It is not possible. You could possibly cluster the data, but not classify it.
In order to classify data you need to have an algorithm that knows what to look for, or you need to create a mathematical model of what kinds of samples belong in which class. In order to create that kind of model, you need some sample data and you need to be told what the correct classification is for that sample data. The two together are used to estimate the parameters of the model. Then the parameters estimated can be applied to data for which the classification is not known, in order to find the most plausible class that the data belongs to.
