Questions tagged [distance]

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

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31 views

How to tell if a set of MCMC chains mixed?

Let's say I have a Bayesian network with both numeric and categorical variables. I run several MCMC chains to collect samples from the distribution. Now, if the chains are "similar enough" after some ...
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23 views

Difference between PCA and Mahalanobis? [closed]

PCA uses the directions of the data with the highest variance and omits those with lower. Next, it constructs a new space with the eigenvectors of these directions. Mahalanobis uses the covariances ...
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How is the mahalanobis distance like the euclidean distance? [duplicate]

Let's say $\vec{x}$ is an $n$ dimensional observation, $\vec{\mu}$ the $n$ dimensional mean of the sample that $\vec{x}$ is from and $\Sigma$ the $n \times n$ covariance matrix of that sample. Then ...
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15 views

Distance metric for sequential spatial data (routes navigated in 2d space)

I'm looking for a distance metric to compute how close certain paths taken by people navigating throughout a city are to a set of 'correct' routes. I have path recordings for some 'correct' routes ...
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25 views

L1 distance between categorical distribution and any arbitrary estimator?

Given an unknown categorical distribution $p$ over $k$ categories, and any arbitrary estimator of this distribution vector $q$ constructed from $n$ i.i.d samples, can anyone point me to some results ...
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distance metric for student course schedules

I'm doing an exploratory clustering analysis of student course schedules at a college. Interpretability by humans is paramount: we're trying to inform future research questions and possibly ...
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40 views

What's the distribution of the closest point from uniform samples?

Suppose you have $N$ values $x_1, \ldots, x_N$ that are uniformly sampled in $[0; 1]$. For a random $x_k$ amongst the $(x_i)_i$ (with equiprobability), what is the expected value of the distance ...
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Wasserstein distance / EMD of two sets of 2D weighted points?

I am trying to implement a 2D version of the EMD/Wasserstein Distance to measure the distance of sets of 2D weighted points. Let $A = \{a_{1}, a_{2}, ..., a_{m}\}$, be a weighted point set such that $...
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Calculate Distance between two vectors and estimate goodness of fit to preestablished histogram shapes

I have a squared gene co-expression correlation matrix of many thousands of pairwise correlations among variables (10290^2 aprox). Each row/column represents a different gene and its pairwise ...
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Compare statistical distances of multiple distributions

I need a metric that not only gives me the statistical distance between two distributions, but that also is comparable to another distance between two completely different distributions, calculated ...
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Can Bhattacharyya coefficient (or distance) be used as an additive measure to compute a metric for performance?

As far as I understand, Bhattacharyya's measure(s) can be used to see similarity between two empirical distributions. Other ways to do so are nicely explained here: Similarity measure between multiple ...
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Learning distance metric from output of knn

Consider a set $\mathcal X$ of points $\{x_1,\dots,x_n,x_{n+1},\dots,x_{n+m} \}\subset \mathbb R^p$. Let $A$ be some $p\times p$ matrix, unknown to you. Consider the set $$\mathcal X_A:=\{y_1,\dots,y_{...
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Distance between objects with different attributes meaningful?

Let's say you have two sets of apples and you assign some attributes to them like color, size...
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Difference between standardizing variables and using Mahalanobis distance

I am wondering how and/or why the Mahalanobis distance is different from using the Euclidean distance on standardized variables?
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How does one apply hierarchical agglomerative clustering when multiple positions are equidistant (non-unique distance matrix)?

I have been following this single/minimum -linkage example to better understand hierarchical agglomerative clustering. I noticed that the entries of d_ij are unique ...
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Is it correct to use “Ward.D2” 's method of R's hclust function with a Gower distance matrix? [duplicate]

I have mixed type variables (3 quantitative and 3 qualitative) and I calculated Gower's dissimilarity distance between my objects. I wanted to do a hierarchical clustering with hclust, but I am not ...
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28 views

Something like Mahalanobis distance when the copula is not Gaussian

Mahalanobis distance accounts for different variances of the marginal variables and correlations between the marginal variables. However, there is an implicit (maybe explicit) assumption that ...
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Distribution $f$ that minimizes $JSD(f||q) + JSD(f||p)$

What can we say about the distribution $f^*$ that is the solution to the following optimization problem: $$\min_f JSD(f||p)+JSD(f||q) ,$$ where $p,q$ are given distributions over some set, and $JSD$ ...
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Comparing which histogram has overall low cost

Let's say there are two histograms which basically is constructed from array of numbers which is measured by, repeatedly performing a task by two different methods and individual numbers are time ...
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535 views

Why is Kullback-Leilbler divergence a better metric for measuring distance between two probability distributions than squared error? [duplicate]

I know that KL-divergence is a metric that is more suitable when we want to measure the distance between numbers which a probability form. However, I am still confused what is the benefit of using KL-...
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Relation Between Wasserstein Distance and Relative Entropy

Consider the Wasserstein metric of order one $W_1$ (aka the Earth Movers Distance). I would like to know whether it is possible to link $W_1$ and relative entropy and what this would mean intuitively. ...
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Distance correlation and a corresponding mapping

I have two long vectors, say X and Y (of equal length). I computed the Distance Correlation as implemented in Scipy and I got a ...
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33 views

Signature of a distribution - Earth Mover distance

I am studying the Earth Mover Distance from here, but I have some difficulty in fully understanding what is the signature of a distribution and how it matches with the last constraint of the Earth ...
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35 views

Total variation norm

I am reading Dwork, C., Hardt, M., Pitassi, T., Reingold, O., & Zemel, R. (2012, January). Fairness through awareness. In Proceedings of the 3rd innovations in theoretical computer science ...
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24 views

estimate equal distribution of few points on a line

I am trying to find the best solution to estimate equal distribution of points over a line. I know I can use relative SD or similar, but I was wondering if there are more "specific" methods that can ...
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How can I analyse simmilarities/differences of one nominal variable of two different groups?

I have two different samples. I want to measure how similar is each individual of the first group with the second group in terms of Var 1 (nominal not ordered), given that they are both categorized ...
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Scoring the difference between a family of distributions and a test distribution

Let's suppose we have a random model that I can sample to generate distributions of a certain 1D variable. I want to score the distance of a test distribution to the model in question. The distance ...
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58 views

Difference between Euclidean ,Pearson, Geodesic and Mahalanobis distance metrics

Given a set of samples $X$. We are tasked to find an appropriate distance metric for $X$ from the given options which are Euclidean Pearson Geodesic and Mahalanobis distance metrics. To solve this, ...
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11 views

Metric learning with respect to an outcome

Suppose I have $n$ datapoints in $p$-dimensional space, and the $p$ variables are highly heterogenous. That is, there is no natural way to combine them. Some are ordinal, some one-hot, some continuous,...
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23 views

What is the specific normalization chi2 in seqdist?

In the documentation for the seqdist() function it is noted that there is "...a specific normalization for"CHI2" and "EUCLID". See the Details section." (p.60). But in the details section there is no ...
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Advantages of Wasserstein barycenters

Which are the advantages of using Wasserstein distance when averaging many probability distribution estimates? How does uncertainty of each affects the computation of the barycenter? Does the ...
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Is there a difference between Hausdorff Distance and Discrete Frechet Distance when working on time series?

I'm currently doing a little research on which kind of distance metric is the best for comparing the time-series I'm working with. To be clear, I'm doing this for a computer science internship, and I ...
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Proxy for Mahalanobis distance when n < p? [duplicate]

I'm working on a ranking problem where I want to measure the distance between a collection of query points (as a group) and each target point in my database. Each query point is part of the set of ...
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Distance / Metric between two regression models? [closed]

I wonder if there is any theory or work about the "similarity" of two regression models. For example, if it is linear regression, the "similarity" could be defined by the l-2 distance between the ...
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Distribution of distance between positions

I have N = 3 billion ordered positions, as in a genome that has 3 billion base pairs. I have R = 3 million, as in 3 million SNPs (Single Nucleotide Polymorphisms) that are (close to) randomly ...
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Distance based Spatial sampling

I am struggling with spatial sampling of data which has Latitude & Longitude for data points. I need to do sampling such that no adjacent or nearby point should get selected ( Need to give some ...
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29 views

Is euclidean distance in pca rotated and scaled when $n < p$ the same for all observations?

I am trying to come up with an appropriate measure of the 'distance to the normal mean' in high dimensional space and I came up with a strange result, and I need some theoretical background to ...
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43 views

How can K-Means clustering work without spatial information?

Just got stuck at working with K-means clustering. I have looked up this python/skimage commands: ...
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Manipulation of asymptotic bounds for distance between estimators

Suppose I know some asymptotic bounds: $$\mathbb{E}(|D(a,\hat{a})|) \lesssim O(n^{-1/2}),$$ where $D$ is some distance between probability measures, and $a$ is a probability measure while $\hat{a}$ ...
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Distance between point process realizations

Is there a valid distance metric for measuring how similar are the realisations of two point processes? E.g. let's say we simulate two histories $ h_1, h_2 $ in the time interval $ [0, T] $ for two ...
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66 views

Dot Product and Distance Matrix

If we want to calculate the squared distance between 2 vectors, $x$ and $y$, we use the dot product: $$||x-y||^2 = (x-y)(x-y)^T = xx^T - 2xy + yy^T$$ The question is, how to generalize this concept ...
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Inferences about leverage score and Mahalanobis distance [duplicate]

I have some inference given below: Given the design matrix $\textbf{X}$, the leverage score is defined as $\textbf{H}_{ii}$ where $\textbf{H} = \textbf{X} (\textbf{X}^T \textbf{X})^{-1} \textbf{X}^T$ ...
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247 views

Hierarchical clustering dendrogram on a distance matrix

When computing hierarchical clustering over a data matrix, a dissimilarity matrix is first computed in order to build the tree (dendrogram). For example: ...
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226 views

Explaining the difference between Pearson correlation and distance correlation

This question and its answer might highlight my naivete regarding Brownian/distance correlation. I'm using the difference between a matrix of distance correlations, as calculated by ...
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135 views

Gower Distance and PAM algorithm with Random Forest for Variable Selection

I am currently working with cluster analysis and am trying to create clusters based on the important variables. My data consists of both categorical and continuous variables thus I have used the ...
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1answer
206 views

What is Intraclass Distance?

For an assignment I have to compute the intra-class distance and use it as an objective function to select features. This is for the MNIST dataset. While I have a fairly good handle on other aspects ...
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R daisy - Gower distance, different values with different number of observations [duplicate]

I have a mixed data set where I want to compute distances between observations with Gower in R (daisy function). When I compute distances between different number of observations, the distances seem ...
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115 views

How is Student's t-distribution related with this similarity/probability equation between data points?

In the t-SNE paper "Visualizing Data using t-SNE" and a Deep Embedded Clustering (DEC) approach "Unsupervised Deep Embedding for Clustering Analysis", they both use the Student t-distribution to ...
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Similarity between observations and an ideal trend

I have a series of well known data showing, for example, the average weight by age in Europe. Let's say yesterday I called a lot of people and I asked for their age and weight. The data coming from ...
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295 views

For calculating the distance between different points, does it make sense to use all Principal Components?

I have a data frame with about 500 observations and 8 variables that I'd like to run through PCA in order to try and reduce the number of variables to only those with the most variance. From here, I ...