Questions tagged [distance]

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

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17 views

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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27 views

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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14 views

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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50 views

$\sqrt{2 KL(f || g)}$ 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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30 views

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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18 views

About the validity of an expansion result

Suppose I have an expansion result: $sup_{p\in P,x\in X}|G_N(p,x)-g_N(p,x)|=O_p(a_N)$. Suppose now I have some (nonparametric) estimator for $p$ denoted by $\widehat{p}=\widehat{p}(x)\in P$ for any $x\...
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26 views

KNeighborsClassifier Score with a precomputed user defined distance matrix

I am trying to implement a KNN from SKLEARN using an user defined distance matrix. I want to know which n_neighbors is giving the minimum error for my dataset. So, to avoid long calculation for ...
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8 views

Distance formula from known reference coordinates X, Y, and Z to the centroid of measured coordinates xi, yi and zi using standard deviations

A device with 1932, 1cm-outer diameter (OD) oil-filled markers embedded in seven parallel flat plastic plates, with marker spacing of 25 mm × 25 mm in-plane and 55 mm through-plane is imaged in an MRI ...
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31 views

Why is it wrong to apply k-means to a distance matrix?

There are several threads discussing clustering analysis of a distance matrix and they dismiss use of the k-means algorithm. Here are two examples: Perform K-means (or its close kin) clustering with ...
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Finding the "center" of many GMMs

Suppose I'm given many GMMs. All have $K$ components. My goal is to find a GMM with $K$ components that can best represent the given GMMs. It is like finding the center of many points but a point here ...
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27 views

Distance Measures between Prior and Posterior

Suppose that I want to measure the distance between a discrete posterior distribution $p(x|Data)$ and each discrete prior distribution $p(x)$. When I have full analytical knowledge of both the ...
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Which NMDS axes should I plot?

I have been running some non-metric multidimensional scaling analysis on a bray-curtis dissimilarity matrix (using ecodist::distance()). Theory suggests that we ...
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194 views

If the curse of dimensionality exists, how does embedding search work?

The curse of dimensionality tells us if the dimension is high, the distance metric will stop working, i.e., everyone will be close to everyone. However, many machine learning retrieval systems rely on ...
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dbRDA and variance partitioning with time series

I'm trying to carry outa distance-based RDA (dbRDA) on some data which comes from repetitive biotic (table of abundances) and abiotic measurements at a single location (i.e. a multivariate time serie)....
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Is the Bray-Curtis dissimilarity/similarity independent of richness/diversity?

I was told about potential issues with the Bray-Curtis dissimilarity/similarity measure. Specifically, I have been asked if Bray-Curtis is independent of richness/diversity. I am unsure how to answer ...
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Distance between stochastic processes controlled by power spectral density

Let $f_1$ and $f_2$ be two stochastic processes over the same domain with finite power spectral densities (PSDs) $S_1$ and $S_2$ respectively. Can I bound a distance between $f_1$ and $f_2$ based on ...
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What distance measure should be used to cluster (A - B) where A and B are correlation matrices?

I have 2 conditions with $m$ variables: Treatment = $X_A$ Reference = $X_B$ I've calculated the pairwise correlation of each condition to have 2 $m x m$ correlation matrices I'm calling: Treatment ...
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104 views

Interpretation of upper bound on the Wasserstein Distance

I am trying to interpret the 2-Wasserstein distance and the upper bound on it. Let's say I have 2-Wasserstein distance between two distributions to be $x$, and I have an upper bound on it which gives ...
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1answer
40 views

Distance of a covariance matrix from a perfect 1:1 relationship

I have a number of estimated variance-covariance matrices, and I would like to know how different these are from a perfect 1:1 relationship. To be specific: They are (genetic) variance-covariances ...
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What is the correct distance metric for hour?

I want to cluster points using time and spatial coordinates. My time dimension is only containing hour of day. In order to have a correct representation of time I transform my hour using ...
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14 views

Correlation-based distance dissimilarity measure is not a metric

Show by an example that the correlation-based distance $d(X,X^\prime)=1-\rho(X,X^\prime)=1-\frac{\sum_{j=1}^p (X_j-\bar{X})((X_j^\prime-\bar{X}^\prime)}{\sqrt(\sum_{j=1}^p (X_j-\bar{X})^2\sum_{j=1}^p (...
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18 views

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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40 views

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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116 views

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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10 views

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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1answer
80 views

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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25 views

About $D(F,G)=\int(F(x)-G(x))^2w(x)dx$ and $D(F,G)=\int(F(x)-G(x))^2w(x)dF(x)$

I learned that statistical distance between two 1-dim distributions F and G $D_E(F,G)=\int(F(x)-G(x))^2dx$ is famous. But what about $D(F,G)=\int(F(x)-G(x))^2w(x)dx$ or $D(F,G)=\int(F(x)-G(x))^2w(x)dF(...
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What is the name of $D(F,G)=\int(F(x)-G(x))^2dF(x)$?

Is there a statistical distance between two 1-dim distribution F and G that $D(F,G)=\int(F(x)-G(x))^2dF(x)$? Or to symmetrize it, take $D^s(F,G)=\int(F(x)-G(x))^2dF(x)+dG(x)$ If not, why? (What are ...
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93 views

Is it sensible to do PCA on a distance matrix?

I have 10x10 distance matrix where the distance metrics is (1 - overlap coefficient). I want to represent the observations in this matrix in a low dimensional space to see how observations relate to ...
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27 views

Significance testing for Jensen–Shannon divergence?

The Jensen-Shannon divergence (JSD) measures the (dis)similarity between multiple probability distributions. How can one determine whether the JSD of (a pair of, or multiple) distributions is ...
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1answer
280 views

KL divergence for joint probability distributions?

I have a pair of joint probability distributions. I want to measure their similarity/dissimilarity. If they were single-dimensional probability distributions, then I could measure the Kullback–Leibler ...
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Significance test for comparing two mean Euclidean distances?

First time poster here, so please let me know if more details are needed! In short, I'm analyzing a dataset that has scores from 98 siblings from 64 families. So some families contributed only one ...
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1answer
36 views

Expected distance to nearest neighbour: Why integral of survivor function? (instead of derivative)

Previously, I asked the question how to calculate the expected distance to the nearest neighbor molecule in 3-dimensional space. This question was fully answered, which is I ask this related question ...
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Composed pair-wise similarity measure

I'm dealing with a graph theory problem for which I have calculated a series of pair-wise similarity measures (several criteria such as ancestrality, co-occurrence, sentence similarity, etc.) between ...
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29 views

Best way to evaluate ranking when one only has pairwise distances?

Let's say I have a strict ranked set of samples. I only have a similarity measure $s$. I want to evaluate how good this similarity measure is at ranking the examples. One approach would be to use a ...
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8 views

Patch wise feature vector comparison

I have a image of size of 64*64. I am trying to compute HOG features for the image. I have skimage for my implementation, with the following parameters: ...
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Distance measure for hierarchical nominal data

I have categorical data which follow a hierarchical structure (in fact they're medical codes). For instance: C10: Diabetes Mellitus E00: Senile dementia E10: Schizophrenia E2B1: Chronic Depression G20:...
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Dice Distance returning nan. Workaround?

Starting Point: I want to calculate the distances between nominal data. Furthermore, I want to see what difference it makes to only use important features (given some feature selection method). So I ...
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26 views

Quantifying if two datasets are from the same distribution, if I only have distances

Let's say that I have two datasets. The target dataset is 1K instances, the "predicted" dataset is 1M instances (but I could downsample). I can compute the distance between instances. How do ...
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89 views

Mantel test alternatives: linear mixed models, with row and column ids of distance matrices as random effects?

Summary: I want to model in R the relationships between pairwise spatial distances, pairwise temporal distances, and pairwise Jaccard distances, with the goal of predicting the Jaccard distance ...
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37 views

Distance to uniform distribution for continuous probability distributions [closed]

I need to quantify the distance of a continuous probability distribution $f(x)$ to the uniform distribution on $x \in (-\infty, +\infty)$. Do you know any distance functions that could help here? For ...
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What are the pros and cons of using mahalanobis distance instead of propensity scores in matching

I learned about this option of using mahalanobis distance instead of PS to do matching from the matchit() function in R. It seems a more nonparametric approach. Could you state its pros and cons and ...
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41 views

Clustering with booleans and continuous data; Gower's coefficient + PAM?

I have a medical dataset with both boolean variables and continuous variables (e.g. age/BMI). I know that clustering with K-means won't work due to the mixed datatypes. I read that I can use the Gower'...
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370 views

Calculate similarity between two matrices

I have two matrices, $A$ and $B$, each of size $n\times m$, where $n$ is discrete time points, and $m$ are the variables measured (specifically, $n$ are dates and $m$ are investments measured in ...
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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 ...
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20 views

Measuring the overlap between two probability distribution [duplicate]

I have many probability distributions, I need to compute the amount of overlap between two probability distributions. I don't know the type of distribution since it really depends on the data itself. ...
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Hausdorff Distance with Manhattan Distance

I'm applying Hausdorff Distance to understand if two datasets are representing the same subset of the space of a particular problem. The point is that I've read the Hausdorff distance computes the ...

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