-Artificial Neural Network- Hopfield Neural Network(HNN) 朝陽科技大學 資訊管理系 李麗華 教授

朝陽科技大學 李麗華 教授 2 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.

朝陽科技大學 李麗華 教授 3 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) Assoicative Memory (AM) - 2 Assoicative Memory X1X2X3:XnX1X2X3:Xn v1v2v3:vmv1v2v3:vm

朝陽科技大學 李麗華 教授 4 Introduction Hopfield Neural Network(HNN) was proposed by Hopfield in HNN is an auto-associative memory network. It is a one layer, fully connected network. X1X1 X2X2 XnXn … …

朝陽科技大學 李麗華 教授 5 HNN Architecture Input ：  X i  ﹛ -1, +1 ﹜ Output ： same as input( ∵ single layer network) Transfer function ： X i new = Weights ： Connections ： +1 net j > 0 X i if net j = 0 -1 net j < 0 X1X1 X2X2 XnXn … … ( X i 是指前一個 X 值 )

朝陽科技大學 李麗華 教授 6 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, W nxn.

朝陽科技大學 李麗華 教授 7 HNN Recall Process Recall a. Read the nxn weight matrix, W nxn. 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 X j old if net j = 0 +1 net j < 0 X j ： （ or net = W ‧ X i ） X new

朝陽科技大學 李麗華 教授 8 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 PX1X1 X2X2 X3X3 X4X4 X5X5 X6X6 X X2X X3X X4X4 X1X1 X2X2 X3X3 X4X4

朝陽科技大學 李麗華 教授 9 W ii =0 PX1X1 X2X2 X3X3 X4X4 X5X5 X6X6 X X2X X3X X4X4 Example: Use HNN to memorize patterns (2)

朝陽科技大學 李麗華 教授 10 Recall Example: Use HNN to memorize patterns (3) 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

朝陽科技大學 李麗華 教授 12 Introduction Bidirectional Associative Memory (BAM) was proposed by Bart Kosko in It is a hetro-associative memory network. It allows the network to memorize from a set of pattern X p to recall another set of pattern Y p Y1Y1 Y2Y2 YmYm ‧‧‧‧‧‧ ‧‧‧‧‧‧‧

朝陽科技大學 李麗華 教授 13 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.

朝陽科技大學 李麗華 教授 14 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) Assoicative Memory (AM) 2 Assoicative Memory X1X2X3:XnX1X2X3:Xn v1v2v3:vmv1v2v3:vm

朝陽科技大學 李麗華 教授 15 BAM Architecture  Input layer ： ‚ Output layer ： ƒ Weights ： „Connection ： Y1Y1 Y2Y2 YmYm ‧‧‧‧‧‧ ‧‧‧‧‧‧‧ It’s a 2-layer, fully connected, feed forward & feed back network.

朝陽科技大學 李麗華 教授 16 BAM Architecture (cont.) …Transfer function ：

朝陽科技大學 李麗華 教授 17 BAM Example(1/4) Test pattern Y1Y1 Y 2 Y3Y3 Y4Y ●●● ○●○ ● ○●○● ○● ○●○● ○ ○●○●○●○●○●○● ● ●● ○ ○○

朝陽科技大學 李麗華 教授 18 BAM Example(2/4) 1. Learning –Set up network –Setup weights Y1Y1 Y 2 Y3Y3 Y4Y

朝陽科技大學 李麗華 教授 19 BAM Example(3/4) 2. Recall Read network weights ‚Read test pattern ƒCompute Y „Compute X …Repeat (3) & (4) until converge

朝陽科技大學 李麗華 教授 20 BAM Example(4/4) 聚類之 Application (1) (2) 二次都相同 test pattern ( ) 1*6  ●●● ○●○