of Electronics and Telecommunications, HUT 1 1 Bangkok, Jun. 14 – 23, 2006
2. Derivation of Delta Rule ∂E ( w0 , w1 , w2 ) 1 ∂(ϕ ( w0 + w1 x1 + w2 x2 ) − d ) 2 = ∂w1 2 ∂w1 1 ∂(ϕ ( w0 + w1 x1 + w2 x2 ) − d ) = 2(ϕ ( w0 + w1 x1 + w2 x2 ) − d ) 2 ∂w1 ∂( w0 + w1 x1 + w2 x2 − d ) = (ϕ ( net ) − d )ϕ ' ( net ) ∂w1 = (ϕ ( net ) − d )ϕ ' ( net ) x1  Tương tự ta nhận được: ∂E ( w0 , w1 , w2 ) = (ϕ ( net ) − d )ϕ ' ( net ) x2 ∂w2 ∂E ( w0 , w1 , w2 ) và  = (ϕ ( net ) − d )ϕ ' ( net ) ∂w0 Faculty of Electronics and Telecommunications, HUT 2 Bangkok, Jun. 14 – 23, 2006
3. Derivation of Delta Rule  Do đó luật update cho weight là: ∆w0 = η( d − ϕ ( net ))ϕ ' ( net ) ∆w1 = η( d − ϕ ( net ))ϕ ' ( net ) x1 ∆w2 = η( d − ϕ ( net ))ϕ ' ( net ) x2 NN Faculty of Electronics and Telecommunications, HUT 3 3 Bangkok, Jun. 14 – 23, 2006
4. Derivation of Delta Rule • Vi phân delta rule cho mạng sau:   w1 x1 u1 w2 y = ϕ ( net ) = ϕ ( y1u1 + y2u2 ) v1 x2 u2 v2 Let net1 = w1 x1 + w2 x2 , y1 = ϕ (net1 ) net 2 = v1 x1 + v2 x2 , y 2 = ϕ (net2 ) net = y1u1 + y2u2 , y = ϕ (net ) NN Faculty of Electronics and Telecommunications, HUT 4 4 Bangkok, Jun. 14 – 23, 2006
5. Derivation of Delta Rule ∂E 1 ∂ (ϕ ( y1u1 + y2u2 ) − d ) 2 1 ∂ (ϕ ( y1u1 + y2u2 ) − d ) = = 2(ϕ ( y1u1 + y2u2 ) − d ) ∂u1 2 ∂u1 2 ∂u1 ∂ ( y1u1 + y2u2 − d )   = ( y − d )ϕ ' ( net ) = ( y − d )ϕ ' ( net ) y1 ∂u1 Tương tự ta có: ∂E = ( y − d )ϕ ' ( net ) y2 ∂u2 ∂E 1 ∂ (ϕ ( y1u1 + y2u2 ) − d )2 1 ∂ (ϕ ( y1u1 + y2u2 ) − d ) = = 2(ϕ ( y1u1 + y2u2 ) − d ) ∂w1 2 ∂w1 2 ∂w1 ∂ ( y1u1 + y2u2 − d ) = ( y − d )ϕ ' ( net ) ∂w1 Faculty of Electronics and Telecommunications, HUT 5 Bangkok, Jun. 14 – 23, 2006
6. Derivation of Delta Rule ∂( y1u1 + y2u2 − d ) ∂( y1u1 ) ∂y ∂(ϕ( w1 x1 + w2 x2 )) = = u1 1 = u1 ∂w1 ∂w1 ∂w1 ∂w1 ∂( w1 x1 ) = u1ϕ' ( net1 ) = u1ϕ' ( net1 ) x1   ∂w1 Do vậy nhận được:: ∂E ∂( y1u1 + y2u2 −d ) = ( y −d )ϕ' ( net ) ∂ 1 w ∂ 1 w = ( y −d )ϕ' ( net )u1ϕ' ( net1 ) x1 Tương tự: ∂E = ( y − d )ϕ ' ( net )u1ϕ ' ( net1 ) x2 ∂w2 ∂E ∂E = ( y − d )ϕ ' ( net )u2ϕ ' ( net2 ) x1 , = ( y − d )ϕ ' ( net )u2ϕ ' ( net2 ) x2 ∂v1 ∂v2 NN Faculty of Electronics and Telecommunications, HUT 6 6 Bangkok, Jun. 14 – 23, 2006