神经网络课件神经网络课51教案n.pptVIP

Chapter 5 Feedback Neural Network 5.1 Hopfield neural network 5.1.1 Discrete Hopfield Neural Network Hopfield network architecture 2 B. Working principle 3. Stability analysis 5.1.2 Associative Memory B. Hetero-association Memory C. Learning rule Hopfield network association and recall algorithm Example 1 Example 2 Association memory function Synchronous（parallel） computing 5.1.3 Continuous Hopfield Neural Network CHNN Model Definition of Energy Function 5.1.4 Computing for optimization * 5.1 Hopfield neural network 5.2 BAM network Feedback network is a nonlinear dynamic system. In 1982, Hopfield J J brought forward a single layer feedback network composed of nonlinear component. Nonlinear difference equation ? Discrete HNN (DHNN) differential equation ? Continuous HNN (CHNN) Applications: associative memory or classification computing for optimization w12 w1n w21 wn, 1 N1 N2 Nn-1 Nn w2n … x1 x2 xn-1 xn wn-1, n wn-1, 1 wn, 2 wn-1, 2 … … v1(t) v2(t) vn(t) y1 y2 yn-1 yn A. Hopfield network architecture ? ? ? z-1 z-1 z-1 w11 w1n wn1 wnn ?1 - - - ?2 ?n u2(t) u1(t) un(t) x1(t+1) x2(t+1) xn(t+1) x1(t) x2(t) xn(t) … … Computing formula: 1. Asynchronous(series) pattern xi(t+1)=sgn[ui(t)] xj(t+1)=xi(t) ( j?i ) 2. Synchronous(parallel) pattern xi(t+1)=sgn[ui(t)] ( i=1,2,…,n ) 3. Network stability Using “energy function” Matrix format: x=1 or –1, w and ? are limited constant, so the energy function is limited constant. If ?E=E(t+1)-E(t) ? 0 then the network converges to a steady status. Assumption: series pattern, wij=wji , wkk?0 ?E=E(t+1)-E(t) ?xk=xk(t+1)-xk(t) only kth node is enabled xk(?)=?1 wij=wji ∵ ∵ wkk?0 ? ?E?0 The energy function is limited constant, therefore the network can converge to a local minimum point. ∵ A. Auto-association Memory The M samples ({xi}, i=1,2,…,M ) are stored in the network through learning process. If input x’=x?+v, x? is one of the M samples v is bi