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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.

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22 views

Find pattern in two numbers

If I'm given two sets of numbers, how can I find out what the fixed amount fee is and what's the variable? Example \$100 - taxes and fees (\$19.7 or 19.7%) = \$119.7 \$200 - taxes and fees (\$33.7 ...
4
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2answers
81 views

Find general term of $1+\frac{2!}{3}+\frac{3!}{11}+\frac{4!}{43}+\frac{5!}{171}+…$ [on hold]

Find general term of $1+\frac{2!}{3}+\frac{3!}{11}+\frac{4!}{43}+\frac{5!}{171}+....$ However it has been ask to check convergence but how can i do that before knowing the general term. I can't see ...
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1answer
36 views

Finding the M.L.E estimates of weight maximizing the Likelihood Function of a Linear Regression

I am reading this book "Pattern Recognition and Machine Learning " - Christopher M. Bishop . My question is around equation $3.13$ page $141$.In the book , he talks of Maximum likelihood estimate of ...
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1answer
11 views

Proportionality term in Normal-Gamma distribution

I am currently learning from Christopher Bihops's Pattern Recognition and Machine Learning book about posterior distributions for the Normal distribution whenever both $\mu$ and $\tau$ (the precision ...
2
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0answers
40 views

Animate this Moire pattern. What mathematical tools could be used to analyze this moving pattern?

For a mathematical art project, I want to animate the following pattern I made on desmos. It seems to be a Moire pattern. However I cannot make the pattern move smoothly and continuously because ...
5
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3answers
201 views

Does this pattern of summing polygonal numbers to get a square repeat indefinitely?

I am using the table of polygonal numbers on this site: http://oeis.org/wiki/Polygonal_numbers The first row of the table gives the value of $n=0,1,2,3,...$. The first column gives the ...
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1answer
111 views

If $5 * 5$ = $10$ , $6*6$ = $18$ , $7*7$ = $36$ ; then $7* 8$ =? [closed]

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 ...
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1answer
68 views

If $\, 5$ & $4\to 100$ , $8$ & $5 \to 400$ , $2$ & $19 \to 361$ , $A$ & $5 \to 625$ , $12$ & $3 \to 324$ , $7$ & $6 \to 441$ ; then $A=?$

Suppose it is given : $\quad \, 5$ & $4\to 100$ , $\quad 8$ & $5 \to 400$ , $\quad 2$ & $19 \to 361$ , $\quad A$ & $5 \to 625$ , $\quad 12$ & $3 \to 324$ , $\quad 7$ & $6 \to ...
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1answer
16 views

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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0answers
28 views

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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0answers
31 views

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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0answers
24 views

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 ...
0
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3answers
49 views

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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1answer
54 views

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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1answer
31 views

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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0answers
40 views

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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0answers
28 views

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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1answer
18 views

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....
2
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1answer
57 views

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. ...
1
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2answers
346 views

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 ...
1
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1answer
22 views

Points on decision hyperplane

I'm reading a chapter on linear classifiers, and the authors define the decision hyperplane as: $$ g(\mathbf{x}) = \mathbf{w}^T\mathbf{x} + w_0 = 0 $$ They say that if $\mathbf{x}_1$ and $\mathbf{x}...
0
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1answer
34 views

Two sequences share a common (yet unknown) term. What is it?

Say you have two sequences which are given by a polynomial of some degree. Both of these sequences share a term. Is there a way to find the missing term, and what is the minimum number of values (or ...
1
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3answers
645 views

What number comes next in this sequence?

$4, 15, 13, 7, 22, -1, 31, -9, 40, -17, 49$. What comes next? The answer is $-25$, but why?
4
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1answer
69 views

In a 7x7 grid, what is the number in the bottom right corner?

My math teacher have presented me with a problem, that in my opinion is quite hard. It goes. "You have a 7x7 grid. Some of the spaces in the grid are already filled with numbers. You have to insert ...
3
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2answers
74 views

Is there an intuitive way to understand $Pair(x,y) = \frac{(x+y)(x+y+1)}{2} + x$?

After a lot of effort I discovered some pattern that the function: $$Pair(x,y) = \frac{(x+y)(x+y+1)}{2} + x$$ essentially zigzags along the grid with $\mathbf N$ vs $\mathbf N$ (natural numbers). So ...
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1answer
30 views

Original Source for Norbert Wiener quote “A pattern is essentially an arrangement…” ?

I found this quote blow supposedly said by Norbert Wiener in at least two books : "Digital image processing" by R. Gonzales and "Pattern Formation and Pattern Recognition — An Attempt at a Synthesis" ...
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0answers
77 views

Is there any pattern in the sequence $125, 2518, 108, 114, \_\_\_,286,144, 3621, 105$?

One of my students came up with the following question- Find the missing number in $125,2518,108,114,?,286,144,3621,105$. At first, I thought it contains $3$ separate sequences viz $125,114,144,\...
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3answers
130 views

Finding the missing term, in matrix arrangement

Find the missing term $x$. I am not able to guess the pattern $$\begin{pmatrix}811 & 236 & 57 \\ 23 & 87 & 119\\ 314 & 70 & x\end{pmatrix}$$
4
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1answer
63 views

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: $$a_{n+1}=\frac{a_n+b_n}{2}$$ $$b_{n+1}=a_n+b_n-\sqrt{a_n b_n}$$ ...
0
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1answer
25 views

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 ...
4
votes
1answer
50 views

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 ...
0
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0answers
37 views

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 ...
0
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1answer
25 views

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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0answers
11 views

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 ...
0
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2answers
71 views

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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1answer
62 views

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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0answers
16 views

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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0answers
17 views

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 ...
0
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0answers
78 views

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 ...
0
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2answers
64 views

Do polynomial expansions have to be in terms of $x$, ie $\sum x^k$?

This seems like a trivial question, but I have not been able to find an answer online. Do power series/polynomial expansions have to be in terms of $x$, ie: $\sum x^k$. For example, would $\sum_{k=0}...
15
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8answers
309 views

General formula for nth element of the sequence 0, 1, 0, 1, …

The sequence is $f = 0, 1, 0, 1, \ldots$ I want to find a general formula for the $n$th element. The sequence starts at $n = 0$ (the $0$ here is not the first element $0$ but rather denotes the $0$th ...
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0answers
59 views

How can I find the Sprague-Grundy function of this game?

The game involves N coins and a player can flip any consecutive $K$ sequence of coins, where $K$ is a perfect square. I have developed a function to list the values, but I am looking for a ...
13
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1answer
429 views

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, ...
0
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1answer
57 views

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) ...
0
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1answer
104 views

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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1answer
54 views

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. ...
3
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1answer
136 views

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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1answer
139 views

$n$ 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 ...
0
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0answers
59 views

Object segmentation in PCL

Sorry because I am not sure if this question fits here. I am new working in object recognition and localisation. I am using PCL to capture a model of an object and localise it. It works well. I ...
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1answer
102 views

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>...