A large variety of sound sources in the ocean, including biological, geophysical, and man-made, can be simultaneously monitored over instantaneous continental-shelf scale regions via the passive ocean acoustic waveguide remote sensing (POAWRS) technique by employing a large-aperture densely-populated coherent hydrophone array system. Millions of acoustic signals received on the POAWRS system per day can make it challenging to identify individual sound sources. An automated classification system is necessary to enable sound sources to be recognized. Here, the objectives are to (i) gather a large training and test data set of fin whale vocalization and other acoustic signal detections; (ii) build multiple fin whale vocalization classifiers, including a logistic regression, support vector machine (SVM), decision tree, convolutional neural network (CNN), and long short-term memory (LSTM) network; (iii) evaluate and compare performance of these classifiers using multiple metrics including accuracy, precision, recall and F1-score; and (iv) integrate one of the classifiers into the existing POAWRS array and signal processing software. The findings presented here will (1) provide an automatic classifier for near real-time fin whale vocalization detection and recognition, useful in marine mammal monitoring applications; and (2) lay the foundation for building an automatic classifier applied for near real-time detection and recognition of a wide variety of biological, geophysical, and man-made sound sources typically detected by the POAWRS system in the ocean.