How should I construct a binary classifier for small set of positive data and million of unlabeled data?
This is called PU Learning, and it can be used when using a probabilistic classifier and certain assumptions are met about how the data is labeled.
If the assumptions are met, you

Label positive, already labeled instances as positive
Labeled unlabeled instances as negative
Train a probabilistic classifier.

This produces the same ranking of class probabilities as a classifier would if trained on a dataset labeled with true positive/negative labels.
This video covers the assumptions pretty well and the Elkan paper is pretty accessible.