Questions tagged [pattern-recognition]

1. From a samples of a small samples of mathematical objects, conjecture a common pattern to all of them. This includes "guess the next terms in the sequence" question (consider checking OEIS first). Please provide as much context as possible. 2. Mathematical ideas related to pattern recognition, subfields of AI and statistics. Please check first if StackOverflow, Computer Science Stack Exchange, or Cross Validated is more appropriate.

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." If there is no explicit mathematical context given, such a question will, typically, be rapidly closed. For such a question that does have an explicit mathematical context, 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.

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How to find pattern in $1,2,8,9,15,20,26,38....$ infinite sequence?

While I was investigating some specific types of prime numbers I have faced with the following infinite sequence : $1,2,8,9,15,20,26,38,45,65,112,244,303,393,560,....$ I tried to find recursive formula using Maple and it's listtorec command, so up…
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Finding $x^n$ patterns

I noticed the other day while computing consecutive powers of $2$ that for $n \geq 1$, the numbers in the ones place of the values of $2^n$ repeat every 4 terms $(2, 4, 8, 6,\ldots)$. In the tens place, we get a repetition every 20 terms for $n \geq…
scohe001
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Crazy patterns arising from recursive sequence of functions

(It should first be stated that I'm all new to this kind of stuff, so do tell if anything turns out to be obvious to the more experienced reader, or even incorrect.) I've been considering the following problem: let $f_n $ be a sequence of…
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Homework problem for a first grader on $9$gag

I saw the below image on 9gag. And naturally I asked myself how many patterns can one find (and justify)? Are there any "fun" patterns, using your "first grader imagination" and your mathematical skills?
Olba12
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What is the pattern or relation in this table?

Here is the table: $$\begin{array}{c} 0\\ 1\\ 1& 1\\ 3& 2& 3\\ 5& 3& 3& 5\\ 11 &8 &10 &8 &11\\ 21 &13 &14 &14 &13 &21\\ 43 &30 &37 &36 &37 &30 &43\\ 85 &55 &61 &55 &55 &61 &55 &85\\ 171 &116 &140 &140 &146 &140 &140 &116 &171 …
Ahmad Faiyaz
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Number pattern or some logic?

I spent an hour attempting to solve this but couldn't find any particular pattern in which the numbers are arranged. I asked my teachers but none of them could solve it. The answer is 8 Can anyone explain it?
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Do the differences of perfect squares apply to perfect cubes and more?

I'm curious about a special property of squares. The difference between perfect squares starting from 0 are 1,3,5,7,9..., where each difference goes up by 2. I want to know if there are any patterns for perfect cubes or quartics. Are the differences…
Jason Chen
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Find the pattern, What is the correct answer

Ok, so this question is from seriously hard IQ test that has been doing the rounds on facebook, ok, 17 questions are easy 3 are hellishly hard, The answer to this one is 17, I do not know why, I found out by trial and error just to test, but It's…
user126285
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Series expansion of $\text{Li}_3(1-x)$ at $x \sim 0$

My question is simple, but maybe hard to answer. I would like to have a series expansion for $\text{Li}_3 (1-x)$ at $x \sim 0$ in the following form: $$\text{Li}_3 (1-x) = \sum_{n=0} c_n x^n + \log x \sum_{m=1} c_m x^m. \tag{1}$$ The first few terms…
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Bishop - Pattern Recognition & Machine Learning, Exercise 1.4

I'm working on exercise 1.4 in Bishops Pattern Recognition & Machine Learning book. This exercise is about probability densities. I've two questions about this exercise. At first I don't understand equation 1.27. He writes: "Under a nonlinear change…
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Stuck with handling of conditional probability in Bishop's "Pattern Recognition and Machine Learning" (1.66)

I've just started working through the book, and I'm stuck with how the author handles conditional probability in (1.66). The context is as follows. In this chapter we are working with a curve fitting task: we try to fit a polynomial $\sum w_ix^i$…
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Formula to this pattern? $1$, $11$, $21$, $1211$, $111221$, $\ldots$

I have this pattern: 1 11 21 1211 111221 I'm guessing it's a fibo pattern, been at it for hours now. Anyone know?
Karl Morrison
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Please, help to identify this numerical constant

I'm trying to find an answer to this question. Let $K(k)$ be the elliptic integral of the first kind and $K'=K(\sqrt{1-k^2})$. According to Abel's theorem (see this link) we know that if $\frac{K'}{K}=\frac{a+b\sqrt{n}}{c+d\sqrt{n}}$ where…
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Has anyone seen this pattern that evaluates to $-\frac{1}{3}$ always?

I was recently doodling and came upon an interesting pattern. Beginning with $0$, add $1$, subtract $2$, divide by $3$, and multiply by $4$. Then add $5$, subtract $6$, divide by $7$, and multiply by $8$. Hopefully it's clear what I'm doing. $$…
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Permutations to satisfy a challenging restriction

In a stack of n distinct cards in order {1,2,3,4,...,n} from top, define distance between 2 cards as the number of cards between them. 2 cards are neighbours if they're adjacent in original stack, if their index differs by 1. How many card…
Y-dog
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