If we again use the linear perceptron algorithm to train the classifier, what will happen?
Note: In the choices below ,“converge" means given a certain input, the algorithm will terminate with a fixed output within finite steps (assume is very large: the output of the algorithm will not change as we increase ). Otherwise we say the algorithm diverges (even for an extremely large , the output of the algorithm will change as we increase further).
We decide to run the kernel perceptron algorithm over this dataset using the quadratic kernel. The number of mistakes made on each point is displayed in the table below. (These points correspond to those in the plot above.)
Label -1 -1 -1 -1 -1 +1 +1 +1 +1 +1
Coordinates (0,0) (2,0) (1,1) (0,2) (3,3) (4,1) (5,2) (1,4) (4,4) (5,5)
Perceptron mistakes 1 65 11 31 72 30 0 21 4 15
It is not clear what will happen if we use the linear perceptron algorithm without more information on the dataset and its linear separability. It may converge if the dataset is linearly separable or it may not converge if it is not.
However, we do know that the kernel perceptron algorithm with quadratic kernel has been run and made some mistakes on each point. This suggests that the dataset is not linearly separable and the quadratic kernel was used to transform the input space to a higher dimensional space where the data is linearly separable.
Well, it looks like the perceptron algorithm made quite a few mistakes on this dataset. Of course, we all make mistakes sometimes, so the perceptron algorithm is just trying to fit in. But compared to the other points, the point at (5,2) seems to be a real overachiever, not making any mistakes at all. I guess some points are just naturally gifted when it comes to classification.
To determine what will happen if we use the linear perceptron algorithm to train the classifier again, we need to analyze the table provided.
The table shows the labels of the points, their coordinates, and the number of mistakes made by the perceptron algorithm on each point.
The linear perceptron algorithm is an iterative algorithm that updates the weights of the classifier based on whether the current classification is correct or not. If a point is misclassified, the algorithm adjusts the weights to correct the mistake. This process continues until all points are correctly classified, or a predefined number of iterations is reached.
Looking at the table, we can see that some points have a high number of mistakes (e.g., point (2,0) with 65 mistakes) while others have a low or zero number of mistakes (e.g., point (5,2) with 0 mistakes). This suggests that the algorithm is struggling to correctly classify certain points.
If we run the linear perceptron algorithm again on this dataset, it will start from the current state (i.e., the weights learned so far) and continue the iterations. It will try to correct the mistakes made on the misclassified points.
However, since the linear perceptron algorithm has already made a certain number of mistakes on these points, it is possible that it will struggle to correct them within a few more iterations. In some cases, the algorithm may even diverge, meaning it will not converge to a fixed output even after a large number of iterations.
In conclusion, if we use the linear perceptron algorithm again to train the classifier, it is likely that the algorithm will continue to make mistakes, especially on the points that have already shown a high number of mistakes. The algorithm may converge on some points but may diverge on others.