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
95 views

Calculation for absolute value pattern

I have a weird pattern I have to calculate and I don't quite know how to describe it, so my apologies if this is a duplicate somewhere.. I want to solve this pattern mathematically. When I have an ...
2
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1answer
644 views

Bottom to top explanation of the Mahanalobis distance?

I'm studying Pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahanalobis distance. The books give sort of intuitive explanations, but still ...
2
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1answer
148 views

How to calculate smallest pattern size based on set of ratios

So I have x number of items, each one has its own appearance ratio for making a pattern, of which I'm trying to determine the smallest possible pattern. The appearance ratios for all items total up to ...
2
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2answers
362 views

Pattern matching circle, square or triangle

I have a set of x, y co-ordinates that are actually taken from hand drawings of a circle, square or a triangle. Using the set of points, I need to mathematically find if the points approximately fit a ...
2
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1answer
22 views

Why Does This Summation Pattern Occur?

This is probably something stupid and for some reason I can't see it, but let's say you are taking the sum of the first $10^{i}$ squares. If $i=1$ we get $385$,$i=2$ we get $338350$, $i=3$ we get ...
2
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1answer
49 views

Using primes to create unique character mappings for scrambled substring searching

Problem: given a string needle, and a string haystack determine if there is there an anagram of needle present as a substring of haystack? (Assume case doesn't matter). One solution is to map the ...
2
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1answer
183 views

What kind of recursion or series is this?

I am developing a language learning program, and would like to know the mathematical expression and description for what I have (perhaps incorrectly) calling a recursive series method of learning the ...
2
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1answer
113 views

How can one classify (match within a certain confidence interval) gestures based on accelerometer readings?

I am using an accelerometer-enabled device (mobile phone, to be specific) that enables sampling acceleration at a rate of about 20 samples per second. The samples contain three values, each ...
2
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0answers
75 views

Unexplanied pattern from increasing rational sequences

I've stummbled upon some strange pattern when working with series of rational numbers. If anyone could shed light on this phenomenon I will be most greatful. Backgroud: Working in an integer lattice ...
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0answers
147 views

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 ...
2
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0answers
110 views

Multiplication structure for finite abelian rings of order $p^2$.

Consider an odd prime $p$ and a positive integer $a$ as close to 2 as possible that is not a quadratic residue $mod$ $p$. If we extend the ring $mod$ $p$ with the element $b = a^{\frac{1}{2}}$ then ...
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0answers
69 views

Algorithm to predict next 3D points

For example, having this data: year x/y/z 2007 10/20/70 2008 20/10/70 2009 30/10/60 2010 40/10/50 2011 40/15/45 We want to predict what will be the x/y/z in ...
2
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1answer
106 views

Selecting and Grouping a set of points in a 2D plane

I am currently working on a project that requires to solve the following problem: Let's say that each time a user access a specific resource on the network from his mobile device, a system stores his ...
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2answers
209 views

In simple terms what is the sequence 220,171700,167167000,166716670000 a part of?

I know that <1,2,3,...,10>$\cdot$<1 0,9,8,...1>=220 <1,2,3,...,100>$\cdot$<100,99,98,...,1>=171700 <1,2,3,...,1000>$\cdot$<1000,999,998,...,1>=167167000 ...
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1answer
187 views

Patterns of no formula.

How do I find the next number if the given pattern is $$1,2,3,2,3,4,1,2,6,23,14,19,64,69,12,78,152,93,108,?$$ (Find the question mark)
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4answers
311 views

Easy as $3.14$ question

I've got the following question with the hint "Easy as $3.14$". $$2003 = 2\\1337 = 4\\7877 = 3\\5732 = 4\\8315 = 3\\4466 = 0\\0354 = 2\\8923 = 2\\8888 = 0\\0000 = 0\\4059 = 1\\2403 = \ ?$$ I need to ...
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2answers
41 views

What is the pattern for this sequence?

I know that it increments by 1 until the (10n + 1)th term, where it increments by the term #. I don't know how to represent this entire pattern as an equation or summation of some sort.
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2answers
52 views

Find if a number lies in this pattern

I have a sequence of numbers below... $1, 2, 4, 7, 11, 16 ...$ You get this list by starting at $1$ then add $1, 2, 3, 4, 5 ...$ Given a number $n$, how can I determine if it will show up in this ...
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4answers
103 views

Finding $n^{th}$ term of sequence

$$3,8,17,32,57,\ldots$$ How do we find the $n^{th}$ term? I have been roaming aimlessly for a few minutes now. A definite pattern is in the differences of differences. Hints will be apreciated.
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1answer
157 views

Is there a pattern in figures whose perimeter is the same as their area?

Here's what I've found so far. Circumference of a circle with identical circumference and area: $4\pi$ Side length of a triangle with identical perimeter and area: $4\sqrt{3}$ And so on... ...
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2answers
171 views

Learning patterns and the maths

I am interested in learning more about patterns. My objective is to learn about how to analyse a set of numbers (not infinite but a large set of numbers in sequence) and see the patterns and then ...
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3answers
2k views

What is the next picture in this sequence?

I was reading a book on logical reasoning and came across the following: Can anyone give me the answer to the question. We want the next sequence ?
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2answers
752 views

How to find the pattern?

I'm challenging myself to figure out the mathematical expression of the number of possible combinations for certain parameters, and frankly I have no idea how. The rules are these: Take numbers ...
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1answer
47 views

Find the next number [duplicate]

I am given a sequence $$1, 11, 21, 1211, 111221, 312211, 13112221, \cdots$$ what is the next number?
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1answer
84 views

How is PI used to predict weather patterns?

I've heard that using PI to predict weather patterns is possible. I would like verification on this, and how this is possible. I can't seem to find any other sources explaining this concept. My ...
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3answers
87 views

finding nth term

Let 3,8,17,32,57 . . . . . be a pattern.How do we find the nth number?My brains are completely jammed,I am tired.I do not even recognize the pattern.I calculated a few ways,but all I want is a ...
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1answer
133 views

Can rainbows be considered to have mathematical patterns?

Of course it is evident that there is physics and mathematics involved in a rainbow, but my question is (as the title suggests) are there patterns to be found in rainbows? By patterns I mean ...
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2answers
257 views

I need to figure out a pattern

Finish the Pattern to the nearest number: 0 0 3 20 115 I need to add in a few more sentences to make this problem meet the standards. If you could solve this pattern, it would help me out alot, its ...
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2answers
157 views

Trying to figure out the pattern in this series (2)

I could use some help figuring out what the next row is in the pattern below (and what the rule is generally for each number in the series). I put it in a triangle because I'm pretty sure it has ...
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1answer
478 views

Softmax function and modelling probability distributions

Hinton in his neural network course on Coursera says that "Any probability distribution P over discrete states (P(x) > 0 for all x) can be represented as the output of a softmax unit for some inputs." ...
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3answers
370 views

Patterns in Sequences

I've heard in a movie that for any sequence of numbers, there is a nice formula for generating that sequence. So, for example if I write: 1,2,1,2,3,3,1,2,3,1,2,4,... There is a formula for ...
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1answer
55 views

T-shaped polygons

Is there any coefficient that can indicate T-shaped polygons ? Examples of T-shaped polygons:
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1answer
73 views

How to determine which encryption system is being used?

I came across this question in a local contest. I was not able to solve it at that time. Also, no solution was provided. I was wondering if someone can help me to understand how to tackle this kind ...
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1answer
411 views

Mutual Information for clustering

I'm working on a document clustering application and decided to use Normalized Mutual Information as one of the measures of effectivenes. But I don't really understand how to implement this in that ...
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1answer
134 views

Understanding the fundamentals of pattern recognition

I'm learning now about sequences and series: patterns in short. This is part of my Calc II class. I'm finding I'm having difficulty in detecting all of the patterns that my text book is asking me to ...
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1answer
91 views

Dimensionality effect on Fisher's Score

Consider Fisher's Linear Discriminant Analysis (LDA). Let $\mu_0 \in \mathcal{R}^D$ and $\mu_1 \in \mathcal{R}^D$ be means of the two classes. Similarly, let $\Sigma_0 \in \mathcal{R}^{D\times D}$ ...
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1answer
290 views

Stuck with handling of conditional probability in Bishop's “Pattern Recognition and Machine Learning” (1.66)

I've just started working through the book, and I'm stuck with how the author handles conditional probability in (1.66). The context is as follows. In this chapter we are working with a curve ...
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1answer
205 views

Pattern Recognition with basic probability

I am a college student and have Pattern Recognition as a course this semester and I am really struggling with it, reasons could be difference in teaching style of the instructor and different type of ...
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0answers
11 views

k nearest neighbor density estimation

In k nearest neighbor density estimation we calculate the density using following formula For given 1D sample X={4,5,6,7,9,10,11,12,13,14) if k=3, and we do not consider on boundary samples inside ...
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0answers
37 views

Leibniz Binary Representation of Squares

Leibniz claims to have found patterns in the square numbers and their binary representations. I cannot see any patterns at all. Here are the first ten squares and their binary representations, can ...
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0answers
121 views

Finding an unknown number in the middle of a number sequence

I've stumbled across a very peculiar number sequence and it was bugging me for a while now, i would really like to find out a way to dissect and work out the number that is missing, here's the ...
1
vote
1answer
85 views

Finding an expression to represent this pattern

Is there a method to find a math expression for a given pattern? I have this pattern and I am very curious to find out how can I generate it. ...
1
vote
0answers
32 views

Trace of a product of a recursive series of non-full rank matrices

Let $H$ be a $m\times n$ matrix that is not full rank. Hence $H^T H \neq \mathbb{1}_{m\times m}$. Can we say anything about the diagonal entries, or the trace, of matrix products of the form: $P_0 = ...
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2answers
71 views

Estimating the mean with least median of squares target

I have a set of real numbers $x_1,\ldots,x_n$. I would like estimate the mean of the set, $y$, such that the median of squares will be minimal : $\operatorname{median}(x_i-y)^2$ Is there a closed ...
1
vote
2answers
74 views

Number pattern problem

I need some help to figure out the following number pattern: Find the next number in the following sequence: $3, 2, 3, 12, 35, 78$. I tired to figure out the difference by ...
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0answers
233 views

Study the number patterns and fill in the missing number

This problem seems easy but I have been working on it for quite some time with little clue. It is about finding number patterns, I have tried many different ways, which seem to work at first but fail ...
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1answer
85 views

Find pattern in recursion

this is a example from my book Write several elements of the recursion, and see if you can find a pattern. T(n) = T(n – 1) + n T(n –1) = T(n – 2) + (n –1) T(n –2) = T(n – 3) + (n –2) T(n –3) ...
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0answers
91 views

Mapping an object's projected 3D path to a pre-defined top-down 2D path.

The title of the question may be misleading and the context simpler. Please suggest more appropriate tags for this question. Consider looking at a plane from two different perspectives. Perspective ...
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1answer
66 views

Is there a shorter way to write an equation with a clear pattern?

I have this simple expression: $$\left(\begin{array}{l} 1\\ +(A)\\ +(A+B)\\ +(A+B+C)\\ +(A+B+C+D)\\ +(A+B+C+D+E)\\ +(A+B+C+D+E+F)\\ +(A+B+C+D+E+F+G)\\ +(A+B+C+D+E+F+G+H)\\ +(A+B+C+D+E+F+G+H) ...
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1answer
145 views

How can I count clockwise vs counterclockwise cycles in a series of (modular) integers?

I'm working with a Markov process that has a state and transition diagram like in the picture: The transition probabilities are not listed, but they are always positive, but not necessarily ...