Generally the term "pattern recognition" would refer to one of the two following type of question:
- The question involve seeing a samples of a small number of mathematical objects, and attempt to figure out what are the rest of the objects are, and what properties would they have, and the properties of the class of objects as a whole.
One frequently seen type of question in this category is "guess the next number in sequence" - wherein the first few terms of a sequence of numbers is given, and the answer would need to explain the pattern (for example, a recurrence formulas) that describes the sequence, and the next term or the next few terms in the sequence. If your question is of this type, consider checking OEIS (On-Line Encyclopedia of Integer Sequences) first to see if your sequences have appeared before.
Other types in this category exist too. For example, a formula might be given that produce a group based on some parameters. After plugging in some small values, one get certain groups, and trying to find a common properties among all those small sample might hint at a theorem about all groups given by that formulas.
Note that by nature, questions in this category do not have any standard for correct answer, as the answer is required to extrapolate a small samples to a general pattern. This is frequently the case with "guess the next terms in the sequence" question as usually seen in school. However, many questions do have such a standard, as long as it is put in a suitable context. Before posting the question, consider adding as much context as possible.
Questions in this category might not have a single answer, as it is not unusual for there to be many correct patterns (perhaps they are logically equivalence, or perhaps there are other reasons).
- The question is about mathematical ideas related to the fields referred to as "pattern recognition", subfields of artificial intelligence as well as statistics.
The various subfields grouped under the term "pattern recognition" concerns with the task of making computer recognize patterns from a large amount of data. Given a large sets of data, the computer is expected to be able to classify them, figure out relationships between variables, extrapolate or interpolate to new data points, figure out global properties to the set of data, etc. A specific subfield, computer vision, is where the term came from, so "pattern recognition" might refer to just that subfield. Before posting a question of this category, consider whether it would be more appropriate to post in StackOverflow, Computer Science Stack Exchange, or Cross Validated.