Question

b) Consider the following single layer perception as shown in the following figure. 

                                      Image ignouassignments-ignouacademy-com--p-shown-90214

and the activation function of each unit is defined as \Phi (v)=\left \{ _{0, otherwise.}^{1, if v \geq 0} \right \}

Calculate the output y of the unit for each of the following input patterns: 

Patterns P_{1} P_{2} P_{3} P_{4}
X_{1} 1 0 1 1
X_{2} 0 1 0 1
X_{3} 0 1 1 1

Also, find the modified weights after one iteration. 

10 Mar 2024
Answer :
Word Count : 555
To solve this problem, we need to calculate the output \( y \) of the unit for each input pattern and then update the weights accordingly. Let's break it down step by step. ### Step 1: Initialize the Weights and Bias Assume the initial weights and bias are given as: - \( w_1 = 0.5 \) - \( w_2 = -0.5 \) - \( w_3 = 0.5 \) - \( b = 0.5 \) ### Step 2: Define the Activation Function The activation function is defined as: \[ \Phi(v) = \begin{cases} 1, & \text{if } v \geq 0 \\ 0, & \text{otherwise} \end{cases} \] where \( v \) is the weighted sum of the inputs plus the bias: \[ v = w_1 x_1 + w_2 x_2 + w_3 x_3 + b \] ### Step 3: Calculate the Output ______ ______ _________ ______ _____ _____ _________ ___ _________ _________ _______ _______.
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Related Questions

Which of the following statements are true or false? Give a short proof or a counter example in support of your answers.

 a) There is chance of occurrence of the premature convergence in Roulett-wheel selection shceme used in GA.

b) Gradient based optimization methods are used when the objective function is not smooth and one needs efficient local optimization.

c) The \alpha - cut of a fuzzy set A in U is defined as A \alpha _{0}=\left \{ x\epsilon \bigcup | \right.\mu _{A}(x)\leq \alpha _{0}\left. \right \}

d) A single perception with preprocessing is neither an auto associative network nor a multiple layer neural network.

e) If W (k_{0})=W(K_{0}+2), then perception is non-linear separable. 

Consider the set of pattern vectors P. Obtain the connectivity matrix (CM) for the patterns in P (four patterns). 

P=\begin{bmatrix} 1 &1 &1 &0 &0 &0 &0 &0 &0 &0 \\0 &0 &0 &0 &0 &0 &0 &1 &1 &1 \\1 &1 &1 &0 &0 &0 &0 &0 &0 &1 \\1 &0 &1 &0 &1 &0 &1 &0 &1 &0 \end{bmatrix}

Let A and B are two fuzzy sets and  x\epsilon U,if\mu _{A}(x)=0.4 and \mu _{B}(x)=0.8 then find out the following membership values: 

i) \mu _{A\cup B}(X),                             ii) \mu _{A\cap B}(X),        iii)  \mu _{\bar{A}\cup \bar{B}}(x),

iv)  \mu _{\bar{A}\\\cap \bar{B}}(x),                            v)  \mu __{\bar{A}\bar\cup \bar{B}}(X),       vi)   \mu __{\bar{A}\bar\cap \bar{B}}(X),

a) Define Kohonen networks with examples.

Consider a dataset of six points given in the following table, each of which has two features f_{1} and f_{2}. Assuming the values of the parameters c and m as 2 and the initial cluster centers V_{1}=(,5,5) and V_{2}=(10,10), apply FCm algorithm to find the new cluster center after one iteration. 

  F_{1} F_{2}
X_{1} 3 11
X_{2} 3 10

 

X_{3} 8 12
X_{4} 10 6
X_{5} 13 6
X_{6} 13 5

 

b) Let an activation function be defined as 

\Phi (V)=\frac{1}{1+e^{-av}},a> 0

Show that \frac{d\Phi }{dV}=a\Phi (v)[1-\Phi (V]). What is the value of \Phi (V) at the origin? Also, find the value of \Phi (V) as v approaches +\infty and -\infty .

a) Find the length and order of the following schema:  

i) S_{1}=(1^{**}00^{*}1^{**})

ii)  S_{2}=(1^{**}00^{*}1^{**})

iii)  S_{3}=(^{***}{}1^{**)

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