In K Nearest Neighbours classification, which of the following statements about K and N (the number of training samples) is/are true?Group of answer choicesK impacts both the accuracy and the computational complexity of the KNN algorithm.K and N should be linearly related, i.e. K/N should be a pre-determined constant.The time taken to perform the classification task increases with N.K should be odd to avoid ties.
Question
In K Nearest Neighbours classification, which of the following statements about K and N (the number of training samples) is/are true?Group of answer choicesK impacts both the accuracy and the computational complexity of the KNN algorithm.K and N should be linearly related, i.e. K/N should be a pre-determined constant.The time taken to perform the classification task increases with N.K should be odd to avoid ties.
Solution 1
The true statements are:
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"K impacts both the accuracy and the computational complexity of the KNN algorithm." Explanation: The choice of K in KNN affects both the accuracy of the predictions and the computational complexity. A smaller K value can capture more fine-grained detail, but may also capture noise and make the model more complex. A larger K value can smooth over details and make the model simpler, but may also lose important detail.
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"The time taken to perform the classification task increases with N." Explanation: The KNN algorithm is a lazy learning algorithm, meaning it does not learn a model from the training data but instead uses the training data itself to make predictions. This means that the time taken to make predictions increases with the size of the training data, N.
The statements "K and N should be linearly related, i.e. K/N should be a pre-determined constant." and "K should be odd to avoid ties." are not necessarily true. The choice of K does not need to be related to N in a linear way, and while choosing an odd K can help avoid ties, it is not a requirement and other methods can be used to break ties.
Solution 2
The true statements are:
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"K impacts both the accuracy and the computational complexity of the KNN algorithm." Explanation: The choice of K in KNN affects both the accuracy of the predictions and the computational complexity. A smaller K value can capture more fine-grained detail, but may also capture noise and make the model more complex. A larger K value can smooth over details and make the model simpler, but may also lose important detail.
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"The time taken to perform the classification task increases with N." Explanation: The KNN algorithm is a lazy learning algorithm, meaning it does not learn a model from the training data but instead uses the training data itself to make predictions. This means that the time taken to make predictions increases with the size of the training data, N.
The statements "K and N should be linearly related, i.e. K/N should be a pre-determined constant." and "K should be odd to avoid ties." are not necessarily true. The choice of K does not need to be related to N in a linear way, and while choosing an odd K can help avoid ties, it is not a requirement and other methods can be used to break ties.
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