Questions tagged [distance]

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

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Shannon entropy and Gini impurity are interchangeable in practice yet different?

Gini impurity, not to be confused with the Gini coefficient, is also an information theoretic measure and corresponds to Tsallis Entropy with deformation coefficient $q=2$, which in physics is ...
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Does Wasserstein distance require the source and target distributions to have the same mass?

If we minimize the Wasserstein loss, $$W_1 (P_S, P_T) = \underset{\gamma \in \Pi}{\text{min }} \sum_{x,y} |x-y|\gamma(x,y)$$ which means we are looking for the coupling that minimizes the cost $\gamma(...
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How to compute Gower distance manually?

Consider the following tuples: a = {1, 0, 13, apple} b = {1, 1, NA, pear} c = {0, 1, 12, apple} The first two elements for each observation are binary, the third ...
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Can any distance be expressed by the product scalar or inner scalar? [duplicate]

I know that a distance could be expressed by inner scalars or scalar products. Is this true for all metrics (i.e., respecting the three axioms: the identity of indiscernible, symmetry, triangle ...
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If entropy is the underlying measure for KL-divergence, what is the underlying measure for the Wasserstein distance?

If entropy is the basis measure underlying KL-divergence (aka relative entropy), what is the basis measure underlying the Wasserstein distance?
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Best way to compare time series data similiarity

I have two time series'. One represents ground truth heart rate in a a subject (top in blue), and the other a prediction of heart rate using a novel method (bottom in orange). It looks like this: ...
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Properties of Sinkhorn distance

I am reading the paper by Cuturi http://www.marcocuturi.net/Papers/cuturi13sinkhorn.pdf and I am curious about the properties of Sinkhorn distance and wondering what properties of the Sinkhorn ...
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What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance?

What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance, and how to know which one to use?
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What are the advantages of Wasserstein distance compared to Jensen-Shannon divergence?

What is the practical difference between Wasserstein metric and Jensen-Shannon divergence? Wasserstein metric is also referred to as Earth mover's distance. From Wikipedia: Wasserstein metric is a ...
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Brier score: $L_1$ instead of $L_2$ [duplicate]

Assume that we have some count data $x_{1}, \dots, x_{n}$, which take values $\{1, \dots, m\}$ and we have some estimator of the probability mass function, $\hat{\mathbf{p}} = (\hat{p}_{1}, \dots, \...
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Intended interpretation of one-mode, three-way (dis)similarities?

I have what I think is a very simple question, the answer has just eluded me so far. A two-way similarity, $s_{ij}$ (for objects $i$ and $j$) can be interpreted fairly straightforwardly as the degree ...
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Which is the 'best' method to detect outliers from a PCoA analysis?

I'm trying to find a suitable method for detection of outliers from a PCoA output. This analysis is used to visualize the results from a distance matrix between a set of sample applying the Chemical ...
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How to compare two set of PMFs?

I'm facing some challenge and I don't know the correct approach for this. I'm having two sets of PMFs $S_1, S_2$ and I need to compare (distance like Jensen–Shannon) $S_1$ with $S_2$. What's the best ...
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Euclidian distance vs cosine similarity

Currently I'm working on facial recognition. If I use encoding/feature vectors of 2 images which method will prove more accuracy, L2 norm or cosine similarity and why? I read "ICA performs ...
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Why clustering in a linear scale using correlation based distance gives better results than clustering in a log2 scale?(PAM clustering)

I have questions regarding cluster analysis. I am trying to cluster data made up of proteins. (23 columns and 1800 rows) I have the data in a log2 scale, some variables range between 2-10 and others ...
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Statistical distance between two matrices

The statistical distance between two probability distributions can be measured with $f$-divergences such as the KL-divergence. The statistical distance between two clusters can be measured with ...
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Are there any linkage functions that can handle signed dissimilarity matrix?

I know that a "distance" matrix is a symmetric positive matrix where the diagonal is zero. A "dissimilarity" matrix, to my understanding, is a generalization of a distance matrix. ...
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What is the appropriate metric for determining distance / dissimilarity of sparse, high dimensional data in PCA space?

I'm working with scRNA-seq data (~96% sparse, high dimensional), and am trying to determine distances between the cells in PCA space - NOT for the specific purpose of clustering. The principal ...
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34 views

Outlier detection in high-dimensional longitudinal data

I'm having a longitudinal dataset with a large number of variables where I would like to use a ML algorithm to inspect possible outliers. What are the techniques you would use for this? I've seen a ...
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Coordinates from noisy distance matrix?

I have a black box in which I know there is a 1D line and points along this line, and as output from this box I can get out a distance matrix for the points, but I know there is noise in the estimate ...
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Is there any divergence like Jensen-Shannon for two vectors which are not distribution? [duplicate]

I know that the Jensen-Shannon is defined as a divergence between two or more distributions ($P_1,P_2,...P_k$). But, instead of distributions, I have some multiplications of two distributions (so they ...
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35 views

Difference between two multi-variable datasets

I have multiple activities that a person performs, and the corresponding multidimensional values [$x$, $y$, $z$ - coordinates] for two devices and their readings. I need to find the difference between ...
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What is the correct way to implement Jensen-Shannon Distance?

I'm trying to use this code to compute the Jensen-Shannon distance: ...
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How important is triangle inequality for statistical estimators?

(Pearson's) correlation is a measure of co-dependence that does not fulfill certain axioms such non-negativity and triangle inequality. In layman's terms, how would you describe what triangle ...
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The first principal component line minimizes the sum of the squared perpendicular distances between each point and the line [duplicate]

I am currently studying An Introduction to Statistical Learning, corrected 7th printing, by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani. Chapter 6.3.1 Principal Components ...
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direction of outlier detected by the Mahalanobis distance

Mahalanobis distance provides a value that might be used for the detection of outliers. My question: how to calculate the direction of the outlier (as a vector)? A simple answer would be to use the ...
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Sensitivity of KL Divergence

I am very new to the concept of KL divergence. Although I have grasped the fundamental formulations, I have a confusion comparing the KL divergence across the different distributions. Suppose I have 3 ...
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How to calculate similarity between two sets of items rated on a single dimension?

(I'm just making up variables for this example.) Let's say I have 100 words rated on their pleasantness. I also have 100 images rated on their pleasantness. I then had participants rate the fit ...
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Grey relation between two datasets?

I am trying to compare two datasets representing the same output. The dataset is categorical. For example, my first data output is (1)100-200 (2)200-300 (3) 200-300 (4) 300-400 etc. Second data ...
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What is the appropriate way to analyze data subsetted into bins and compare those bins across conditions?

I am wondering how to approach the analysis of a data set that I've obtained. I have animal trajectories moving toward a target under multiple experimental conditions. One of my analyses was to look ...
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Inconsistent results from partial Mantel test on (non)distance matrices

Currently I am trying to look at the correlation between three matrices of ecological data. All three are forms of distance matrices (two matrices of pairwise community dissimilarities and one matrix ...
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32 views

Euclidean distance from zero

I am trying to create my own weights for relative work task importance, or weight. For every task, I have a value of importance, ...
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What test to use on distance data inside SPSS?

I have a set of GPS points that I have put inside a GIS software to obtain their distance from the Florida coast. These points represent litter found on the ground. So for each point, I have data as ...
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distance between two points (x,y) weighted by location (x)

a new on algebra. I am trying to create an indicator of the distance between two points (x,y) from a (0,1) scale, but I want to create a weight that reduces such distances as the point x is closer to ...
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How is pairwise PERMANOVA/adonis a valid non-parametric approach for pairwise comparisons

Assume that we have taken independent random samples of several individuals from 5 locations that represent 5 populations. The design is fairly unbalanced: the number of individuals sampled from each ...
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Clustering given “distance” matrix and K in python

INPUT ($D$, $K$): I have a symmetrical "distance" matrix $D$ of size $N \times N$ which tells me how distant one object is from another. Function used for calculating the distances is not a ...
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Interpreting results of ANOSIM conducted on non-abundance data

I am trying to understand how to implement and interpret an analysis of similarities (using the vegan package in R) in the following situation. Consider the following data frame: ...
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Mahalanobis Distance for Continuous and Ordinal Covariates

My dataset of home sales includes covariates such as square_feet which are continuous and others like num_bedrooms which are in <...
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How to calculate the similarity of data with noise?

I'm stuck on calculating similarity. Please tell me in which direction to move. There are three files of different lengths that need to be compared for similarity. It is supposed to use the cosine ...
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Asymptotic equivalence and Kolmogorov-Smirnov Distance

Suppose we have two sequences of random variables $\{X_k\}$ and $\{Y_k\}$, both converging to the same distribution, say $N(0,V)$, for some covariance matrix $V$. Does this imply that $$\sup_{u}\left|...
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Estimating the actual distance by using a series of measurements in between

An object is moving along a single axis, back and forth. We take $N$ snapshots of the object. For all pairs of snapshot positions $i$ and $j$, we can make signed measurements of distance $x_{i,j} = -...
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Multivariate Wasserstein metric for $n$-dimensions

I am a vegetation ecologist and poor student of computer science who recently learned of the Wasserstein metric. Application of this metric to 1d distributions I find fairly intuitive, and inspection ...
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Approximating a distribution with an integer histogram

Given a distribution $f:[0,a)\rightarrow\mathbb{R}$, is there a simple algorithm by which to find a sequence $\{h_i\in\mathbb{N_0}\}$ such that $f(x)$ is approximated by $h_{floor(x)}$ as a histogram ...
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Is 'symmetry' the only requirement for a distance matrix to perform hierarchical clustering with complete linkage?

I have a dissimilarity measure for pairwise comparison of my subjects and want to perform hierarchical cluster analysis with complete linkage. The dissimilarity measure is not a distance metric. It ...
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Detection Function in Distance Sampling, R

I'm fitting detection functions on whale data using the ds function in Distance package in R. I am having difficulty choosing the best detection function to then use in a density surface model. I ...
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Gap statistic slow (fviz_nbclust)

I have a big kendall's tau correlation matrix (2676x2676). I'm interested in clustering and check for possible samples associated variables overrepresention at each of the given clusters. Firstly I'm ...
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Does the 1-Wasserstein distance have an upper and a lower bound?

Given $u$ and $v$ two probability distributions and U and V their respective $CDFs$, the $1$-Wasserstein distance is formulated as follows: $l_1(u,v)=\int_{-\infty}^{+\infty}|U-V|$ Does $l_1$ have ...
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Distance metric for probability distribution

I'm looking for a distance metric that would be good for what I think is a probability distribution: I have a fixed number of samples I have a fixed number of features Each sample can have, at most,...
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How to calculate similarities/distances and conduct cluster analysis from contingency table

I have an 18x25 contingency matrix, rows are behaviors observed and columns are environmental features. I conducted a correspondence analysis via the CA() function in R and then clustered using the ...
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Creating a fraud score for an image fraud detection workflow

So to set the context. I'm working on an image fraud detection workflow for an insurance company. The idea basically is: There are a number of cases (car accidents). Each case contains a set of ...

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