Questions tagged [vector-fields]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3
votes
1answer
102 views

Expected value notation

I come across the notions $\mathrm{E}[wage]$ and $\mathrm{E}[wage_i]$. I would like to clarify if they have different meanings. Take the first expression. $\mathrm{E}[wage]$ could represent the ...
0
votes
0answers
76 views

Correlation 2D vector fields

Having multiple (hundreds) of 2D flow maps, ie vector fields how would one find statistical correlation between these? Plotting yields, for visualization purposes only: I am thinking about comparing ...
1
vote
1answer
167 views

How do I get the density of a region in a vector space?

I have a simple problem, which I think must have an easy solution. I have a vector space say with a 1000 dimensions for each vector. Now, I have a large number of sample vectors from this vector ...
1
vote
0answers
51 views

Extrapolating a 2D vector field in four dimensions

I'm not really sure how to explain this, but I've got several 2D vectors located at points in 4-space and I want to generate a continuous approximation(?) of this. My data looks like this: ...
0
votes
1answer
122 views

Variance of sum of random vectors - a proof

For nonrandom matrices $A(rXk)$,$ B(rXm)$, and $c(rX1)$, how does one show that $$\newcommand{\Var}{{\rm Var}}\newcommand{\Cov}{{\rm Cov}}\newcommand{\*}{{\times}} \Var(AX+BY+c)=A\Var(X)A′+ B \Var(...
0
votes
0answers
24 views

Spatio Temporal Interpolation of Vector Fields

I'm looking around for interpolation methods for vector fields, and RBFs seem to be a recommended approach. I've seen ALGLIB specifically mention that it is not suitable for spatio-temporal ...
4
votes
1answer
86 views

Vector with elements from a uniform distribution, to be made unit

I have a two dimensional constant vector $\mathbf{A} = \left < 2,1 \right>$. Also, I have a vector $\mathbf{e} = \left < \epsilon_x, \epsilon_y\right >$. Both $\epsilon_x$ and $\epsilon_y$ ...
3
votes
2answers
90 views

Intuition behind word vector representations

How is it possible for a vector space to represent words so that it is coincident to our intuition of words? What does the orthogonality concept in such a space mean precisely? I think we can present ...
-1
votes
1answer
91 views

Constructing feature vectors for clustering from row values

Thank you for some ideas regarding my question below. Background: I have an excel file with each row representing transactions (or transaction id's) in the format below and I am creating a feature ...
0
votes
1answer
162 views

Linear Regression feature transformation

One way of making linear regression applicable more widely is to use basis expansions, i.e., adding more features to the input set. Suppose that the data is described by a p-tuple, $(x_1 , x_2 , . . . ...
1
vote
0answers
116 views

Difference between Medoid and Centroid [duplicate]

For a certain dataset, I am finding the k closest points in my dataset to the centroid of the dataset. Are these k points the k medoids or are medoids something completely different. If so, is there ...
1
vote
0answers
66 views

Quantifying tendency of vector field to align

Not even sure this is the correct SE site to ask this, but here goes. If I have a random vector field, for simplicity I'll make it 2D and on a grid. I generate it by (python, since I'm not sure how ...
2
votes
2answers
728 views

Tests of significance for vector-valued distributions

I have a distribution that assigns 3 numbers to each data point instead of one scalar number. These numbers can be e.g. the weight of a person measured at 3 specific ages. (The distribution can of ...
1
vote
0answers
245 views

Parameter uncertainty in Least Squares fit to Vector Valued Function

Suppose I have to fit a vector field $\vec{y}_i$ with a vector valued function $\vec{f}_i = \vec{f}(\vec{x}_i; \vec{p})$, so both $\vec{y}_i, \vec{f}_i \in \mathbb{R}^m$, where $\vec{x}_i \in \mathbb{...
1
vote
1answer
304 views

Constructing N-dimensional vectors out of point distances

I was wondering if anyone had any insight or information on how one might go about determining point coordinates in an n-dimensional space from point pair distances. For example, say I start with a ...
0
votes
2answers
2k views

How to test if two sets of vectors are statistically different from each other

I have a set of 2-dimensional vector observations (like to wind vectors), and I have separated them into subsamples based on whether an event that is independent of the observations occurred or not. ...
2
votes
0answers
54 views

Changing the basis of random variables

Let $X_1$ and $X_2$ be two independent (1-dimensional) random variables and let $Y_1 = f^1(X_1, X_2)$ ($f^1$ is a deterministic function) be a (1-dimensional) random variable too. Question Does ...
-4
votes
1answer
579 views

How to define the covariance for a finite set of vectors in an inner product space space V? What object is it? [closed]

Motivation: This question is motivated by a type of problems in medical imaging and computer vision as follows: suppose we've a set $A$ of points ("shapes") $\{x_1, ...x_d\} $in a Riemannian ...
-2
votes
1answer
80 views

Merge column vectors from the loop in to a single matrix *.mat in matlab [Solved] [closed]

I have an iteration of my algorithm and it gives me a column vector as a result (1899x1 double). I want to form a new matrix composed of these column vectors together sequentially (for example, the ...
2
votes
2answers
111 views

Detecting a difference in the direction of two groups of vectors

I have two groups of patients, one group obese, one non-obese. I have vectors representing the longitudinal axis of the kidneys in each patient. I am comparing the orientation of the right kidneys ...
0
votes
0answers
32 views

How would I go about using regression to estimate a change in direction or movement in n-space?

I have a dependent variable which is a position in n-space (so a vector of length n). I want to use regression (or some other method if you have a suggestion) to determine whether independent ...
0
votes
0answers
53 views

A small help in understanding basic SVM

I am on the course of learning SVM. So, I am having a doubt. Suppose in the case of 2D, a point needs to be classified. So, let say I am having a point x(2,3). So according to the equation wx+b >= 1 ...
6
votes
2answers
1k views

Difference between Bag of words and Vector space model

I am searching for the intuitive difference between Bag-of-words and vector space model? Is there any relationship exists between bag-of-words and vector space model. I tried searching but couldn't ...
2
votes
3answers
82 views

What is the term for E[x*y']

I know this is probably a very simple question, but I recall learning that for 2 random vectors, x & y, with mean mx & my, E[(x-mx)(y-my)'] is the covariance & E[xy'] is the correlation ...
0
votes
0answers
584 views

Convert time scalar field to velocity vector field

I am trying to figure out if it's possible to create vector velocity field from some raster containing spatial distribution of scalar variable (timestamp of some mass-media event in my case). Here is ...
9
votes
2answers
140 views

Visually summarising a mess of directed line segments

I have a data set of millions of directed line segments. The line segments are sequential - it's a climatic variable (sensible heat), with observed and simulated values at half-hourly intervals. I'm ...