Questions tagged [data-analysis]

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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 ...
apg's user avatar
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5 votes
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2k 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 ...
noncom's user avatar
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4 votes
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355 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 ...
Andrea Marino's user avatar
4 votes
0 answers
498 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 ...
Mauricio Tec's user avatar
2 votes
1 answer
96 views

PCA-like method for filtering known variances

Principal Component Analysis is used to reduced the dimensions of atmospheric pressure grids (lat X long X time) into their most important modes of behaviour (e.g, the North Atlantic Oscillation is ...
Will Rust's user avatar
2 votes
0 answers
42 views

Robustness of largest singular vectors with respect to noise

I would like to find a result that shows that the largest right-singular vectors of a data matrix are in some sense robust with respect to low-variance noise perturbations. Specifically, let $X = U D ...
foobar_98's user avatar
2 votes
0 answers
181 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 ...
apg's user avatar
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2 votes
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201 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 ...
WhitAngl's user avatar
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2 votes
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858 views

Classical Multidimensional Scaling

Hi, I am doing an MDS with a distance matrix coming from geodesic distances between points X on a 3d mesh (ie., not euclidean distances), and try to find points Y in euclidean space which best ...
WhitAngl's user avatar
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1 vote
0 answers
39 views

Multidimensional scaling with partially known distance matrix

As far as I know, multidimensional scaling requires a matrix of pairwise distances between the data points to be available. What if I only have distances between some pairs of points, but not all of ...
user3749105's user avatar
1 vote
0 answers
128 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 ...
K.Cl's user avatar
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1 vote
0 answers
78 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}, ...
Sketos's user avatar
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1 vote
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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 ...
niloofar jamshidi's user avatar
1 vote
0 answers
48 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 ...
IHitSquirrel's user avatar
1 vote
0 answers
196 views

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 ...
np20's user avatar
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1 vote
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57 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 ...
sav's user avatar
  • 191
1 vote
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108 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 $\...
Felix Goldberg's user avatar
1 vote
0 answers
197 views

Database of non-isomorphic trees

As there are several free prime number databases, is there something similar for non-isomorphic trees?
Ian Gleason's user avatar
1 vote
0 answers
552 views

Cluster-preserving and distance-maximizing embedding into Hamming Space?

I have a set of data, each instance in the real $[0,1]^{d}$. However, it's actually all in a relatively small range around 0.5, clustered into classes in even smaller ranges. The actual origin of the ...
DoubleJay's user avatar
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42 views

Persistent diagrams for images : existing implementations or packages?

I am interest to compute the persistent diagram associated to the image of a persistent module as in ''Persistent Homology for Kernels, Images, and Cokernels'' : https://epubs.siam.org/doi/epdf/10....
BabaUtah's user avatar
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116 views

Can you explain to me how to decompose this persistence module and why?

I am learning topological data analysis on my own. I am currently basically watching This course. But there this thing in the course note that I didn't understand. So for this persistence module: $$ \...
egrr's user avatar
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0 answers
33 views

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 ...
Min Wu's user avatar
  • 461
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0 answers
164 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 ...
Paul B. Slater's user avatar
0 votes
0 answers
82 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 ...
Manfred Weis's user avatar
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0 votes
0 answers
203 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: $\|f\|^2_{H^{-1}}=\sum\limits_{k\in Z, k\neq 0}\dfrac{\hat{f}^2_k}{k^2}$, ...
mystupid_acct's user avatar
-1 votes
1 answer
48 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 ...
Hephaes's user avatar