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.

604 questions
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Finding a combinatorial formula for the following sequence of tables

While studying a subject in mathematical physics and topology (which is not necessarily relevant to this question anyway), I bumped into the following sequence of tables, let's call them $M_0, M_1, M_2, M_3, M_4, \cdots$. (The table goes on, but it…
Henry
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Relationship between primes and practical numbers

This is my first post here. I am a musician, and not a mathematician, but I enjoy doing things to prime numbers and seeing what comes out. I have defined a sequence which takes the following values for $n$: -1 if $n$ is prime 1 if $n$ is a…
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Digital root of twin prime semiprimes

It appears that the product of any pair of twin primes (excluding the first pair 3 and 5) yields a semi prime whose digital root is equal to $8$. Example: $$ 17 \cdot 19 = 323 $$ The digital root of $323$ is $8$. I've tested the first twenty and a…
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Is this (deceptive) pattern just a coincidence?

I've come across this nice pattern start: $$ \begin{align} 1^2-2^2+3^2 &= 6\\ 1^4-2^4+3^4 &= 66\\ 1^6-2^6+3^6 &= 666\\ \end{align} $$ I read somewhere the third line, I remembered that I already knew the first, I immediately tested the second and I…
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Has anyone noticed this pattern?

I've been messing around a bit and I noticed a curious pattern when it comes to progressions of powers. Let's take the progression of consecutive integers: $1,2,3,4,5,6,7,...$ Obviously it's an arithmetic progression with a common distance of 1. And…
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What are the use cases of the Dirichlet energy in computer vision?

I am reading a paper, in the context of computer vision, that mentions the "famous" Dirichlet energy. I am not familiar with this Dirichlet energy, but apparently we can minimise it. What are specific use cases of the Dirichlet energy in computer…
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Is kernel density estimation a GMM with uniform mixture weight?

recall that for a Gaussian Mixture Model, the density of p(x) (multivariate) is $$P(x) = \Sigma_{i=1}^{C}\pi(c_i)\mathcal{N}(\mu_i,\Sigma_i)$$ On the other hand, non-parametric density estimation using kernel can be stated as…
Jing
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Consecutive Prime Gap Sum (Amateur)

List of the first fifty prime gaps: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4. My conjecture is that the sum of consecutive prime gaps is…
Tony
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Why does this pattern repeat after 14 cycles instead of 256, can you give a proof?

I have 8 numbers in an array: the numbers are either 1 or 0 and are initially random. example: [0,1,0,1,1,0,0,1] every cycle, the array changes as follows: If a cell has two adjacent values that are both equal, then the value becomes 1. Otherwise…
Jerm
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Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

Consider the sequence: $$a_0=x,~~~b_0=y$$ $$a_{n+1}=\frac{1}{2} \left(a_n+\sqrt{\frac{a_n^2+b_n^2}{2}} \right),~b_{n+1}=\frac{1}{2} \left(b_n+\sqrt{\frac{a_n^2+b_n^2}{2}}\right)$$ $$\lim_{n \to \infty} a_n=\lim_{n \to \infty} b_n=l(x,y)$$ I can't…
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Predict next number from a series

Which methods I can use to predict next number from a series of numbers ? I know the min & max possible number in advance.
Sourav
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Does this "almost all integers in order" sequence have a closed form?

Can you help me define a formula for the following sequence (first $130$ terms) : 0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 10, 11, 12, 13, 12, 15, 15, 17, 18, 18, 20, 21, 22, 23, 22, 25, 26, 27, 28, 28, 30, 31, 32, 33, 32, 35, 36, 37, 38, 38, 40, 41, 42, 43,…
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How to Characterize Clumps in a Large, Semi-Random Graph

Consider large (100,000+ vertices, say) graphs, which we think of as representing some population with edges representing some form of symmetric relation. They might be the Friend graph of Facebook, mathematicians with the collaboration relation,…
Greg Muller
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Finding pattern

Just a puzzle. \begin{matrix} 2 & 9 & ? \\ 11 & 33 & 66 \\ 8 & 3 & 27 \\ \end{matrix} The options are $35$, $40$, $45$, $55$. $45$ is false. I thought the answer was $15$ since they are of the form $3a + b = c$, but…
leafpile
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Fractals - when the number of seed shapes that can fit into the scaled-up copy is non-integer.

I've heard people say (for eg. here) that the dimension of fractal patterns (particularly, in this question, Lindenmayer fractals) can be formulated as follows: $$D=\frac{\ln N}{\ln S}$$ Where $N$ is the number of copies of the seed shape that fit…
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