Questions tagged [vector-fields]
The vector-fields tag has no usage guidance.
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How to test the directionality trend and significance of a set of vectors?
I calculated a directionality map, where at each point (x,y) I have a jackknife sample (n=8) of 2d vector displacements $\vec{D}_k$ ($k=1,...,8$ are the black ...
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The moose must flow, but how?
Background
Suppose I collected a data set of the latitude and longitude of moose tracks within an irregular polygon, and also took a compass bearing of the direction that the hooves pointed in.
Image ...
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Quantify smoothness of vector field
I have different vectors field and I want to characterize their "smoothness" or tendency to align, or like their heterogeneity. Here are two examples, a relatively smooth vector field on the ...
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Is there a distance metric between ordered vectors?
I am looking for a distance metric between vectors whose elements are ordered,
i.e so the vectors:
[1,5,0,0,0,0,1], [1,0,4,0,0,1,0]
will be considered closer than
[1,5,0,0,0,0,1], [1,0,0,1,5,0,0]
for ...
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1
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Multivalued feature construction
I have a task of representing a users feature matrix to be input for statistical machine learning classifiers, i have features like gender , age etc but I also have a multivalue feature called as "...
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329
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Principle component analsysis of 3D vector fields
I have a data set consisting out of approximately 1000 3D vector fields. Each vector field is a collection of approx. 100 3D vectors in 3D space. So overall I have an array with dimensions (1000,100,6)...
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Calculation of Vector RMSE
I have 2 sets of 2-dimensional vectors, one from observations and one produced by a model. I would like to calculate a statistic similar to the RMSE for these. I believe the correct way of doing this ...
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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 ...
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1
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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 ...
- 1,345
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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:
...
- 111
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595
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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(...
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2
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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 ...
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1
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549
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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 ...
- 189
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2
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1k
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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 , . . . ...
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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 ...
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152
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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 ...
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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 ...
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333
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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{...
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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 ...
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2
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4k
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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. ...
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91
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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 ...
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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 ...
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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
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2
answers
475
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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 ...
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0
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108
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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 ...
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57
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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 ...
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2
answers
2k
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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 ...
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3
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115
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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
...
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798
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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 ...
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2
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172
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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 ...
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