In SVM we generally draw a hyperplane and classify data points based on which side of hyperplane they lie. What happens in the case where the data point falls on hyperplane itself. Test data may have such a case. How does SVM treat it ? Does it arbitrarily assigns it into one of the sides ?
I think Simon's explanation is perfect, but I may add that in any classification or decision problem, if your data lie exactly in the threshold (or the hyperplane in this case) you may choice any of the involved classes. Probabilisticly, it means that you are under a 50% choice; in SVM terms, your structural risk is the same for both classes. You might establish a "consistent choice" (i.e. always class1, or always class 2) or a random choice (sometimes class 1, sometimes class 2). Anyway, the probability of this case to happen is so low that any choice may be fine.
Best regards.
svm is large margin classifier,constant c controls the trade off between smooth decision boundary and classifying training points correctly. A large value of c means you will get more training points correctly. large value of c means your datapoints will never be in the hyperplane,gamma defines how far the influence of a single training example reaches. If it has a low value it means that every point has a far reach and conversely high value of gamma means that every point has close reach. i don't see any example where test data point stays right in the middle of hyperplane.it would be nice if you could redirect me toward such example,on such case the svm might will misclassify data points. the closer points get more weight so don't worry weight will tell which class the data point belongs
Dear Karandeep,
I agree with Syed that it is almost impossible that an SVM will give a result that is exactly on the hyperplane. This means that the weighted sum over all "unknown vector - support vector Kernel transformations" is exactly zero, or is exactly the bias term (up to the numerical precision) . But if this happens, it depends on your implementation of your SVM. I think in Matlab it is implemented with ">=0" for class 1 and class 2 otherwise. So the result will be "class 1". If you use another implementation you should find something like this in the documentation.
Simon
I think Simon's explanation is perfect, but I may add that in any classification or decision problem, if your data lie exactly in the threshold (or the hyperplane in this case) you may choice any of the involved classes. Probabilisticly, it means that you are under a 50% choice; in SVM terms, your structural risk is the same for both classes. You might establish a "consistent choice" (i.e. always class1, or always class 2) or a random choice (sometimes class 1, sometimes class 2). Anyway, the probability of this case to happen is so low that any choice may be fine.
Best regards.
the problem is that you have not characterized well you shape
the separator (hyperplane) is based on the descriptors
you must separate the classes
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