does entity recognition comes under classification problem?
Simply put, Named Entity Recognition (NER) is a multi-class structured prediction (classification) problem, so you have a sequence of words and you want to label each one most of the time with these labels ( start-of-a-person-name, continue-of-a-person-name, start-of-an-org-name, continue-of-an-org-name, start-of-a-location-name, continue-of-a-location-name, other). Note that these are not the only classes, classes with different granularity can also be used.

If you want to solve this problem with SVM you can use StructSVM or other  variations of SVM for structure prediction. Though the common baseline for this task uses Maximum Entropy (Maxent)(log-linear) models.