Questions on the use of mathematical techniques to extract properties from given data. Consider if your question might be more suited for Cross Validated (stats.SE) instead.

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28 views

Model for headphone quality as a function of price

I've looked for any mathematical model that shows headphone quality as a function of the price of the headphones, but have not found anything yet. Of course, "quality" is quite subjective, which could ...
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0answers
9 views

How to crop a matrix/array based on a condition [on hold]

I have a matrix consisting of 10 columns/arrays. First 9 are my data. The 10th column/array is a "trigger channel" which has sharp spikes from baseline 0V to 5V and back down to 0V. I need to crop all ...
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0answers
27 views

Prediction for time series

Suppose we have several weeks (say, 30) in a row and number of advertisements sent on e-mails on each week and number of the following orders of the product. How can I estimate the necessary number ...
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0answers
19 views

Topological (Hierarchical) Ordering of the Data

I want to graph a data depicting the correlation and frequency. Mathematics-wise, it's not hard. It's matter of how to construct the algorithm for sorting and ultimate graphing (but more importantly ...
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0answers
22 views

Activity recognition: energy of user acceleration; inconsistent values

I'm trying to implement a model for activity recognition (running, climbing up/down stairs, walking, etc...) based on the work of Bao & Intille. I'm using the iPhone accelerometer to gather the ...
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0answers
23 views

data compression average number of bits

consider the following data file. AAACAAABAAACAAADAAAE implement a Huffman code to compress this file. What is the average number of bits per symbol?
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8 views
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1answer
30 views

Creating Formula from Data Series

I have a power-law-ish data series and need to back my way into a formula for it, such that it can be generated for any number of points. This is the n=20 version (value rounded to nearest 0.25). ...
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1answer
25 views

Best fit with unknown functional form

I have data from a simulation of a certain function $F(x)$ for a discrete set of values $\{x_i\}$. I know that $$F(x) = A \ f(x) + B \ g(x)$$ where $A,B$ are (real, positive) constants and $f,g$ ...
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3answers
74 views

Meaning of mathematical symbol $\pm$

What is the meaning of the $\pm$ symbol in relation to this expression? For example, the perceived area of a circle probably grows somewhat more slowly than actual (physical, measured) area: $$ \...
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1answer
1k views

How to see that K-means objective is convex?

I'm trying to proof that the objective of the K-means clustering algorithm is non-convex. The objective is given as $J(U,Z) = \|X-UZ\|_F^2$, with $X \in\mathbb{R}^{m\times n}, U\in \mathbb{R}^{m\...
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0answers
22 views

Comparing the task complexity of installing three different offenses for American style football in three days

I want to identify the inherent difficulty of installing three separate American rules football offenses by their complexity of practice schedules in three days then relate those offenses back to one ...
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0answers
6 views

Plot large high dimensional dataset

I have a high dimensional dataset (12 variables) with 42000 observations. I made a clustering and i have evidence to choose five cluster.So i want to plot with some tools my dataset to show (if it is ...
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1answer
15 views

Relationship between subset medians and the median

Suppose we have a set of data $A = \{a_1, a_2, \dots, a_n\}$ and $B = \{b_1, b_2, \dots, b_n \}$. So there are $2n$ elements in total. Further suppose the median of $A$ and $B$ is $a$ and $b$, ...
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0answers
115 views

Optimizing Overwatch Team Composition by Player Hero Preference [closed]

I am wordy by nature - my apologies. My attempt at a TL;DR - I want to design a small tool that optimizes the team composition of a video game based on minimizing the sum of provided player ...
0
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0answers
13 views

how to produce data for filtering (specifically ekf and ukf)? -or- can you supply me with data?

I am currently implementing Kalman filters (I have EKF and UKF) and need some data to test my codes in matlab. I have a set of samples I used, but I need more. How do i produce more data? Say I wrote: ...
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0answers
9 views

Validate a trained system

I had trained a system to detect some features from a set of scenarios. Now it can detect and classify that set. How to validate that system work in real world? What mathematics tools should i use?
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1answer
1k views

Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
0
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1answer
26 views

What is the difference in how $\mathrm{R}^2$ and $\mathrm{R}$ values are interpreted?

In statistics, there is the $\mathrm{R}$ value for the product moment correlation coefficient and the $\mathrm{R}^2$ value for the coefficient of determination. In both cases they are described as a ...
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1answer
20 views

Hypothesis testabout the variability of 2 Samples

The hydrocarbon emissions are known to have decreased dramatically during the 1980s. A study was conducted to compare the hydrocarbon emissions at idling speed, in parts per million (ppm), for ...
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1answer
38 views

Snakes and Ladders and Sample Space

for my Data class project we had to play a board game and do an analysis of it. My group chose rehashed version of Snakes and Ladders. I am almost done the majority of the project, but am stuck on ...
0
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1answer
15 views

Using a continuous function to describe discrete data

I've always been told to use discrete functions with discrete data and continuous functions with continuous data. This especially comes to light when talking stats and people emphasize the difference ...
2
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1answer
354 views

Kalman filter for acceleremoter and gyro

I have read a lot of literature on this topic, but many questions still remain. (Many formulae are here below, so, who prefers to look at them in a more comfortable manner can find a MathCAD sheet ...
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1answer
21 views

Calculate confidence interval when only given alpha?

Is there a formula to properly calculate the confidence interval when you're only given alpha and sample data? Thanks!
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0answers
9 views

Estimate Results From a Database

I have some data in an Excel document, from differents projects i've made. Now I would like to use this data in order to estimate the results for new projects with different input values. Each ...
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1answer
32 views

Type 2 Error Question - How to calculate for a two tailed?

The modulus of rupture (MOR) for a particular grade of pencil lead is known to have a standard deviation of 250 psi. Process standards call for a target value of 6500 psi for the true mean MOR. For ...
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1answer
39 views

How to prove MLE of theta is unbiased?

Let $X_1, X_2, . . . , X_n$ be a random sample from a uniform distribution on $[0, \theta]$. Suppose results $x_1, x_2, . . . , x_n$ are observed. Since $f(x) = 1/\theta$ for $0 \leq x \leq \theta$, ...
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1answer
37 views

Uniform Distribution Question - Help Needed

Let $X_1, X_2, . . . , X_n$ be a random sample from a uniform distribution on $[0, \theta]$. Suppose results $x_1, x_2, . . . , x_n$ are observed. Since $f(x) = 1/\theta$ for $0 \leq x \leq \theta$, ...
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0answers
24 views

Numerical Analysis Stability or Condition

Im not sure if its the right place to ask this question since it may be more of an informatics problem and I apologize if its the case: I want to evaluate a certain function, $\frac{log(cos(x))}{x}$ ...
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1answer
45 views

Conditional Probability of a group of Mice

There are six female and four male mice in a group of 10. One of the female mice and two of the male mice have a particular disease. Suppose that two mice are selected at random from the group without ...
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1answer
19 views

Predicting values based on given data

num value 8 ? 10 ? 12 24.33 16 22.5 20 22.29 24 22.41 28 22.55 32 ? 36 ? let's say i have the following ...
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0answers
20 views

Can I use the dispersion index for a variable that is NOT normally distributed?

If I have a variable graphed as a function of time, that is not normally distributed, does it make sense to use its (time-varying) dispersion index, $\mathrm{Var}(x)/E(x)$ to compare its volatility ...
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0answers
3 views

Show that the maximum of a function is achieved in one of the data

I'm new to data analysis, and started working with circular data. Let $t_1,\dots,t_n\in [0,2\pi\rangle$. If we want to find the representative of the data on the unit circle, we must maximize the ...
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5answers
371 views

Finding the orientation of a noisy ellipse

This question comes from a neuroscience study which generates $12$ vectors. The vectors are evenly spaced, $30 n$ degrees for $n=0,\dots, 11$, each with their tail centered on the origin. I am ...
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0answers
24 views

Relationship between eigenvectors of correlation and covariance matrices

For the purpose of computing principal components of a dataset, represented as matrix $X$ of dimensions $n \times p$ with $n$ samples and $p$ features, we can compute sample covariance matrix $S$, and ...
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0answers
10 views

Understanding the bound given by Johnson–Lindenstrauss lemma

Here I choose to use the statement made by S.Dasgupta: For any $0<\epsilon<1$ and any integer $n$, let $k$ be a positive integer s.t. $$k \geq 4(\epsilon^2/2-\epsilon^3/3)^{-1} \ln n $$ Then ...
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0answers
12 views

Curve fitting: How to identify the appropriate function for a beat-like phenomena?

I have a time series data which shows some beat like behaviour. The envelope does not look exponentially decreasing, as it is impossible from a physics point of view. The envelope is likely to be a ...
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0answers
16 views

Getting a feel for the Normal-Inverse-Wishart conjugate prior to multivariate normal distribution

I am trying to get a feel for the Normal-Inverse-Wishart conjugate prior, which I have started to use, sparingly, in my work, where I am trying to cluster multivariate normal data. As Wikipedia ...
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0answers
30 views

Spectral relaxation of k-means clustering

I am working on a presentation on Spectral relaxation of k-means clustering (http://papers.nips.cc/paper/1992-spectral-relaxation-for-k-means-clustering.pdf) and I am a bit stuck. I understand ...
1
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1answer
57 views

Tropical geometry: practical applications?

In 1960, E. Wigner published a paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Theoretical mathematical structures pave the way to further advances and ...
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0answers
17 views

What is trend analysing

Hi I'm just started learning DFA for stochastic processes and I faced to the "trend".I've looked around the internet about trend analysing but still I don't understand it completely.can you define "...
1
vote
1answer
18 views

Alternatives to Shephard interpolation?

I am a chemist, so I have little experience in the field of math. My program is that I have a set of points (approx. 20000) in some larger dimensional space (like 10-20 dimensions), and I want to be ...
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2answers
30 views

How can I determine the best relationship for 3 variables, given several data points?

What is the best way to determine the relationship for three apparently related variables? The relationship does not appear to be linear, and may follow a combination of non-linear functions. I have ...
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0answers
12 views

likelihood function when data and model share a common parameter

I'm having some conceptual difficulty with how to describe, and deal with, a problem related to constructing a likelihood function that will be used to fit a model to data. Sorry in advance if I ...
1
vote
1answer
28 views

How to prove convergence of a sequence maximizing a sum of exponential distances?

I want to find the argument $x$ that maximizes $f(x)=\sum_i e^{-(x-d_i)^2/c}$ for some data values $d_i$ and an arbitrary positive constant $c$. I assume that $f(x)$ has only a single maximum (most ...
0
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0answers
32 views

Random walk in high dimensional space with stationarity

I have a vector of high dimension ( say 100). When I take a random walk ( i.e add a step value to each components of the vector, the step value being drawn randomly drawn from standard normal ...
0
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0answers
10 views

Minimal sufficient statistics for log-multiplicative/log-nonlinear models

I am interested in minimal sufficient statistics of Association models for variables for ordered categories developed by Goodman (http://doi.org/10.2307/2287833). In particular, consider an $I\times ...
0
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0answers
21 views

Number of clusters in $k$-means clustering for higher-dimensional data.

I've read the Wikipedia article and a lot of posts on stackexchange (like this really thorough one) on determining the number of clusters in a data set. Based on that, I am currently using the ...
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0answers
16 views

Calculate the difference of binary vectors

I have a matrix with 579 columns (points of data) and 138 rows (objects I am comparing). The points of data is binary - either it matches or it doesn't match. I am working under the assumption that ...
2
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1answer
33 views

Proving relations between square cosines

I am studying data analysis and especially PCA (principal component analysis) and reviewing the very course i took a few years ago, i found a result that seems interesting but there is no proof and i ...