State whether the following statements are True or False. Give short proof or a counter example in support of your answer.
a) In the Hopfield network, the neurons belonging to the same layer receive input from the neurons of the previous layer and send their value only to the neurons of the next layer.
b) The length of chromosomes to determine the maximum value of the set:
is 12.
c) The fuzzy relation (R) given below, is an equivalence relation.
d) The Self Organizing Map (SOM) is a supervised learning technique.
e) In a single layer neural network, if , then the output is -1.
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State whether the following statements are True or False. Give short proof or a counter example in support of your answer.
a) In the Hopfield network, the neurons belonging to the same layer receive input from the neurons of the previous layer and send their value only to the neurons of the next layer.
b) The length of chromosomes to determine the maximum value of the set:
is 12.
c) The fuzzy relation (R) given below, is an equivalence relation.
d) The Self Organizing Map (SOM) is a supervised learning technique.
e) In a single layer neural network, if , then the output is -1.
Approximate the function for
, by solving 1-2-1 network, using Back propagation algorithm. The weighted structure and initial input are as follows:
Weighted structures are: and bias
and bias
The initial input is 1.
Draw the architecture of the model. Perform one iteration.
(क) क्या निम्नलिखित फलन श्वार्ज़-प्रमेय की आवश्यकताओं को (1,1) पर संतुष्ट करता है? अपने उत्तर की पुष्टि कीजिए। (4)
(ख) निम्नलिखित के स्तब्ध बिन्दु निर्धारित करके उनका वर्गीकरण कीजिए : (6)
(i)
(ii)
(क) वक्रों और
से परिबद्ध और
के घनत्व वाले एक पतली शीट का गुरुत्व केन्द्र ज्ञात कीजिए।
(ख) और
से परिबद्ध ठोस घनाकृति का द्रव्यमान ज्ञात कीजिए, जबकि घनत्व फलन,
हो।
Consider a dataset of five observations given in the following table, each of which has two features f1 and f2:
| x₁ | x₂ | x₃ | x₄ | x₅ | |
|---|---|---|---|---|---|
| f₁ | 2 | 3 | 4 | 3 | 5 |
| f₂ | 6 | 7 | 5 | 4 | 6 |
Assume the number of cluster and the real number
. Also, assume the initial cluster centers as
and
. Apply fuzzy c-mean algorithm to find the modified cluster center after one iteration.
Determine the -cut of the fuzzy set (A) are given below, at 0.7 and 0.2.
Also, compare the -cut of the two outcomes, and give comments for status of
-value variation.
क) यदि तो a और b के मान ज्ञात कीजिए।
(ख) मान लीजिए कि S और C के उपसमुच्चय हैं। S मूल-बिन्दु पर केन्द्र वाला एकक विवृत गोलक है तथा C विवृत घन
।
निम्नलिखित में से कौनसा कथन सत्य है? अपने उत्तर की पुष्टि कीजिए।
(i)
(ii)
(ग) निम्नलिखित फलनों के स्तर वक्र ज्ञात कीजिए :
(i)
(ii)
(iii) x-y
(iv) y / x