Hopfield Discrete

Hopfield Discrete Hopfield Method The Hopfield Artificial Neural Network algorithm was introduced in 1982 at the California Institute of Technology. In a Hopfield network all neurons are fully interconnected. One neuron outputs and then becomes the input for all other neurons. This process continues to repeat until the desired output is achieved. Hopfield Network Architecture The Discrete Hopfield Network is a fully connected artificial neural network, which means that every unit is connected to every other unit. This network has symmetrical weights. In a Hopfield network, each unit has no connection with itself. Mathematically this satisfies wᵢᵢ = wᵢᵢ for i ≠ j and wᵢᵢ = 0 for i = j. The activation function used in Hopfield networks is the Lyapunov energy function, which is a finite and decreasing function to obtain stability in its activation. Algoritma Jaringan Hopfield Diskrit 1. Initialize the weight matrix W 2. Enter the input vector (invec), then initialize the output vector (outvec), namely outvec = invec. 3. Start with counter i = 1, as long as invec ≠ outvec do steps 4-7, if I reaches max then reset mjd 1 4. Calculate i-th value = dotproduct (invec, i-th column of W) 5. Calculate i-th outvec = f(i-th value), f is a threshold function 6. Update invec with outvec 7. i = I + 1 Example There are 2 patterns to be recognized: Pattern A (1,0,1,0,1,0) Pattern B (0,1,0,1,0,1) The weights are as follows: Answer: 1. First Node Activation Pattern A 0 −2 2 (1 0 1 0 1 0). −2 = 0 + 0 + 2 + 0 + 2 + 0 = 4 2 −2 [] [] [] [] [] 2. Second Node Activation Pattern A −2 0 −2 (1 0 1 0 1 0). 2 = (-2) + 0 + (-2) + 0 + (-2) + 0 = -6 −2 2 3. Third Node Activation Pattern A 2 −2 0 (1 0 1 0 1 0). −2 = 2 + 0 + 0 + 0 + 2 + 0 = 4 2 −2 4. Fourth Node Activation pattern A −2 2 −2 (1 0 1 0 1 0). 0 = (-2) + 0 + (-2) + 0 + (-2) + 0 = -6 −2 2 5. Activation of the fifth node pattern A 2 −2 2 (1 0 1 0 1 0). −2 = 2 + 0 + 2 + 0 + 0 + 0 = 4 0 −2 6. Activation of the sixth node pattern A −2 2 −2 (1 0 1 0 1 0). 2 = (-2) + 0 + (-2) + 0 + (-2) + 0 = -6 −2 0 [] The result of nodes 1-6 of pattern A is 4, -6, 4, -6, 4, -6 1. First Node Activation pattern B 0 −2 2 (0 1 0 1 0 1). −2 = 0 + (-2) + 0 + (-2) + 0 + (-2) = -6 2 −2 [] [] [] [] 2. Second Node Activation pattern B −2 0 −2 (0 1 0 1 0 1). 2 = 0 + 0 + 2 + 0 + 2 + 0 = 4 −2 2 3. Third Node Activation pattern B 2 −2 0 (0 1 0 1 0 1). =−2 = (-2) + 0 + (-2) + 0 + (-2) + 0 = -6 2 −2 4. Fourth Node Activation pattern B −2 2 −2 (0 1 0 1 0 1) 0 = 0 + 2 + 0 + 0 + 0 + 2 = 4 −2 2 5. Activation of the fifth node pattern B 2 −2 2 (0 1 0 1 0 1). −2 = 0 + (-2) + 0 + (-2) + 0 + (-2) = -6 0 −2 [] [] 6. Activation of the sixth node pattern B −2 2 −2 (0 1 0 1 0 1). 2 = 0 + 2 + 0 + 2 + 0 + 0 = 4 −2 0 The result of nodes 1-6 of pattern B is -6, 4, -6, 4, -6, 4 The activation results of the nodes in pattern A (4,-6,4,-6,4,-6) and pattern B (-6,4,-6,4,-6,4) are compared with the activation function. f(t) = 1 if t ≥ 0 f(t) = 0, if t < 0 Testing: Conclusion A Hopfield network is said to reach its maximum limit (successfully recognizing a pattern) when a certain pattern but is called repeatedly. The iteration limit is usually just one cycle after a particular pattern is called stably.