Questions tagged [distance]

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

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Intuition behind log in kl distance

So, let's start stating that I already read both Why KL-Divergence uses "ln" in its formula? and What is the role of the logarithm in Shannon's entropy?. However, I still have no ...
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Euclidean distance between points in PCA space along different principal component dimensions

I've picked up this project half way through, and I'm working through the last guy's code, so please bear with me. So the original data consists of 500+ points in 150 dimensions, and I want to ...
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Decomposing Distance Matrix D for approximating Original Matrix A

Let's say we have a matrix $A \in R^{n \times d}$ where n is the number of elements and d is the dimension size. And we calculate the pairwise distances between each elements; say cosine for instance ...
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Sorting samples from distribution before calculating the distance [duplicate]

I have to evaluate different methods for distribution fitting. So, given an sample set A I get a fitting distribution B or I might get another sample set C that is much like A. Now I need to do a ...
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Computing distance and standarization of features

Intro: suppose we have $n$ observations with $m$ features, represented by a $n\times m$-matrix $X$, and two specific points $x,y\in\mathbb{R}^m$, and we are interested in distances between $X$ and $x,...
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similarity metric for two characteristics

I am trying to develop a way to compare items. Each item has the same two properties associated with it, say, $p_{1}$ and $p_{2}$. All I am given are these two measures for each item, each of which ...
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What metric is best fitted for comparing encodings?

I am trying to compare two distributions, that each correspond to different numerical encodings, e.g. compare fp32 encodings to various other encodings on a same set of values. However I do not know ...
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Cluster confidence scoring

I have a scenario where I am provided a list of clusters and pairwise distance only between items in same cluster. I need to rank these clusters based on some kind of relative score from this info. e....
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Generalize Kendall tau distance to ordered groups?

If we have two ordered lists, e.g., A=[1,2,3,4,5], B=[3,5,4,2,1], then we could use Kendall tau distance (which is 0.8) to ...
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Finding a Size Invariant Pattern in Noisy Data

I want to find similar patterns in my data, I assume that the patterns will be of different sizes both in time and in amplitude. The usual distance metrics will not work here, since the window size is ...
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How to choose a fair gamma value when performing k-prototypes clustering?

In the k-prototypes clustering algorithm, the distance function consists of two dissimilarity components - one for the numerical elements of the observations, and one for their categorical elements. ...
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How to infer nearest neighbors using distance metrics

My team and I are trying to identify group of customers to target for an investment promotion exercise. We decided to use the control group (which already are a part of this investment exercise) and ...
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What is the maximum number of dimensions in MDS?

If I have an arbitrary Euclidean distance matrix $D=(d_{ij}:i=1,\ldots,I; j=1,\ldots,I)$ and I want to reconstruct its elements (pairwise Euclidean distances) via classical Euclidean MDS. That is find ...
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Distance metric that is robust to collinearity

I'm trying to find a distance metric that takes into account the correlation between vectors. That is, suppose we have matrix $M$ of dimensions $n \times k$, and we take the pairwise distance between ...
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Are the distances on a hierarchical clustering dendrogram in the same units as the input distance matrix?

I use Aitchison distance as the input to a hierarchical clustering dendrogram. I started labeling and interpreting the dendrogram but wasn't sure about a few aspects: Are the vertical distances on ...
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Which distance to assess equality between discrete distributions?

I have approximated a discrete distribution via Monte Carlo in two different ways, which metric would you use to check the distance between the two distributions? I want to use it to diagnostic ...
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Convergence in distribution and convergence in Kolmogorov distance

Let $X, Y$ be two random variables with laws $F$ and $G$ respectively. The Kolmogorov distance between these two laws is defined as: $$ d_{Kol}(F, G) = \sup_{x \in \mathbb R} |\mathbb P(X \leq x) - \...
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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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Similarity and distance measures from Presence-Absence data

I am doing some ecological analysis with presence-absence count data. I am interested in similarity and distance measures that have the form using the standard notion of: $$ \begin{array}{c|cc|c} &...
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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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using Jensen-Shannon Divergence for more than two data sets as a distance metric

I know that Jensen-Shannon Divergence for two distribution is symmetric. Is it possible to use JSD as a distance? In other words, is there a version of JSD that satisfies all the requirements for ...
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Asymptotic value of an integral related to distances in a unit n-ball

In trying to find out the pdf of the range $T$ of euclidean distances of $m$ randomly and uniformly chosen points from the origin in an $n$-dimensional unit ball, I have obtained the following : $$...
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Distance measures for row ordering of a sparse heatmap with discrete row data

I have a list of protein indexes. Each protein can be either (i) a feature component F in a feature group G (in which case the index is included in the list) or (ii) a background component B (in ...
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Best distance measure for cluster analysis of time series data with a circular variable

I'm doing hierarchical clustering on a set of time series (say 21 time series of 400 time points), however the variable I want to cluster is a circular variable, i.e. a directional vector between 0 ...
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Distance between data in two dimensions with different units

I have data in two dimensions, one is a count and one is a distance from a mean value. I'd like to calculate a distance, but I'm not sure I can calculate a simple Euclidean distance when the ...
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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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Selecting "Statistical Distances" for "Fuzzy Match"

I am trying to better understand how to select "statistical distances" for "fuzzy matching". To illustrate my problem, consider the following two datasets (I created this using the ...
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Preference of Probabilistic or Non-Probabilistic distance?

Suppose that we have a posterior density $p(w|x)$ and a prior $p(w)$ and I want to measure the information gained from the data. I can measure that information gain in two different ways: A non ...
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Scale Invariant Statistical Distances

Problem Suppose we have empirical distributions to two $n$-dimensional random variables $X = (X_1, X_2, ..., X_n)$ and $Y = (Y_1, Y_2, ..., Y_n)$. The goal is to find $k < n$ components, such that ...
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Distance between hazard functions? [closed]

Let $F$ and $G$ two cumulative distribution functions with support on $(0,\infty)$. I know of many distances between distributions: Total Variation, Wasserstein, Hellinger, Kullback Liebler (...
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What to consider when choosing between f-divergence measures? (e.g.: kl-divergence, chi-square divergence, etc.)

I have some baseline population, and I have a non random sample from that population. For both the population and the sample I have observation of some measure (for simplicity, let's say age). I would ...
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Dissimilarity only between different treatments in dataset

I am studying the impact of wildfires on vegetation species composition. I have surveyed the burnt and unburnt areas on six sites which burned at different points in time from which I now have species ...
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Distance measure for ordinal data (multiple measures)

I have collected user ratings for 4 different ordinal variables. Variable A has (likert) scale from 1-7 but can be collapsed to 1-3, Variables B, C, D have (likert) scale from 1-4. For each item, x (a ...
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2 votes
1 answer
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Obtain a between-class similarity. And is the way to do it through PCA valid?

Context: I have a dataset containing instances labeled into different classes, and for all the classes, I have the same set of features. My research question is to identify classes that are more ...
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Can I measure the Mahalanobis distance of observations in a dataset to the mean of another dataset?

I am trying to measure the "disruption" of different observations a dataset using several variables at the same time. However, this cannot work with a traditional Mahalanobis distance to the ...
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A "multidimensional d" to include uncertainty in distance matrices

We're all familiar with Cohen's d, difference between means divided by pooled standard deviation. Is it valid to incorporate the concept to create a "deviation adjusted distance matrix"? ...
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PCA or Drop high correlated variables for clustering

I am performing clustering on mixed data type. I have few features which are high correlated. We generally use PCA before clustering and reduce the feature space, as its a mixed data I have used FAMD ...
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Distance between two categorical distributions

I want to test whether two (empirical) categorical distributions taking on $K$ possible values (e.g. 5, with no innate underlying ordering) with associated (empirical) probabilities $p_k$ are the same....
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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 [closed]

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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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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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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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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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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