Questions tagged [data-analysis]

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Invariants ("checksums", "hash") for collection of integers

The sum of a collection of integers doesn't depend on the order of the integers and can detect the corruption of one element of the collection (but multiple elements can get corrupted without their ...
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1 vote
0 answers
34 views

Find Kullback-Leibler distance between two densities [closed]

can someone help me with this exercise? (look at the image). How can I find Kullback-Leibler distance between this two densitie? I have no idea how to arrive at the solution. Every suggestion is ...
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-2 votes
1 answer
199 views

Can the same dataset be described as Chaotic & Pareto/ Power law distribution?

I'm trying to abstract the mathematical part of the problem as much as possible before the details follow, There's this dynamic data set that's $O(2^{32})$, a recent result described it as a power-law ...
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4 votes
0 answers
259 views

Persistent homotopy groups

Everybody in algebraic topology loves homology and cohomology, but sometimes we like homotopy groups also, since they detect different things (think about spheres) . An interesting and recent ...
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1 vote
0 answers
68 views

Implementation of Mellin transform of exponential decay

I'm trying to understand this paper: 10.1016/j.jmr.2010.05.015. It is about using a Mellin transform of curves that contain multiple exponential decays of varying contributions (CPMG data from Nuclear ...
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  • 111
-1 votes
1 answer
32 views

Linear operator over a simplex space in a multinomial distribution parameter estimation problem

This is actually a variant of a well-known problem of how the parameters of a multinomial distribution can be estimated by maximum likelihood, and this arises from a final year project I undertook ...
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1 vote
1 answer
33 views

Represent multivariate data [closed]

I am not sure if this is the best place for my question. Please delete if it is not, but I would really appreciate some suggestions. I want to graphically represent multivariate data. I have 7 ...
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1 vote
0 answers
61 views

Bayesian inference of stochastically evolving model parameters

I have a question related to self-calibration in radio interferometry, but I will try to phrase it as generic as possible. I have a set of data points, $D = \{ d_{0, t_0}, d_{1, t_0}, ..., d_{M, t_0}, ...
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2 answers
1k views

What is the uncertainty on the (Pearson) correlation coefficient?

Do you know what is the uncertainty on the Pearson correlation coefficient as a function of the uncertainty on the measurement in the data set. I know of an expression giving the uncertainty related ...
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4 votes
2 answers
247 views

Is there an upper bound on the number of points in point cloud for which we compute the persistent homology?

I am interested in the topic of persistent homology (topological data analysis). According to what I read, there is some roadblock in the analysis of "big data" using persistent homology as it is ...
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3 votes
1 answer
191 views

Advantage of fractional Fourier transform over multiscale wavelet

What is the best argument of fractional Fourier transform over multiscale wavelet in data analysis purpose. Optimization of the good time-frequency domain parameter ? "Good" will be, find the %time-%...
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1 answer
166 views

What subjects of Fourier analysis have had more effect on machine learning? [closed]

What is the salient uses of Fourier analysis in machine learning? What subjects of Fourier analysis have had more effect on machine learning? Please mention the references.
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Condition on the point cloud matrix making the points "generic" in the uniform sense

For a matrix $X\in\mathbb{R}^{d\times n}$, what condition can I impose on $X$ to make the collection of its columns generic in the sense that they look like the result of uniformly sampling a convex ...
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2 votes
0 answers
147 views

Discrete Morse theory, choice of Morse function, and removing noise

If I have a simplicial complex, and a discrete Morse function defined on the simplices, I can use persistent homology to produce a barcode which helps me distinguish "persistent" shape from noise. To ...
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  • 466
1 vote
1 answer
57 views

Performing Statistical Analysis on a Data Set With a lot of Null Responses

I am currently trying to perform some statistical analysis on some data to see if there is any meaningful conclusion for a research project I am working on; however, I have come across a problem. ...
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6 votes
1 answer
284 views

Approximate homology of a large simplicial complex

I can use software to calculate the Betti numbers $\beta_0,\beta_1,\beta_2,\dots$ of a finite simplicial complex. This is prohibitive for large complexes, built on say > 100,000 nodes. Is there some ...
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  • 466
1 vote
0 answers
90 views

What is intuitive perception of $T_{\alpha_1} \circ T_{\alpha_2} \circ ... \circ T_{\alpha_M} $ in graph domain?

if $G(V,E,W)$ be a weighted graph and $\vert V \vert =N $. for any vertex $i \in \lbrace 1,2,...,,N \rbrace $ define a generalized translation operator $T_i:\mathbb{R}^N \to \mathbb{R}^N $via ...
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3 votes
1 answer
190 views

Why do we consider some weakening frames like K-frames, frame sequences, and upper semi-frames?

I have found some applications of the Frame Theory in engineering sciences like signal processing, image processing, data compression, sampling theory, optics, filter-banks, signal detection. As we ...
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3 votes
2 answers
143 views

Checking $f(x_1,y_1)f(x_2,y_2)-f(x_1,y_2)f(x_2,y_1) \ge 0$

I am working in data science and I have to deal with the following problem for which I would like to find a simplification: We call a function almost positive if $f(x_1,y_1)f(x_2,y_2)-f(x_1,y_2)f(x_2,...
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0 votes
0 answers
152 views

What functions can one try employing to fit an apparently doubly-periodic real function over $[0,1]$?

I have a cosine-like data curve over $x \in [0,1]$ that I can rather well-fit by a function of the form $a \cos{2 \pi x} +b$. Although good, the fit is still lacking, in that the residuals from the ...
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2 votes
1 answer
150 views

On the entries of a matrix representation for a boundary operator of a persistence module

In equation 6 of Computing Persistent Homology (page 8), the authors put forward the following identity: $$\deg \hat{e_i}+\deg M_k (i,j)=\deg e_j$$ Where $\hat{e_i}$ and $e_j$ are elements of ...
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1 vote
0 answers
39 views

Calculating the density of data points around a specified point in a k-dimensional space [closed]

I am looking for a way of calculating how close data points are to a specified point in a k-dimensional space. My current method involves pythag to calulate the distance between the specified point ...
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2 votes
1 answer
442 views

Latent Dirichlet allocation - math words digest ?

Latent Dirichlet allocation - is quite a popular topic in data-mining. Wikepedia mentions thousands citations in few years. Question 0 Can one give some digest for a math minded person of the key ...
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5 votes
0 answers
182 views

Gaussian curvature/Euler characteristic of Facebook clusters

If I look at a connected subgraph on a small collection of actors (such as a small cluster) in the Facebook social network, and I find that 1) The Euler characteristic of the clique complex built on ...
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  • 466
1 vote
1 answer
123 views

Two theorems about incoherence

These are two theorems I have heard being referred to in "folklore" but I cant find the proofs for these in any compressed sensing or high-dimensional probability reviews (like, https://www.math.uci....
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3 votes
1 answer
228 views

Topology data analysis - faster algorithm

The Topology Data Analysis uses the Mapper algorithm, but computational complexity is not good. Is there an alternative algorithm for algorithm Mapper? Is there an algorithm that works faster?
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2 votes
1 answer
84 views

Quantifying an increasing spacing between data points

Is there a measure or statistic that could quantify a steady increase in the spacing between data points in a time series? For instance, in the figure, the points are clustered and dense near 0, but ...
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0 answers
71 views

Euclidean or Minkowski Metric for Clustering Spatio-Temporal Data?

Question: when does using Minkowski metric $\quad\sqrt{x^2+y^2+z^2-t^2}\quad $for clustering $(x,y,z,t)$ data yield better results than using Euclidean metric $\quad\sqrt{x^2+y^2+z^2+t^2}\ $? I ...
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4 votes
1 answer
1k views

How to measure distribution of high-dimensional data

I have to methods of projecting random samples in $\mathbb{R}^n$ onto a manifold defined by $C(q)=0$, which is a lower-dimensional subset. Now, samples in $\mathbb{R}^n$ are uniformly distributed. ...
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0 votes
0 answers
161 views

Negative Sobolev norm of non-zero mean non-periodic function on bounded space

The usual formulation of $H^{-1}$ norm for a zero-mean periodic function on some domain $\Omega\in\mathbb{R}$ is as follows: $\|f\|^2_{H^{-1}}=\sum\limits_{k\in Z, k\neq 0}\dfrac{\hat{f}^2_k}{k^2}$, ...
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12 votes
3 answers
567 views

Category of data sets, motivated by persistent homology?

Is there a useful or agreed-upon category of data sets? In particular, I'm thinking about a point cloud and wondering what an acceptable morphism between point clouds "should" be. Edit/Clarification:...
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3 votes
1 answer
59 views

Are Optimal Tours Sensitive to Clusters?

Background of this question is that I had been asked for advice in clustering a very big set ($10^6$ to $10^8$) set of points in Euclidean 3D-space; these points in turn lie on 2D manifolds. I ...
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1 vote
0 answers
43 views

How to define a harmonic coordinates on data graph?

Suppose I knew the Ricci curvature at some point of the Manifold along several directions (the number of directions should be much more than the dimension of the manifold). Can I decompose the Ricci ...
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5 votes
1 answer
1k views

t-Stochastic Neighbor Embedding vs Topological Data Analysis

The shortest form of this question is: How much TDA can be done with tSNE? Specifically, I'm referring to the application of TDA to clustering data, so, think along the lines of Ayasdi's ...
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2 votes
1 answer
130 views

Solution of the k-means problem in a simple case

Consider the setup of the $k$-means problem and assume that the data points are confined to $k$ balls of radius $\varepsilon$ while the pairwise distances between the centers of the balls are $> 2 \...
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5 votes
0 answers
1k views

Find the axis of symmetry in a point cloud

I have some dataset which describes a spherical cloud of points in 4D space. Actually, the coordinates of the points are the coefficients of unit quaternions, so you get the idea on what the data is ...
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1 vote
0 answers
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Quantification of the extent of periodicity in a time series using fractal analyses

I need metrics to quantify and compare the extent of periodicity between any two given time series, considering the time series were "almost periodic". By "almost periodic" I mean: if I were to take ...
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1 vote
0 answers
54 views

Open volumetric time series data set

Does anyone know where I can find a good open volumetric time series data set? I had a look at some of Stanford's open data sets (https://graphics.stanford.edu/data/voldata/ ) But these do not seem ...
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1 vote
0 answers
101 views

An exact fraction of a matrix

Let $A$ be a $n \times m$ real matrix with $n<<m$ and of rank $r<n$. It is known that $A$ has exactly two distinct non-zero singular values: $\sigma_{\max}$ and $\sigma_{2}$, and also that $\...
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1 vote
0 answers
178 views

Database of non-isomorphic trees

As there are several free prime number databases, is there something similar for non-isomorphic trees?
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4 votes
0 answers
484 views

Implications of a recent result on Benford's law

I want to the discuss the implications of a theorem by J. Morrow (2010) regarding Benford's law. There are many papers written about Benford's law with a comprenhensive discussion of the advantages ...
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36 votes
5 answers
6k views

Inference using Topological Data Analysis: Is it worth it for a regular statistician to learn TDA?

After having read Gunnar Carlsson's Topology and Data I feel enthusiastic to use some topological data analysis (TDA) methods in my current research, mostly in social sciences. We often handle huge ...
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20 votes
4 answers
3k views

Easier reference for material like Diaconis's "Group representations in probability and statistics"

I'm teaching a class on the representation theory of finite groups at the advanced undergrad level. One of the things I'd like to talk about, or possibly have a student do any independent project on ...
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1 vote
2 answers
1k views

Appropriate histogram comparison distance measure

I am working with hyperspectral image data in R, so I have subset an image to a region of 5000 pixels, each containing a vector 254 bands in length. I would like to cluster this data in order to try ...
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2 votes
1 answer
563 views

correlation for three variables? [closed]

suppose we have three variables here, x,y, z now, what we know is that the correlation between x and z is 0.6, the correlation between y and z is 0.65. Here is the question, is there any formula to ...
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1 vote
2 answers
938 views

Interpolating a "manifold" between two points

Edit: I have reworded the question. This may be a basic question but I am having trouble figuring out the correct answer. I want to find a local coordinate chart that fits a d-dimensional ...
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11 votes
3 answers
2k views

Higher categories as data structures

Still wading through higher category theory. I find the subject a bit intimidating, not so much for technical reasons, but because I lack sufficient intuition as to the motivation(s)/heuristics one ...
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2 votes
0 answers
186 views

isomap and self intersections

I sample a 2D surface in $\mathbb{R}^3$ with $N$ points, and compute an isomap using pairwise weighted geodesic distances. I am thus able to embed this surface into a $M$ dimensional space in which ...
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5 votes
2 answers
2k views

Solving for Moore Penrose pseudo inverse

I have a system to solve, set up as : $$Ax = b$$ with a square rank deficient matrix $A$. The paper suggests to use a Moore Penrose pseudo inverse, which in my case can be computed using the ...
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  • 461
2 votes
1 answer
708 views

name for $\underset{x}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n |x_i - x|$

Given a real-valued data set $ x_1, \dots, x_n $, what do you call the quantity $$\underset{x}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n |x_i - x|$$ This seems like a pretty basic ...
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