# Questions tagged [distance-functions]

Distance functions refer to functions used for quantifying the notion of distance between members of a set, or between objects.

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### Differences between Bhattacharyya distance and Jensen–Shannon divergence

Based on Wikipedia, both the Bhattacharyya distance and Jensen–Shannon divergence are a method of measuring the similarity between two probability distributions. But now curious about - how are they ...
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### Wasserstein distance between multivariate lognormal distributions

Wikipedia gives the following formula for normal distributions: What changes, if any, do I need to make to handle multivariate lognormal distributions instead?
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### Different distance matrixes result in the same clustering

I am using: the cluster::pam function in R for clustering distance matrix computed using Gower distance in cluster::daisy in R The issue I am having is that I run pam 2 times, with a different ...
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### Dynamic Time Warping: Why does a Sakoe-Chiba band take much more time to calculate than no window?

I'm using dynamic time warping to calculate a distance matrix for a set of about 25 multivariate time series. Each individual time series has over 1000 timestamps, and they are all the same length. ...
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1 vote
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### What are the moments of the Beckmann distribution?

Let $U=(u_1, u_2)$ and $V=(v_1, v_2)$ be two randomly distributed points on the Euclidean plane assuming bivariate normal distributions $U \sim N(\mu_u, \Sigma_u)$ and $V \sim N(\mu_v, \Sigma_v)$ with ...
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### difference between sets of ordered categorical variables

I have two sets (S1, S2) of answers to a typical survey question with ordered categorical (discrete) answers (“strongly disagree”, “disagree”, … ,” strongly agree”). I need to test whether I should ...
1 vote
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### What is the correct expression of the Hellinger Distance equation?

I am aware there are various ways to calculate the Hellinger Distance (H) depending on the context and data. One of these ways, as I understand, is via the Bhattacharyya coefficient (BC). For discrete ...
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### How to find the 'distance' between two populations?

I am somewhat new to these concepts, so please bear with me. I have two datasets: Data set A is collected by monitoring the network data of a device when it is ...
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### A distance function between music playlists

I am looking for a way to measure the dissimilarity/distance $d$ between a set of music playlists $\{P_i\}$ with possibly different number of songs. We may assume that a playlist contains a specific ...
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### Why is the covariance matrix inverted in the definition of the Mahalanobis distance? [duplicate]

I'm on my first course on data science, and I encountered the Mahalanobis distance for the first time. It was mentioned that intuitively, what it does is that it corrects for the fact that some ...
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### How to test the similarity between two labelled datasets?

I have two different functions with I can draw labelled data $(x, y)$ from, where $x$ is multi-dimensional, and $y$ is a real number value. There exist a $y$ value for any possible $x$ in the input ...
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### Is the expected distance of two random variables a Metric?

This is purely for more understanding and not an assignment. I understand the definition of a metric https://en.wikipedia.org/wiki/Metric_(mathematics). I also understand that the following is a ...
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1 vote
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### Is Jaccard similarity/distance suitable for non-binary, quantitative data?

I have a dataset with each row a country and 10 columns with numerical features like GDP,Electrcity consumption, GNI etc. I am trying to use distance metrics to find similarity between the countries ...
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### Creating a covariance matrix from a distance matrix—normalizing matrix with infinity

I'm trying to simulate spatially autocorrelated data by creating a covariance matrix from a distance matrix and using said covariance matrix as the $\Sigma$ parameter of a multivariate normal. I have ...
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### Dissimilarity or distance metrics between pairs of values

I have cubes (objects) in which their volume was manually calculated (let's call this method the "manual method". Assume that the volume measures obtained by this method are considered the "true" ...
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### Am I right that Calinski-Harabasz index (Pseudo-F) can not be calculated from a distance matrix other than euclidean?

Part: I wonder if one could calculate the Calinski-Harabasz index when only having a distance matrix (and a cluster solution, of course). As you need the within and between sum of squares to come up ...
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### Does Mahalanabis Distance have something to do with Min-Max normalisation? [duplicate]

Does Mahalanabis Distance have something to do with Min-Max normalisation? I know that it has something to do with Z-score normalisation, but when I tried Mahalanabis Distance on the Min-max ...
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