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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Transforming $[-3, -2, -1, 0, 1, 2, 3]$ to $[0.125, 0.25, 0.5, 1, 2, 4, 8]$

Given the range of negative/positive numbers $[-3, -2, -1, 0, 1, 2, 3]$, is there a transformation that gives me $[0.125, 0.25, 0.5, 1, 2, 4, 8]$?
Robert Kubrick
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Scale invariance prior distribution. Prove the following statement.

Consider a density of the form $$ p(x|\sigma)=\frac{1}{\sigma}f(\frac{x}{\sigma}). $$ where $\sigma>0$. Note that this will be a normalized density provided $f(x)$ is correctly normalized. The parameter $\sigma$ is known as a scale parameter,…
Frank
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What is the closed form for the sequence $1,0,1,1,0,0,1,1,1,0,0,0...$?

I thought about $$\frac{1+(-1)^k}{2}$$ but it didn't work ! Is there any closed form for it ?
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Question on Irrationality of Irrational Numbers

As we know that $2^{1/n}$ is an irrational number for all natural number greater than $1$. But if we do $2^{n/n}$ then it will be a rational number or in simple words it will become a natural number. Now as we know $\pi$ and $e$ is also irrational…
user586560
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A Problem on Prime and Composite Numbers Relation

I was fighting with this question for about five days and I’m unable to get a mathematical proof. Question: Let imagine a natural number and a prime number $q$ and $k$ respectively such that $k>q$ and $k$ is the nearest prime number with respect to…
Adarsh Kumar
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What is the pattern in this set of numbers?

$[3,6,11,18,27,38,...]$. I need to write this set in set-builder notation but I can't find any pattern, I see no common multiple, it doesn't appear to be a geometric or arithmetic series. The problem comes from the book of proof.
Andres Romero
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Select the option for “?” that continues the pattern in each question.

i'm no to sure where to start with these pattern. If they were in an ordinary descending or ascending order it'd be easier. There's a pattern here, What would be the next number after 20? Can anyone assist please 3, -6, 12, 4, 20, ?
Jane
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How to find the 999th shape in a pattern?

The pattern is of a triangle followed by 3 stars and 4 circles and it continues to repeat. What will the 999th shape in the pattern be? Explain how you can tell.
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I found a strange number pattern in Base 10. Does anyone know what it means?

I was trying to think of a good equation for texture smoothing to be used in programming. I came up with this. With texture smoothing however it must be based on division. $01$ to $10$ = $9$ or $3^2$ $02$ to $20$ = $18$ or $2\times 3^2$ $03$ to $30$…
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Find the next number in the sequence

I am giving this question to see how much time people take to solve such problems and to know how the idea struck their minds . I solved but it took a lot of time(12 minutes) for the solution to strike my mind .I want to check how much time…
Harish Kayarohanam
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Coordinates reachable from $(x, y) = (2,5)$

If we are on coordinate $(m,n)$ then we can either go to coordinate $(m + n, n)$ or $(m, m + n)$. If we start at $(2,5)$ then what all coordinates we can reach in finitely many moves? In our case we have: From coordinate $(2,5)$ we can go to $(7,5)$…
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If $5 * 5$ = $10$ , $6*6$ = $18$ , $7*7$ = $36$ ; then $7* 8$ =?

If $$\quad 5 * 5 = 10$$ , $$\quad 6*6=18$$ $$\quad 7*7=36$$ then $$\quad 7* 8 = ?$$ a) $54 \quad$ b) $51 \quad$ c) $30$ NOTE: Here '$*$' is not simple multiplication It is some logic or combinations of operations from which we are getting…
Suresh
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$n$ such that the digits immediately after the decimal point of $\pi^n$ give $n$ again

I was doing something with value of $\pi$ as I know that the beauty of numbers will always exist , doesn't matter either number is real or complex it must be beautiful. I observe something strange by using Wolfram alpha's calculator: $$ \pi^4 =…
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Find mising numbers from a sequence 1,4,?,16,?,36,?

Please help me find the number absent in the line for the follow sequence $1,4,?,16,?,36,?$. For example I know the absent number in the sequence $5,0,-5,\_,\_,$, they are $-15,-20$. But I didn't now how to find number in the above sequence. Help…
he hehi
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What is the member in the last set of this pattern?

(42,15,3) (24,20,2) (?,12,4) ? indicates the number I do not know
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