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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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1answer
16 views

Recognizing a Factoring Pattern (Pt. 2)

I am trying to identify a pattern in the following set of equations; $N_{-1}=1$ $N_{0}=2y$ $N_{1}=2y^2+z$ $N_{2}=2y^3+3yz$ $N_{3}=2y^4+5y^2 z+z^2$ $N_{4}=2y^5+7y^3 z+4yz^2$ $N_{5}=2y^6+9y^4 z+...
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1answer
43 views

Recognising a Factoring Pattern

I am trying to identify a pattern in the following set of equations; $$N_0=y$$ $$N_1=y^2+z$$ $$N_2=y^3+2yz$$ $$N_3=y^4+3y^2z+z^2$$ $$N_4=y^5+4y^3z+3yz^2$$ $$N_5=y^6+5y^4z+6y^2 z^2+z^3$$ Essentially, ...
2
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1answer
37 views

How does this entropy equation simplify?

This is from the bok "Pattern Recognition and Machine Learning" By Bishop. I am having a hard time following the last step of this equation Where Stirlings approxaimation is subtituted for $\ln N!$ to ...
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1answer
27 views

Pattern in Squared Numbers and their Digit Sum

So this has been boggling my mind for some time now. On spring break I was really bored and started messing around with numbers when I noticed something. I was squaring each number (1-9) when I ...
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0answers
9 views

Bayesian curve fitting vectorized mean calculation

In the book "Pattern Recognition and Machine Learning" by Bishop, there is a section on Bayesian curve fitting where he gives some calculations in figures 1.69, 1.70, 1.71, and 1.72 which I found hard ...
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1answer
32 views

Prove that a series of numbers are random

I have a series of randomly generated numbers (3, 1,-3, 2, -1,6). I want to prove that the numbers are not random but have an increasing/decreasing pattern. The source of the numbers isn't really ...
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1answer
22 views

Pattern Recognition and Machine Learning: Maximizing log likelihood with respect to Beta

On page 29 in Christopher Bishop's Pattern Recognition and Machine Learning book he gives the following two equations 1.62 $$ \ln p(t|\pmb{x}, \pmb{w}, \beta) = - \frac{\beta}{2} \sum_{n=1}^N \{ y(...
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0answers
19 views

Encryption and Decryption of Alpahabets to Integers

I'll explain my case with an example. Say, I've 2 words, FOOTBALL FOOD Let f(FOOTBALL) = 845614, f(FOOD) = 74312 and f(FO) = 132 Is there any method to get f'(845614, 2) = 132 and f'(...
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0answers
20 views

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 ...
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0answers
264 views

How can I solve a chessboard puzzle of size 100X100? [closed]

I have 800 rooks. How can I place them on a chessboard ?
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0answers
59 views

Are the digits of $\log 2$ and $\log 3$, or $\sqrt{2}$ and $\sqrt{3}$, or $e$ and $\pi$, cross-correlated?

I try to find sequences of digits (in base $b$, with $b$ not necessarily an integer) that are not cross-correlated. While the digits in base $b$ of (say) $\pi$ and $e$ do not exhibit auto-correlations ...
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2answers
114 views

Finding a pattern, I'm stuck

I have a friend who knows how much I love math, (I imagine new problems just to do the math behind them and to see if I can expand my understanding) and so he brings me the stuff that stumps him. ...
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2answers
36 views

Find the number pattern [closed]

Goal: find 1 equation to generate -4,2,10,6,3 on looping Output -4 on 1st iteration Output 2...
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1answer
76 views

Find a formula, in terms of n and k , for the number of leaves of G.

Let G be a tree having n n vertices. Suppose that every vertex in G which is not a leaf has degree k, where k > 1 . Find a formula, in terms of n and k , for the number of leaves of G. I started ...
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1answer
23 views

Maximum combinations of emails for a domain

According to my understanding, there can be a maximum of 64 characters before the @ symbol in an email. The allowed characters can be found here. Using that ...
0
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1answer
51 views

How to identify the next number to complete the table?

Consider the following table \begin{array}{c|c|c|c|c|c|c|lcr} &the&A.J.& team &the &G.N.&team \\ \hline & 1 & 2 & John & 1 &2& Mark \\ \hline ...
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1answer
37 views

Mean of the posterior distribution in bayesian linear regression with infinitely broad prior

Currently reading from Christopher Bishop's Pattern Recognition and Machine Learning book about parameter distribution under a bayesian linear regression. On page 153, the author deduces that the ...
0
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1answer
21 views

Next triplet in the series [closed]

What is the next triplet in the below series of triplets: (2,3,4), (47,48,49), (674,675,676), (9407,9408,9409), ___? Few points about the above series: (i) the terms of the triplets are consecutive ...
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2answers
23 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
votes
2answers
96 views

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

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
42 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
21 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
43 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 ...
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3answers
205 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
123 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
111 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 ...
1
vote
1answer
22 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: ...
0
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0answers
38 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
35 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
55 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
32 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
30 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
59 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
352 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
36 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 ...
2
votes
3answers
743 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?
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1answer
75 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
76 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
89 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
139 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
votes
1answer
64 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
28 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
64 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 ...
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0answers
54 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 ...