# Questions tagged [distance]

Measure of distance between distributions or variables, such as Euclidean distance between points in n-space.

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### 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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### 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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### 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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### 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 (sqrt(1-...
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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### Is there any way to define a distance metric given a Hidden Markov Model?

Let's say I've gotten a HMM that describes user search strings for my e-commerce website. Let's also say that I've just received a search string from a customer that doesn't have any search results. ...
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### 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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### 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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### 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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### 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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### Mahalanobis Distance on Singular Data

I have an issue which I could not solve, although I tried and I got some help on R forum. I am trying to calculate Mahalanobis ...
158 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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### 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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### 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 ...
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### Mahalanobis distance for vector-classification

B"H Hello, Assume I have a very large set of vectors ($X_i$) over some feature space ($F_i$), each vector is labeled as either $+1$ or $-1$. For convenience lets refer to this set as "the history ...
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### Gower's (dis)similarity index

I would like to ask a question about Gower similarity/dissimilarity index. Is it ok to use the Gower dissimilarity measure with Ward linkage clustering? I was reading that the Gower similarity index ...
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### Distance metric and curse of dimensions

Some where I read a note that if you have many parameters $(x_1, x_2, \ldots, x_n)$ and you try to find a "similarity metric" between these vectors, you may have a "curse of dimensioality". I believe ...
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### Link between variance and pairwise distances within a variable

Please, prove that if we have two variables (equal sample size) $X$ and $Y$ and the variance in $X$ is greater than in $Y$, then the sum of squared differences (i.e., squared Euclidean distances) ...
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### Can I use log-likelihood distance on data of only continuous variables?

I have to run a SPSS two-step cluster analysis. All my 4 variables are continuous scalar standardized parameters (with normal distribution). The dataset includes 10,000 cases. SPSS suggest to use ...
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### Simple distance measure for financial time series

I have a large quantity of financial trading systems that I believe are highly duplicative, meaning that I believe a large number of the trading systems are essentially the same thing. I am looking ...
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### Clustering with some cluster centers fixed/known

Thanks for reading my question. I have several thousand data points scattered on an (x,y) grid that I am trying to cluster. The data points are not uniformly distributed across the grid, but are ...