Questions tagged [data-analysis]
The data-analysis tag has no usage guidance.
65 questions
37
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5
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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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21
votes
5
answers
4k
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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 ...
- 44.7k
14
votes
4
answers
762
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:...
- 1,466
11
votes
3
answers
2k
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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 ...
- 7,853
8
votes
2
answers
895
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Can you do geometry with persistent homology?
Setup
In practice, persistent homology of data $X$ is often used to infer the homology of the underlying (Riemannian) manifold $M$ that the data is sampled from.
However most filtrations (Vietoris, ...
- 159
8
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1
answer
1k
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Transitioning from pure mathematics to applied mathematics/machine learning
I recently completed a doctorate in pure mathematics. While in the program, I decided that research was not my ultimate goal/calling. Applied mathematics and machine learning seemed to grab my ...
7
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3
answers
57k
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Correlation between 3 variables
For correlation measurement betweeen 2 variables, I use Pearson formula.
What formula can use to find degree of correlation between 3 variables ? My variabes are not symmetric: The correlation in ...
- 195
6
votes
1
answer
344
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 ...
- 640
5
votes
2
answers
371
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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 ...
- 1,229
5
votes
1
answer
2k
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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 ...
- 4,952
5
votes
2
answers
2k
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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 ...
- 481
5
votes
0
answers
189
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 ...
- 640
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 ...
- 151
4
votes
1
answer
2k
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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. ...
- 49
4
votes
1
answer
277
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-%...
- 41
4
votes
0
answers
440
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 ...
- 2,152
4
votes
0
answers
502
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 ...
- 729
3
votes
1
answer
731
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 ...
3
votes
1
answer
201
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 ...
- 4,058
3
votes
1
answer
292
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?
3
votes
2
answers
150
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,...
- 119
3
votes
1
answer
66
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 ...
- 13.2k
2
votes
1
answer
475
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 ...
- 24.8k
2
votes
1
answer
185
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 ...
- 437
2
votes
1
answer
135
views
Compact objects in persistence modules and interval decomposition
$\newcommand\Mod{\mathrm{Mod}}\DeclareMathOperator\Fun{Fun}$If $k$ is a field, a persistent $k$-module is a functor $\mathbb{R}\to \Mod_k$ where $\mathbb{R}$ is a poset under the natural ordering of $\...
- 213
2
votes
1
answer
117
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 ...
- 167
2
votes
1
answer
134
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 \...
- 1,731
2
votes
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 ...
- 23
2
votes
0
answers
117
views
Error in discrete FFT
I am interested in taking an FFT of an image which is periodic in space (does not decay) across a finite window of size $L\times L$. The image has triangular symmetry; for simplicity one could imagine ...
- 21
2
votes
1
answer
146
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 ...
- 29
2
votes
0
answers
53
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 ...
- 61
2
votes
0
answers
197
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 ...
- 640
2
votes
1
answer
591
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 ...
- 21
2
votes
0
answers
209
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 ...
- 481
2
votes
0
answers
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 ...
- 481
1
vote
2
answers
1k
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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 ...
- 508
1
vote
2
answers
3k
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 ...
- 223
1
vote
1
answer
60
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. ...
1
vote
1
answer
139
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....
- 2,246
1
vote
1
answer
129
views
Morlet wavelet transform of binary dataset in R
I want to perform a Morlet Wavelet transform analysis (WTA) on a sequence of binary data (0, 1), length about 19000 observations. The result seems reasonable, but I have my doubts whether WTA can be ...
1
vote
1
answer
227
views
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 ...
- 159
1
vote
1
answer
191
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.
- 4,058
1
vote
0
answers
100
views
PageRank in directed graphs: equivalence of iterative and eigenvalue methods
Given a directed graph $ G $ with $ n $ nodes, we can represent this graph using an adjacency matrix $ A $. The stochastic matrix $ S $ can be derived from the adjacency matrix using the following ...
- 4,058
1
vote
0
answers
52
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 ...
- 101
1
vote
0
answers
70
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 ...
- 11
1
vote
0
answers
137
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 ...
- 111
1
vote
1
answer
49
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 ...
- 11
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}, ...
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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
52
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 ...
- 11