The third assignment of artificial intelligence at Beijing University of Technology

Question 1: use an artificial neural network to represent the following Boolean functions :.

Answer:

1) first obtain the input/output ing set

2) determine the hidden layer function to obtain the output layer neuron ing set.

{

(,)-> 0,

(0, 0, 0, 0, 0, 0)-> 1,

(,)-> 0,

(,)-> 1,

(0, 0, 0, 1, 0, 0)-> 1,

(0, 0, 0, 0, 0, 0, 0)-> 0,

(0, 0, 0, 0, 0, 1, 0)-> 0,

(0, 0, 0, 0, 0, 0, 1)-> 1,

}

Apply LMSAlgorithmAfter learning on this set, we can get the connection weight vector from the hidden layer to the output layer as (,). Obviously, this network meets the requirements. The network structure is as follows:

 

Correction: Describes the integration and activation functions of neural networks.

 

 

 

 

Correct: Correct

 

Question 3: What is the main role of the hidden layer in artificial neural networks when it is used in pattern recognition? From this point, why does the radial basis function network solve the non-linear classification problem?

Answer:

The hidden layer increases the number of dimensions. The hidden layer is mapped from the original space to the K-dimensional space by adding hidden layers. In the K-dimensional space, the problem becomes a linear severable problem. Radial Basis Functions can solve the interpolation problem under linear severable conditions.

 

Correction: inaccurate. in pattern recognition, the hidden layer of the neural network is mainly used to extract the category information of input features to achieve pattern classification. In radial basis neural networks, each neuron in the hidden layer represents the center of a category. The input feature vector can identify its nearest neuron through distance measurement, thus realizing pattern classification.

 

 

 

Question 4: Solve the TSP problem using the Boltzmann Machine. Give the corresponding algorithm pseudo code and key data structure.

Answer:

// Define integer s [N] [N] to indicate the network

// S [I] [J] = 1, it indicates neuron excitation.

// When s [I] [J] = 0, it indicates neuron inhibition.

 

T = t0 // (high value)

Do

{

// Reduce the tvalue by a certain policy

For I = 1: N

{

For j = 1: N

{

Flag = 0;

// Calculate network energy e_before

// Change the status of S [I] [J]

// Calculate network energy e_after

If (e_before> e_after)

{

Flag = 1;

// Jump out of a Two-For Loop

}

Else

{

If (RAND <1/(1 + exp (-ε/t )))

{

// Jump out of a Two-For Loop

}

}

// Change the status of S [I] [J.

}

}

} While T> 0 | flag = 1

 

Correct: Correct

 

 

 

Question 5: How to Use SOFM networks to implement data clustering? An example is provided.

Answer:

In the self-organizing Feature ing Network, a weight vector corresponding to the input vector and the output neuron exists. Each output neuron calculates the distance between the input vector and the weight vector, and then adjusts the Weight Vector Based on competition learning rules. The neighbor of each neuron can be square, rectangular, or circular, the initial neighborhood is usually half or 2/3 of the network size. Then, as the algorithm goes on, the neighborhood decreases according to certain rules. In competitive learning, the winner and its neighboring neurons use the weight adjustment algorithm to adjust their weights, while other neurons keep their weights unchanged.

For example, when clustering is performed on different color points, each time a sample is input, the newest vertex closest to the sample color and the neuron near the vertex won the competition, the color of these neurons approaches the color of the input sample points. If you enter another color, the color of the other area will be closer to the color of the input. After repeated many times, each color corresponds to a relatively fixed area, and color clustering is realized.

 

Correction: Are you from the teaching website? Why is it different from my questions?