Questions tagged [data-analysis]
The data-analysis tag has no usage guidance.
26
questions with no upvoted or accepted answers
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188
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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 ...
5
votes
0
answers
2k
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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 ...
4
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0
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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 ...
4
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0
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498
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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 ...
2
votes
1
answer
96
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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 ...
2
votes
0
answers
42
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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 ...
2
votes
0
answers
181
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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 ...
2
votes
0
answers
201
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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 ...
2
votes
0
answers
858
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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 ...
1
vote
0
answers
39
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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 ...
1
vote
0
answers
128
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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 ...
1
vote
0
answers
78
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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}, ...
1
vote
0
answers
91
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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 ...
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 ...
1
vote
0
answers
196
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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 ...
1
vote
0
answers
57
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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 ...
1
vote
0
answers
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 $\...
1
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0
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197
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Database of non-isomorphic trees
As there are several free prime number databases, is there something similar for non-isomorphic trees?
1
vote
0
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552
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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 ...
0
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0
answers
42
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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....
0
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0
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116
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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:
$$
\...
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0
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33
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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 ...
0
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0
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164
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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 ...
0
votes
0
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82
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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 ...
0
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203
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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:
$\|f\|^2_{H^{-1}}=\sum\limits_{k\in Z, k\neq 0}\dfrac{\hat{f}^2_k}{k^2}$, ...
-1
votes
1
answer
48
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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 ...