# Questions tagged [distance]

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

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### How does the Bhattacharyya distance doesn't satisfy triangle inequality?

Googling doesn't seem to show many informative results. I don't know if the concept is too trivial that I should know immediately or it's an old topic. It's either article / blogs repeating the wiki ...
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### How to compare two pairwise dissimilarity matrices to see if one of them has higher values?

I'm looking for a way to compare two dissimilarity matrices each having pairwise dissimilarities between the same set of pairs but for different time steps (years in my case) to see if one of them has ...
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### Clustering method for Gower distances

I am having a mixed data type and I want to implement cluster my data set into 3 clusters. Because I have mixed data I have to compute gower distance as part of a distance matrix.Now that I have this ...
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### Measure for evaluating a density estimation procedure

Given an implementation of a multivariate density estimation scheme, what would be a suitable measure to evaluate the accuracy of the procedure? I am currently evaluating the procedure using three ...
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### Finding an appropriate formula to measure mutual information between pairs of observations, with K independent features

I am currently looking for some variant of mutual information, which I can use for the following setup: I have an N (subjects) x K (features) matrix: each column (feature) follows roughly N(0,1). (...
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### $\sqrt{2 KL(f || g)}$ interpretation?

I have seen in some papers that instead of using the Kullback-Leibler divergence $KL(f || g)$ between two probability density functions, $f$ and $g$, they use $$\sqrt{2 KL(f || g)}.$$ Is there any ...
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### Number of samples necessary to model pmf (up to some error)

Suppose I can sample outcomes from an unknown discrete probability distribution $P$ (the state space $\Omega$ is known). Let $Q$ be the distribution obtained by obtaining $s$ samples from $P$. Clearly ...
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### How to cluster points spatially using a maximum radius as a constraint?

I am building an app to optimize video packet sharing between users that are watching the same video stream at the same time. I do not want to have to guess the number of clusters up front because I ...
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### How to make a Bayesian adaptation of a null hypothesis test?

I am trying to make software to detect anomalies from our instruments. We have a pair of instruments that each measure the same quantity but in a different way. Both instruments report a probability ...
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### Reconciling cosine similarity between vectors and subsets of these vectors

I'm seeing something that I'm having a hard time reconciling in my head. Essentially, the cosine similarity between two vectors I have is very low, but cosine similarities of their subsets are very ...
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### Intuition on Wasserstein Distance

I've been trying to familiarize myself with the Wasserstein distance and saw this answer on StackExchange by @antike that at first made a lot of sense, but then it didn't (to me, of course). In the ...
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### Using Logistic regression in record linkage

I am curious as to how logistic regression handles string variables in a training matched data set I am aware many use Logistic regression to categorize data that includes the process of matching ...
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### Non-logarithmic approaches to compositional data

Background Compositional data ($x_i>0, \sum_i x_i=c$) are usually analyzed using some kind of log-transformation (alr/clr/ilr), to take into account naturally the fact that, in presence of the sum ...
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### Ranking items by the magnitude of their effect on dissimilarity?

[reposting with more detail, after previous question was removed due to lack of detail or clarity] I am working on getting a better understanding of my company's user base. We have distinct ...