What are the fundamentals of pattern recognition theory? Related theories?

Question

Mathematics

What, besides mathematical statistics, is the theory of pattern recognition based on? Are there any theories that are similar, related or complementary to the theory of pattern recognition, especially applicable to the construction of intelligent systems?
UPD: And also, if it's not difficult, advise good books. In return, I will answer the same:
Fukunaga - Introduction to the theory of pattern recognition
Nilsson - Learning systems

Answer 1

The fact is that the name "theory of pattern recognition" first appeared in the Russian-language scientific literature in the 60-70s of the last century as a very unsuccessful translation of the English "Pattern recognition". And this theory meant what is meant by Machine Learning today - i.e. a science that deals with methods for extracting hidden patterns (patterns) - static or dynamic - in data. Accordingly, if you are interested in the methods of building "intelligent systems" (although I really don't like this term) - you should look in this direction, including Data Mining, ANN, Deep Learning, etc.
On the other hand, today, when people talk about "pattern recognition" they often mean visual recognition.images - face detection in photographs, image recognition in pictures, handwriting recognition and derivatives of these tasks. I note that often (or rather, as a rule) methods and tools from the paragraph above are used to solve these problems. However, I'm not sure that systems of this class can be classified as "intelligent" - because. as a rule, they solve one, special problem and there is exactly as much intelligence as in any modern numerical method for solving mathematical problems.
I do not give the names of specific books on either the first or the second topic - there are a huge number of them. Each adviser has his own "best" books. Even on the toaster there are dozens of topics where such books can be found. But I hope that my post will help you to more clearly define what exactly interests you and continue to purposefully look in the right direction, understanding where and why you are going.

Answer 2

Except mat. statistics, there is an idea - to highlight the characteristic features (features) and the calculation model - neural networks.