# Questions tagged [data-analysis]

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1 vote
162 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 ...
1 vote
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 ...
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 ...
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 ...
1 vote
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 ...
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 ...
1 vote
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 ...
1 vote
61 views

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 ...
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 ...
1 vote
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 ...
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 ...
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 ...
1 vote
123 views

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....
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?
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 ...
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 ...
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. ...
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: $\|f\|^2_{H^{-1}}=\sum\limits_{k\in Z, k\neq 0}\dfrac{\hat{f}^2_k}{k^2}$, ...
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:...
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 ...
1 vote
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 ...
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 ...
130 views

1 vote
178 views

### Database of non-isomorphic trees

As there are several free prime number databases, is there something similar for non-isomorphic trees?
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 ...
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 ...
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 ...
1 vote
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 ...
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 ...
1 vote
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 ...
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 ...
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 ...
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 ...
### 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 ...