How to identify similar data points?
Well, thats a question that institutes at univiersities, among others, are trying to solve since several decades and where millions of money currencies are spent in each country every year.

Short answer: for now, nothing general is known to perform good. 

Long answer: it depends completely on your image domain. Do you want to recognize suns in a picture? That possible up to some false discovery rates. Do you want recognize familiar faces? Possible, see automated passport controls at airports. Emotion recognition? Good luck with that! Grouping by persons? Possible, but statues will be included. etc...

Something really general:  Grouping by colors? Totally viable! But will not mean much. Something that includes some hint to the structure? Well, the easiest way is to compute color histograms and use them as feature vectors for (like suggested) nearest neighbor calculation - (watch out for normalization, color space, and other sources of information distortion)

Basic answer: take some Computer Vision courses either online (e.g. https://youtu.be/skaQfPQFSyY?list=PL7v9EfkjLswLfjcI-qia-Z-e3ntl9l6vp) 

There is also an intersting TED talk to that topic https://youtu.be/40riCqvRoMs

On the other side: don't let yourself down! Understand the #basics of data processing and break the structures! Develop that algorithm we are all hoping to use some day!