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## -Artificial Neural Network- Hopfield Neural Network(HNN)

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**-Artificial Neural Network- Hopfield Neural Network(HNN)**朝陽科技大學 資訊管理系 李麗華 教授**Assoicative Memory (AM) -1**• Def:Associative memory (AM) is any device that associates a set of predefined output patterns with specific input patterns. • Two types of AM: • Auto-associative Memory: Converts a corrupted input pattern into the most resembled input. • Hetro-associative Memory: Produces an output pattern that was stored corresponding to the most similar input pattern.**v1**v2 v3 : vm Assoicative Memory X1 X2 X3 : Xn Assoicative Memory (AM) - 2 Models: It is the associative mapping of an input vector X into the output vector V. EX: Hopfield Neural Network (HNN) EX: Bidirectional Associative Memory (BAM)**…**… X2 X1 Xn Introduction • Hopfield Neural Network(HNN) was proposed by Hopfield in 1982. • HNN is an auto-associative memory network. • It is a one layer, fully connected network.**…**… +1 net j > 0 Xi if netj = 0 -1 net j < 0 X1 X2 Xn HNN Architecture • Input： Xi ﹛-1, +1﹜ • Output：same as input(∵single layer network) • Transfer function：Xi new= • Weights： • Connections： (Xi是指前一個X值)**HNN Learning Process**• Learning Process： a. Setup the network, i.e., design the input nodes & connections. b. Calculate and derived the weight matrix C. Store the weight matrix. The learning process is done when the weight matrix is derived. We shall obtain a nxn weight matrix, Wnxn.**（or net = W‧X i）**HNN Recall Process • Recall a. Read the nxn weight matrix, Wnxn. b. Input the test pattern X for recalling. c. Compute new input （i.e. output） d. Repeat process c. until the network converge （i.e. the net value is not changed or the error is very small） +1 net j > 0 Xj old if net j = 0 +1 net j < 0 X j： X new**Example: Use HNN to memorize patterns (1)**• Use HNN to memorize the following patterns. Let the Green color is represented by “1” and white color is represented by “-1”. The input data is as shown in the table X3 X4 X2 X1**Example: Use HNN to memorize patterns (3)**Recall The pattern is recalled as:**-Artificial Neural Network-Bidirectional Associative Memory**(BAM) 朝陽科技大學 資訊管理系 李麗華 教授**Ym**Y2 ‧‧‧‧‧‧ Y1 ‧‧‧‧‧‧‧ Introduction • Bidirectional Associative Memory (BAM) was proposed by Bart Kosko in 1985. • It is a hetro-associative memory network. • It allows the network to memorize from a set of pattern Xp to recall another set of pattern Yp**Assoicative Memory (AM) 1**• Def:Associative memory (AM) is any device that associates a set of predefined output patterns with specific input patterns. • Two types of AM: • Auto-associative Memory: Converts a corrupted input pattern into the most resembled input. • Hetro-associative Memory: Produces an output pattern that was stored corresponding to the most similar input pattern.**v1**v2 v3 : vm Assoicative Memory X1 X2 X3 : Xn Assoicative Memory (AM) 2 Models: It is the associative mapping of an input vector X into the output vector V. EX: Hopfield Neural Network (HNN) EX: Bidirectional Associative Memory (BAM)**Ym**Y2 ‧‧‧‧‧‧ Y1 ‧‧‧‧‧‧‧ BAM Architecture • Input layer： • Output layer： • Weights： • Connection： It’s a 2-layer, fully connected, feed forward & feed back network.**BAM Architecture (cont.)**• Transfer function：**BAM Example(1/4)**● ○● ○● ○ ○●○●○● ● ●● ● ●● ○ ○○ ○ ○○ ●●● ○●○ Test pattern**BAM Example(2/4)**1. Learning • Set up network • Setup weights**BAM Example(3/4)**2. Recall • Read network weights • Read test pattern • Compute Y • Compute X • Repeat (3) & (4) until converge**BAM Example(4/4)**• 聚類之Application test pattern (1 1 1 -1 1 -1)1*6 (1) (2) 二次都相同 ●●● ○●○