Is a new datapoint similar to my reference set?
If you have many features, likely meaning many columns in your table of data, then you could try clustering. Something as simple as k-Nearest Neighbours could work nicely.

You would first fit a model using your available data, then look at the resulting clusters. Each cluster will represent combinations of your features.

Next you can put new data points into the model and it will tell you to which cluster it would best fit.

This would actually be a fully fledged predictive model! It is unsupervised learning, because you are not using and pre-existing labels (for each cluster in this case).

If you are working with Python, the Sci-kit Learn documentation is a good place to start. There are many other clustering algorithms, which might work better for you, depending on your type of data (if it is spatial, DBSCAN is good, for example).