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, ...

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1answer
168 views

Expression for Sum of Multivariate Gaussian Random Vectors

Consider two multidimensional random vectors $x$ and $z$ having Gaussian distributions $P(x)=N(x\mid\mu_x,\Sigma_x)$ and $P(z)=N(z\mid\mu_z,\Sigma_z)$, respectively, together with their sum $y=x+z$. ...
0
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1answer
132 views

What is the pattern here? Q-function - SOLVED

I've got the following problem: The difinition of the funtion: Q(S,M). The purpose is to find the max number of possibilities how to write the funcition. ...
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1answer
62 views

Identifying a pattern in an array

Is there a way to identifying a pattern and/or recursive function for an array? If yes, how can I do this. Could anyone please help me with some information and/or resource for this? Any help is ...
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1answer
143 views

Finding the mean (or pattern) of a set of related values in a matrix discarding those that are too different.

this is my first question here so I am not sure if it is a valid one. I am currently facing a mathematical problem that is not so hard to solve, but given the accuracy i need in the results I would ...
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1answer
516 views

Math problem in Pattern Recognition and Machine Learning

I had been carefully following Bishop's Pattern Recognition book and came across some of difficulties due to my merely basic math ground.First begin by the Gaussian section on page 80. The ...
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1answer
444 views

Equations and Pattern formulas problem solving

I have this question to answer and I need help with finding or creating a equation. You own a license plate manufacturing company. Write a formula or equation that takes a population and ...
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1answer
32 views

Hypersphere - Pattern matching using Centroid, Radius and Diameter

I have a hyper-sphere formed with set of $n$-dimensional data points. I could calculate centroid ($X_0$), radius($R$) and diameter($D$). Using these $X_0, R, D$, how I can find whether the a given ...
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0answers
27 views

In kernel rules, why is a regular kernel necessarily bounded?

Request from a dabbler in measure theory. Here a kernel merely designates a real-valued function. Quoted from "A Probabilistic Theory of Pattern Recognition", Luc Devroye, Laszlo Gyorfi, Gabor ...
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1answer
24 views

proof that a density proportional to Gaussian is Gaussian

I try to develop bayesian estimation for one dimensional Gaussian with unknown $\mu$ and known $\sigma$. I got $$p(x\mid D) = \int p(x\mid\mu)p(\mu\mid D) \, d\mu =\int \frac{1}{\sigma ...
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0answers
34 views

Find the pattern

Can you spot the pattern? €41.04 = €58.84 €48.17 = €91.11 €59.41 = €140.04 €65.65 = €184.15 I am getting the first rate back from a web service, but when I visit their site it is suppose to be ...
0
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1answer
26 views

Trying to figure out a Mathematical pattern

I am given a start point, a, an end point b, and a number of values x. With that I am supposed to come up with the points between the start and end point. Below is an example ...
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0answers
27 views

Estimate prior for normal distributed data

I have successfully implemented a bayesian classifier using maximum likelihood. In my case I've got 2 classes and I have calculated the two $\mu$ and $\Sigma$. In my problem with a 3-dimensional ...
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1answer
51 views

how to calculate the marginal distribution of probabilistic principal component analysis

In the book Pattern recognition and machine learning from Bishop equation 12.33 states: $\mathbf{x} = \mathbf{W} \mathbf{z} + \boldsymbol\mu + \boldsymbol\epsilon$ Here $\mathbf{z}$ has a normal ...
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0answers
12 views

Is auto-correlation a particular and simple form of pattern in time series?

In a time serie context and considering the sign of the variation of the variable auto-correlation means that for couple of measures at (time t, time t+1) the ...
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0answers
16 views

Kernel Method for complex valued problems

Kernel Method are widely used in Pattern Recognition and Machine Learning. e.g Kernel PCA and Kernel Regression are used as some extension of the regular PCA and Regression. However all the kernels I ...
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0answers
23 views

Pattern Recognition terms a little fuzzy

I've been trying to learn more about probability and the websites I have visited are not describing the relationship to each other that well (when to use what, for what purpose in conjunction with ...
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0answers
23 views

Common or distinct covariance matrices for mahalanobis distance classifier

I'm very new to pattern recognition so apologies in advance for a newbies question. I've been experimenting with mahalanobis distance to class mean based classifiers to predict diagnoses from ...
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1answer
37 views

Sequence and Pattern Problem of Marbles

Ellie is dropping marbles into a box one at a time in the following order: red, white, white, blue, blue, blue: red, white, white, blue, blue, blue: ... How many marbles will be in the box right ...
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0answers
47 views

Pattern recognition next shape pattern

which one of the above do you think is the the right answer? i guess it's B but not sure, maybe C. http://tinypic.com/r/nwfqpx/8 thanks.
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0answers
15 views

LDA find densities

I have the predictor-response (X,Y) with response Y={-1,+1}. The predictor X is a pair (X1,X2) independent, uniformly distributed on [0,1]. I am given the prediction rule for Y=+1, eta(X1,X2)= ...
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0answers
18 views

Computing Object Classification with bayesian statistics

Say I want to know if there is a zebra $\theta$, in an image $x$. According to Bayes statistics applies to image recognition, I should be computing: ...
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0answers
22 views

Pattern embedding method

There are three defined functions; $a_n=A(n), b_n=B(n), c_n=C(n)$ and an unknown function $d_n=D(n)$. It has been found out that $d_1=a_1$$d_2=b_1$$d_3=c_1$$d_4=a_2$$d_5=b_2$..... Is there a method ...
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1answer
39 views

How to complete a table of probabilities ?

Im baffling myself as to why I cannot understand where it came from. Someone please explain to me like I'm five. $$\begin{array}{c|c} x & p(x) \\ \hline 0 & 0.73 \\ 1 & ? \\ 2 & 0.06 ...
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0answers
106 views

Number of differently-sized squares needed to fill a rectangle; is there a visible formula? [Pattern spotting]

Consider a game in which we tile a given rectangle with the largest squares that will fit. We record the number of squares of each size that we can use, until the rectangle is completely covered. ...
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1answer
78 views

Digit sum of the sum equals digit sum of the addends

This may be a simple question and I am not a mathematician. I recently noticed that 11+12+13 = 36 whose digit sum is 9. And that the digit sum 1+1+1+2+1+3 also equals 9. Is there a pattern here that ...
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1answer
79 views

Finding a generating function for a pattern

I was working on this projecteuler.com problem, and I was very interested by the premise. Essentially, given n terms, find an ...
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1answer
36 views

Making the Smallest Number of Mistakes Possible

I have the following problem. I have a set of $k$ labelled points, $\left\{\mathbf{x}_i, y_i\right\}_{i=1}^{k}$, where $\mathbf{x}_i\in \mathbb{R}^{2}$, and $y_i\in\left\{-1,1\right\}$. I want to ...
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1answer
290 views

Pattern recognition next shape [closed]

Is there any logic for finding the next shape in the blank? I think it's an hard one.
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0answers
131 views

Understanding Gray-Level Hit-or-Miss-Transform Definition

From a paper I am using for my Bachelor thesis: The HMT transform by the pair $(A,B)$ associates to a binary image $X$ the set $X\otimes(A,B)$ of positions where the translate of $A$ fits inside ...
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1answer
87 views

How to calculate a result based on an exponentially changing pattern/sequence. [duplicate]

Given any number (including decimals) between 12.5 and 87.5 I need to calculate another number based on these results:  Input = 12.5 | 31.25 | 50 | 68.75 | 87.5 Result = 12.5 | 64.5  | 78 | ...
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0answers
38 views

Estimating $p(x)$ with a nonparametric method

"Pattern Classification" book I study that in nonparametric methods we need to estimate $p(x)$, and we don't want just the averaged version of it. They give an example of theoretical procedure to ...
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3answers
2k views

Logical Reasoning: Identify next figure

I came across this logical reasoning/ abstract reasoning question in my logical reasoning book. Can somebody please help me identify the next pattern: Thanks!
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0answers
370 views

Pattern matching questions

I saw the below questions and was curious regarding the logic behind the answer. I will be grateful is some one could help me So the question is given the patter, identify the next one
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0answers
123 views

Matrix & Partition & Natural Number & Pattern

I would like to know if someone know, how is called a matrix M*N, where m represents the row index in the matrix and the sum of the N columns at this row. Meaning that each row represents a possible ...
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votes
2answers
348 views

Guess the terms in the sequence?

I am writing GRE in 2 two months, and I just can't solve these sequence question. Can anyone tell what the missing terms are and what is the pattern here? Find the next 4 terms in this sneaky ...
-1
votes
2answers
51 views

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 $3^2$ ...
-1
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1answer
23k views

I don't see the pattern.. does anyone understand this..? [duplicate]

Note.. the numbers are actually in a 7 x 6 grid.. graphics did not show here.. ...
-2
votes
1answer
33 views

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 $[0.125, 0.25, 0.5, 1, 2, 4, 8]$?
-4
votes
2answers
595 views

How many pairs of integers $(A, B)$ are there in the range $[1,\ldots, N]$, such that $\gcd(A,B) = B$? [closed]

I am given a positive integer $N$ ($N\leq 10^9$). How many pairs of integers $(A, B)$ exist in the range $[1,\ldots, N]$ such that $\gcd(A,B) = B$?