The correct answer is: A. we can still classify the data correctly for given setting of hyper parameter c.
The slack variable $C$ is a hyperparameter in support vector machines (SVMs) that controls the trade-off between maximizing the margin and minimizing the number of misclassifications. A larger value of $C$ will result in a smaller number of misclassifications, but at the cost of a smaller margin.
If we use a very large value for $C$, then we will minimize the number of misclassifications at all costs. This means that we will allow some of the data points to be misclassified, but we will ensure that the margin is as large as possible.
In practice, it is often not necessary to use a very large value for $C$. A value of $C$ that is too large can result in overfitting, which can lead to poor generalization performance.
Here is a brief explanation of each option:
- Option A: We can still classify the data correctly for given setting of hyper parameter c. This is the correct answer, as explained above.
- Option B: We can not classify the data correctly for given setting of hyper parameter c. This is not correct, as we can still classify the data correctly even if we use a very large value for $C$.
- Option C: We can not classify the data at all. This is not correct, as we can always classify the data correctly if we use a large enough value for $C$.
- Option D: Data can be classified correctly without any impact of c. This is not correct, as the value of $C$ does have an impact on the classification performance of SVMs.