The distance tag has no wiki summary.
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Distance Metrics For Binary Vectors
I have vectors of same length consisting of 1 and 0. I am trying to find out how similar they are. So far I am using hamming distance that I calculate sum of one vector then sum of second vector and ...
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0answers
29 views
Hilbert curves: bounds / probabilities of preserving neighbors
Hilbert Curves (Wikipedia) are space-filling curves said to "fairly well preserve locality".
Do you know any theoretical results here, such as bounds that neighbors within a radius of $\varepsilon$ ...
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9 views
association of data problem (multitarget tracking)
I have sensors, and each of them after applying filtering created me a list of objects. I want to do the fusion, and firstly have to perform a proper association to know which objects from various ...
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1answer
90 views
Finding a known number of circle centers that maximize the number of points within a fixed distance
I have a set of 2-D data where I want to find the centers of a specified number of centers of circles ($N$) that maximize the total number of points within a specified distance ($R$).
e.g. I have ...
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2answers
54 views
Non-distance metrics in hierarchical clustering? [closed]
What happens, intuitively, when one uses non-distance metrics to calculate the distance matrix that feeds into a standard hierarchical clustering algorithm?
What mistakes will the algorithm make and ...
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1answer
47 views
What is the optimal distance function for individuals when attributes are nominal?
I do not know which distance function between individuals to use in case of nominal attributes.
I was reading some textbook and they suggest Simple Matching function but some books suggest that I ...
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0answers
35 views
geographic distance and mahalanobis distance
I am trying to match individuals based on monthly consumption and geographic consumption in a dense metro area. Essentially I want to create treatment and control pairs with the having both geo ...
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36 views
Measuring distance between geographic coordinates among other variables
I am setting up a quasi-experimental design and I need to compare each treatment account to all potential control accounts within a certain geographic region. I would like measure the distance ...
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2answers
247 views
How to find the expected distance between two uniformly distributed points?
If I were to define the coordinates $(X_{1},Y_{1})$ and $(X_{2},Y_{2})$ where
$$X_{1},X_{2} \sim \text{Unif}(0,30)\text{ and }Y_{1},Y_{2} \sim \text{Unif}(0,40).$$
How would I find the expected ...
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0answers
75 views
How to make results using Hellinger distance comparable with Euclidean distance outputs?
I have a two kinds of data for the same geographic region. One is presence-absence data of species (for amphibians, reptiles and birds) and the other has several environmental variables for the same ...
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1answer
236 views
Bhattacharyya distance for histograms
One of the ways to measure the similarity of two discrete probability distributions is the Bhattacharyya distance.
In computer vision, for example, it is used to evaluate the degree of similarity ...
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1answer
218 views
Why use the Mahalanobis distance
I understand in theory why the Mahalanobis distance is a good measure for mutlivariate outlier detection. However, everything I tend to read warns against calculating the inverse/pseudoinverse of a ...
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109 views
Multidimensional scaling on distance or similarity matrix
Why doesn't the scatter plot change when I perform multidimensional scaling on distance or similarity matrix?
This figure uses similarity matrix
And this figure use distance matrix ...
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1answer
74 views
How to calculate the HHG (Heller Heller Gorfine) distance in R
In looking at this question and investigating some recent developments in measuring correlation, I came across the HHG (Heller Heller Gorfine) test. Heller et al. promote it as superior to the ...
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1answer
119 views
How to convert a dendrogram back into a distance matrix?
Example code:
our_dist <- dist(USArrests[1:4,])
dend <- as.dendrogram(hclust(our_dist , "ave"))
plot(dend )
I would now wish to have a "dend2dist" function ...
3
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1answer
84 views
How is the distance formula related to the formula for standard deviation
The formula for the standard deviation of n numbers is the same as the formula for the distance between two points in n dimensions. Could someone explain why this is and how these are related?
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1answer
47 views
Finding an appropriate distance/divergence/similarity measure in a real 2D phase space
At first, I have to excuse my sloppy terminology, as I am pretty new to the whole topic.
Imagine a real twodimensional phase space representing climate-related properties. I have a set of N variables ...
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1answer
164 views
KL divergence or similar “distance” metric between two multivariate distributions
I have a large dataset composed of many samples; each sample is as follows:
imagine a grid indexed by i,j
for a sample k, I have Y_k, where Y_k(i,j) is the probability density for k at (i,j)
of ...
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0answers
20 views
Multidimensional d prime
If you have a one dimensional space, like you have one variable, and two sets of observations, and want a measure of separation between the two sets of observations you can calculate a d prime like
...
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1answer
122 views
What are the use cases related to cluster analysis of different distance metrics?
I'm trying to use different distance metrics like Euclidean, Manhattan, cosine, chebyshev among other distance metrics in my k-means algorithm to calculate distances between the data points and the ...
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1answer
185 views
Does Mahalanobis distances have “significance” associated with them?
I have a "distance matrix". let's say a 6x6 distance matrix, each cell is the Mahalanobis distance of two "clusters" (or sets/groups of things in a multidimensional space),
I want to "count" the ...
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0answers
153 views
Statistical distance of arbitrary multivariate distributions
What meaningful statistical distance measure can be used for computing in a meaningful way a distance between two arbitrary multivariate probability distributions? I am interested in doing this ...
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1answer
95 views
Cluster analysis with skewed distibutions
For my master's thesis I would like to use different clustering algorithms to cluster municipalities (as objects) in regard to their land-use characteristics (as variables).
Analyzing my data ...
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2answers
109 views
kNN search using distance fitted to a training set of similar pairs
I want to perform k-nearest neighbor search in multidimensional space but not using for example L2 distance but I want user to specify some "similar" pairs-examples and then perform search using this ...
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0answers
26 views
The product distribution: how fast does dissimilarity increase as a function of number of samples?
If $\mathcal{D}$ is a distribution, let $\mathcal{D}^n$ denote the $n$-fold Cartesian product of $\mathcal{D}$. In other words, $\mathcal{D}^n$ is the distribution of $n$-tuples $(x_1,\dots,x_n)$ ...
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1answer
250 views
Mahalanobis distance on singular data
I have an issue which I could not solve, although I tried and I got some help on R help forums too.
I am trying to calculate Mahalanobis distances on a data frame, where I have several hundreds of ...
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2answers
87 views
Is concept of similarity objective?
Imagine following example:
We have two pairs of points (i.e. 4 objects in some space) and two similarity measures.
According to first similarity measure, objects from first pair are more similar then ...
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83 views
Joint distribution of two distances
Suppose there are three points in 3D space, each with coordinates $A_i=(X_i,Y_i,Z_i)\leadsto \mathcal{N}(\mu_i,\tau^2\mathbb{I}_3)$. We compute the distance between the three points, e.g. $D_{ij} = ...
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0answers
35 views
How to find nearest neurons to neuron-winner on hexagonal topology map [closed]
I have self-organization map (SOM) with hexagonal nodes. Which algorithm and metrics can I use for finding nearest neurons to BMU?
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66 views
KL distance in R
I am trying to compute the KL-distance between two columns in a data-frame. Whats the best way to implement this?
I have seen FNN and FLEXMIX packages and their examples, but it is implemented for ...
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2answers
300 views
Can the covariance matrix in Mahalanobis distance definition be zero?
The statistical distance or Mahalanobis distance between two points $x = (x_1,\dots,x_p)'$ and $y = (y_1,\dots,y_p)'$ in the $p$-dimensional space $\mathbb R^p$ is defined as $$d(x, y) = \sqrt{ (x-y)' ...
2
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1answer
761 views
Converting similarity matrix to (euclidean) distance matrix
In Random forest algorithm, Breiman (author) constructs similarity matrix as follows:
Send all learning examples down each tree in the forest
If two examples land in the same leaf increment ...
4
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1answer
297 views
What is the distance between a finite Gaussian mixture and a Gaussian?
Suppose I have a mixture of finitely many Gaussians with known weights, means, and standard deviations. The means are not equal. The mean and standard deviation of the mixture can be calculated, of ...
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2answers
166 views
(hierarchical) cluster analysis with non-standard distance
My question is triggered by a question that was asked on stackoverflow: http://stackoverflow.com/questions/12198115/using-different-metric-for-hclust-linkage.
The thing is this:
I can formulate an ...
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1answer
3k views
How to calculate Mahalanobis distance in SPSS for an exploratory factor analysis?
I have a question regarding data screening for an exploratory factor analysis (EFA).
I am conducting an EFA to identify the factor structure of 20 questions that I created on the topic of ...
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2answers
168 views
Specifying the number of clusters in nearest neighbor clustering
I've got a distance matrix between examples. I want to cluster them into m clusters with a nearest neighbor algorithm which works like this:
...
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0answers
122 views
Can the Mantel test be extended to asymmetric matrices?
The Mantel test is usually applied to symmetric distance/difference matrices. As far as I understand, an assumption of the test is that the measure used to define differences must be at least a ...
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0answers
91 views
$\chi^2$ distance and multivariate gaussian distribution
I want to know how to write the $\chi^{2}$ distance between two multivariate Gaussian distributions $f$ and $g$ in terms of their parameters only. The parameters of $f$ is the vector $\mu_{1}$ and a ...
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0answers
106 views
Comparing model fit with heteroscedastic data
I am developing a physiological test using R that requires some parameters optimised. In comparing the new method against the existing method, the values of individual readings correlate in a linear ...
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7answers
1k views
How to perform k-means clustering with only a distance function, not euclidean points?
I want to perform k-means clusteirng on some objects I have, but the objects aren't described by "points". However, I am able to compute the distance between any two objects (it is based on a ...
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3answers
728 views
Pairwise Mahalanobis distance in R
I'm trying to calculate a Mahalanobis-type pairwise distance matrix in R. I have 33 individuals, each with 10 variables. The idea is to get a distance matrix D, where
...
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0answers
298 views
Distance threshold for clustering
Usually online clustering methods (based on kmeans or not) define a distance threshold value. If a new data-point $x$ is far enough from the nearest center $c$ (i.e. the distance from $x$ to $c$ is ...
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0answers
149 views
AIC with Mantel's tests
Mantel's tests are commonly used to compare genetic distances (say, between a number of individuals) with true or hypothesized landscape distances between those same individuals. For example, “does ...
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1answer
256 views
Distance between two points with covariance
I would like to find the distance between two points locaion1 and location2.
In 2D, location1 is represented by a Gaussian distribution with mean m1 and co-variance matrix P1. Similarly location2 is ...
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3answers
719 views
Using a cosine similarity does not work for any dataset
I have a clustering algorithm, where if I use an euclidian distance as similarity, it works well on any dataset. If I replace it by a cosine similarity (see my code bellow), it will give a degenerate ...
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0answers
363 views
How to compare two distance matrices?
Suppose that I have two distance matrices for the same set of items.
By a distance matrix I mean a square matrix whose (i,j)th entry holds the distance (in terms of cosine similarity) between ith and ...
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2answers
417 views
When is brownian covariance less appropriate than linear covariance?
I've just been introduced (vaguely) to brownian/distance covariance. It seems particularly useful in many non-linear situations, when testing for dependence. But it doesn't seem to be used very often, ...
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102 views
Use of autoregressive metric for ARIMA clustering and analysis
I wonder if anyone has put into use the autoregressive metric for ARIMA clustering proposed by Corduas and Piccolo (2008).
The authors define the distance autoregressive metric between two processes ...
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3answers
539 views
How to measure distance for features with different scales?
I'm reading the book "Collective Intelligence" and in one chapter they introduce how to measure similarity between users on a movie review website with euclidean distance.
Now are the movies rated ...
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2answers
695 views
Probability that uniformly random points in a rectangle have Euclidean distance less than a given threshold
Assume we have $n$ points in a rectangular with bound $[0,a] \times [0,b]$, and these points are uniformly distributed in this plane. (I am not quite familiar with statistics, so I don't know the ...
