# 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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### High Dimensional Swiss Roll? (For Metric Learning/Dimensionality Reduction)

So I've just started a project which includes some metric learning, and came accross this swiss roll in 3D to 2D problem. Ideally, you should 'unroll' the roll. My question is, can this be extended ...
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### Splitting method for time series

Say I have a website with a lot of pages and traffic. Some of them are more visited, some of them a less. My task is to split pages into two groups for the given time period, so that the total traffic ...
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### How to Show Wasserstein Metric is Sum Invariant?

A paper I'm trying to understand states that that Wasserstein metric obeys certain properties, which I'd like to prove. This metric is defined for two random variables $U, V$ and $p \in (1, \infty)$ ...
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### Measuring the amount of total influence between variables?

I have a group of people with a series of yes/no questuins about preferences in various topics. The thing is they could see each other answers and change theirs hence might be influenced by a common ...
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### How to unsupervised-cluster of binary vectors?

I have a set of binary vectors of roughly 500 dimensions. For EDA purposes mainly, I'd like to cluster them, maybe hierarchically. What could be the right distance metric for my problem? Is the ...
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### Determine outliers for robust Mahalanobis distance

I want to apply a robust mahal distance and found an implementation in scikit: https://scikit-learn.org/stable/auto_examples/covariance/plot_mahalanobis_distances.html but there is the number of ...
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### Distance measure for two probability distribution of unequal sample size

Context: I have 100 stores and these stores are divided into 10 business markets. I want to select 3 markets where each market is a good representation of the 100 stores i.e. the population. There ...
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### Understanding the kdist graph used to select DBSCAN epsilon parameter

I need to use DBSCAN for my research and am having trouble understanding the kdist graph used to select the epsilon parameter - specifically, I do not understand what is happening behind the scenes ...
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### How to transform $P[k_1\leq (x_i-\mu - \sigma\cdot Z)^2 \leq k_2]$ to $P[k_1\leq \frac{(x_i-\mu)^2}{\sigma^2}+e \leq k_2]$?

Taste estimation As an example consider an experiment conducted to determine the optimal concentration of salt in popcorn. The concentration of salt in sample $i$ is denoted by ${x_i}$. The subject ...
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### Understanding PAM - why is it greedy?

I've been studying k-medoids for a while but i can't understand the first step or BUILD step: in particular i can't get how the initial medoids would be "greedy". I'm not much confident with the ...
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### How to measure the difference between two random forest models?

Suppose that I have training data defined as a set of N records (or samples) defined by its attributes (or descriptors, features, as you prefer), and I trained two random forest models with two parts ...
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### Mahalanobis distance - understanding the formula [duplicate]

I've read quite a few explanations on this topic, liking this one the most: https://mccormickml.com/2014/07/22/mahalanobis-distance/ But there is still one thing I don't understand. I understand ...
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### Is one-hot encoding and standardization of data equivalent to Gower's distance?

For clustering and other techniques for mixed data (numerical and categorical), Gower's distance is usually more preferred than Euclidean distance because the former computes distance differently for ...
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### Distance between two distributions

I am analyzing time-series data, and I would like to detect a significant change in data distribution. I already know about Bhattacharyya distance, but that requires histograms of equal-sized bins. ...
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### Calculation of relative distance

I have 100 term triplets as shown in the below mentioned figure. Each triplet contains 3 objects namely x, y and z. I want to rank the triplets according to the following two properties. y should be ...
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### The violation of triangle inequality in KNN

If the 0<p<1 in the distance metrics, then the triangle inequality is violated. The question as follows Does the violation of this inequality affect the ...
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### Distance metrics [closed]

I read about different distance metrics, such as Euclidean distance and so on. What are the machine learning algorithms that use distance metrics in their calculations?
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### How can I order kmeans clusters?

I have a kmeans cluster object and I would like to order the clusters. Not the observations within the clusters, rather the clusters in order of each other. Is there a way of doing this? I found ...
Assume that we want to compare the forecast quality of various forecasters $f$ on $n$ values such as stock-market prices or whatever. We could then define a "Mahalanobis-Distance" (MD) (or rather ...