# 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.

453 questions
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### Can FFT be used to cluster sound waves based on their similarity?

I am new to this so apologies if the question appears trivial. Say we have n sound files and we want to cluster them to identify which ones are more similar. I ...
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### What's the generalised formula for this sequence?

Suppose we have two integers 'n' and 'k' and we have to find the formula for the sequence: ...
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### A-priori probability in pattern recognition problem

I am trying to evaluate a formula for a pattern recognition problem but am having difficulty understanding what an a-priori probability is. Suppose I have a dataset with 4 classes. 25% of the ...
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### what is fuzzy svm?

I have to solve this question for my homework but I don't get how to formulate svm to FSVM. can someone please guide me? What is your idea to have a model of SVM classifier in which instances can ...
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### Which row consists 2017 in the following pattern?

In the pattern here, in which row 2017 will be located? Source: Bangladesh Math Olympiad 2017 Junior Category I can not find what pattern the table is using.
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### Deriving a formula for an arbitrary term in $1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, \ldots$

A sequence of numbers is given as: $$1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \text{and so on}$$ (Each integer $n$ is repeated $n$ times.) What will be the 50th term of that sequence? Let's say $x=50$. Then ...
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### Magic Square: Missing Entry

I found a $3 \times 3$ magic square and cannot figure out the missing digit. It is multiple choice (and just a game) but I want to know the pattern. \begin{align*} 65 && 69 && 13\\ 14 ...
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### Prove the following inequality (number theory) [duplicate]

If $2^m > 3^n$ for some $m>n>1$ then show that $$2^m - 2^{(m-n)} > 3^n$$ I've verified the inequality for a large number of values of $n$ and $m(n)$, where $m(n) = \lceil n\log_23\rceil$, ...
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### Finding pattern in a Eigenvalue BVP [Analytic possiblity] ??

I have the following two third order linear ODEs which have been arrived at after applying separation of variables to a coupled system of three PDEs. \begin{eqnarray} \lambda_h F''' - 2 \lambda_h \...
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### Need help with Pattern problem

Letters $A$ to $J$ is a random number. If only $A$ is used. There is just $A$. Which is $1$ scenario If $A$ and $B$ are used. There are $2$ scenarios. $(A=B) (A<>B)$ If$A, B$ and $C$ are used....
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### Interesting Pattern - Adding or Multiplying Sequential Integers and Then Reducing

I noticed that if you sequentially add integers together, or even multiply them, and then reduce the result, an interesting pattern emerges. ...
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### Is it possible to know if a number exists within one of these sequences?

Question: Given a number, I need to find out which of the following rows/lists it exists in. But I don't want generate them, given that there are a lot of lists and they grow bigger over time. We ...
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### Finding the missing term, in matrix arrangement

Find the missing term $x$. I am not able to guess the pattern $$\begin{pmatrix}811 & 236 & 57 \\ 23 & 87 & 119\\ 314 & 70 & x\end{pmatrix}$$
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### What is the general term of this series (obtained from an iterated mean)?

This is a long overdue follow up to another question, but it's worth asking separately. Consider the following iterated mean: $$a_{n+1}=\frac{a_n+b_n}{2}$$ $$b_{n+1}=a_n+b_n-\sqrt{a_n b_n}$$ ...
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### Algorithm to find amount of unique number sequences without repeating numbers?

Basically what I am wondering is what the algorithm would look like to find the amount of number sequences without repeating numbers for any given positive number? For Example, if you use 3 (which ...
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### Why does Pascal's triangle follow a pattern using derivatives?

I was learning the derivatives and I remembered Pascal's triangle and I discover that I can write it with derivatives without having to draw it. Let's see Pascal's triangle: Any row can be written ...
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### Can a carrom board striker path be determined

When a carrom board striker is strike to one side of the board(4 sided), it continue hitting all the side. Does the pattern repeat, assuming the striker doesn't slow and stop. I mean, can the point ...
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### How to find a particular number in a triangular arrangement of numbers

I can see the first entry of each row is added to an increase of 1. So 2 = 1+1, 4 = 2+2, 7 = 4+ 3, etc. So I know that the 64th entry is $x_{64} = x_{63}+63$ But I am stuck on how to calculate it. ...
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### What are the coordinates of a 1st degree Hilbert curve in a finite 4D space

I am trying to build some intuition about Hilbert curves, and I am trying to get some sort of understanding of them in N-dimensional space. And it really helps if I am able to see a pattern. I can ...
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### Finding a formula for a sequence or proving it is impossible [closed]

I tried to search for a formula that produces the following sequence: 35 49 55 65 77 85 91 95 115 Etc, a larger sequence is in the following link: https://pastebin.com/HDDHe7bz Or proving that such ...
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### Finding the $2n+1$ th derivative of $\frac{y^{2n+1}xy}{1-x^2y^2}$ with respect to $x$.

$f(x,y) = \frac{y^{2n+1}xy}{1-x^2y^2}$. I made the following table: \begin{align} & 2n+1 = 1 \implies f^{(1)} = \frac{1!y^2(1+x^2y^2)}{(1-x^2y^2)^2}\\ & 2n+1 = 3 \implies f^{(3)} = \frac{3!y^...
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### Finding any correlation between curves

Say i have 2 curves A/B. I would like to find out the points where at least twice (a pattern) when something happen in A, it affect B. I dont care what it is, i just look for points of correlation ...
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### Designing perceptron for given problem

I encountered following problem in one of the paper: Consider 2-class PR problems with n Boolean features. Consider two specific classification tasks specified by the following: (i) a feature ...
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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 ...
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### How does the SMO algorithm for SVMs guarantee the KKT condition “primal feasibility”?

I'm reading Andrew Ng's lecture notes on support vector machines (SVMs) and the sequential minimal optimization (SMO) algorithm (see here). The notes first introduce the Karush-Kuhn-Tucker (KKT) ...
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### An unknown pattern in $π^k$.

While trying to find a pattern in $π$, by taking the idea from $n$ such that the digits immediately after the decimal point of $\pi^n$ give $n$ again By using wolfram alpha calculator first I am ...
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### Question on Irrationality of Irrational Numbers [closed]

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. ...
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### Pattern Recognition and Machine Learning (Bishop) - Exercise 1.28

1.28 In Section 1.6, we introduced the idea of entropy $h(x)$ as the information gained on observing the value of a random variable $x$ having distribution $p(x)$. We saw that, for independent ...
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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 ...
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>...