Questions tagged [distance]
Measure of distance between distributions or variables, such as Euclidean distance between points in n-space.
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Is Euclidean distance the same as distance-from-correlation as $d(x, y) = \sqrt{2m[1 - r(x, y)]}$
I found in a couple of documents (e.g. this) that the Euclidean distance $d(x, y) = \sqrt{\sum_{i = 1}^{n}{(x_i - y_i)^2}}$ can be obtained from correlation coeffcient if $x$ and $y$ are standardised ...
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9 views
Similarity Metric Validation
I want to score a number of similarity metrics, i.e. given a function s(x,y) which returns a number that is higher the more similar x and y are. I'm want to objectively score a number of different ...
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14 views
Gaussian Mixture Models and distance matrix
I have a (euclidean) distance matrix and I want to perform GMM clustering.
I read in another post (gaussian mixture model - approximate a matrix) that I could apply MDS or PCA to this matrix and use ...
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9 views
MDS as input for K-means
I have a distance matrix, which I know is in the Euclidean space. Then I performed PCA on the distance matrix to obtain MDS or PCoA result matrix. I read in multiple posts that I could use this as ...
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13 views
Dissimilarity matrix, Euclidean distance and Kmeans
I was wondering whether the Sklearn Kmeans and AgglomerativeClustering with Ward linkage takes as input regular Euclidean ...
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13 views
Wasserstein distance for categorical data? Relationship to TVD?
Is the Wasserstein distance applicable for categorical data? e.g. if we have the distribution of different coloured balls in two bags,
...
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1answer
23 views
Is the set of distribution $\{ X | \max_t |f_X(t) - f_Y(t)| \leq \epsilon \}$ convex, where f is the cdf or inverse cdf?
I'm trying to figure out if the set is convex, where the maximum difference between cdf(or inverse cdf) of X and a reference distribution Y is smaller than $\epsilon$.
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Let $f_X(t)$ denote the cdf ...
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11 views
i.i.d data for computing distance correlation
When computing an estimate of the distance correlation of random vectors $X$ and $Y$ using paired samples of the vectors, should the samples be i.i.d? Can I have data in which $X_i$ and $X_j$ are ...
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1answer
30 views
Probability of points less than a fixed distance apart in a vector space
I have a distribution $D$ of points in a normed vector space (it's $\mathbb{R}^n$ using the $L_\infty$ norm, but I don't think that matters).
In this particular space, points that are less than a ...
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15 views
Computing the most representative sample of a random variable
Let $X$ be a real-valued random variable and $n > 0$. Using numerical methods, how can we find the vector $\vec v$ of $n$ real numbers that is most characteristic of $X$, in the sense that the ...
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1answer
23 views
Measure of distance between two survey responses
I've found some survey data where respondents answer 63 question by giving a response for each question between 0-10 (0 for strong disagreement, 10 for strong agreement). So I can view every ...
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1answer
25 views
Similarity/dissimilarity matrix over classes
I am trying to get something like a confusion matrix for different classes, but without training a model.
The idea is to use some kind of distance between classes.
The data set is like this, just for ...
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13 views
J-S Divergence as a Percentage
Is there a way to interpret the Jensen-Shannon divergence which is normalized to be between 0 and 1 between two probability distributions as a "percent difference", i.e., there is a x% ...
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10 views
Clustering - Distance Metric for Comparing Short Lists of Terms (non-repeating, no frequency)
Clustering involves using some distance or similarity metric.
What is the best way to score the similarity of these small sets of words? Criteria: These are technical terms which are extracted from ...
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1answer
40 views
Using $\chi^2$-Distance for Histogram-Comparison with 0-Valued Elements leads to NaNs
I want to compare two histograms by using the $\chi^2$-distance. There is a definition in the OpenCV-library. Also this question gives a lot of insight about this distance-metric. Because i didn't ...
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9 views
K-Means transform function does not match pairwise_distances_argmin_min centar calculation
I need to be able to select first N most representative points from each cluster calculated by K-means. To do so, I am aiming to calulate the distance of each point to its own cluster center and take ...
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20 views
Specific proof related to MDS distance matrix
Given a symmetric, positive semidefinite matrix A, and matrix D, where $D_{ij}=A_{ii}-2A_{ij}+A_{jj}$, prove that there exist n vectors {$\vec{v_1},...,\vec{v_n}$} such that $D_{ij}=||\vec{v_i}-\vec{...
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27 views
Product of two probability density function
Suppose $f$ and $g$ are two probability density functions. I have seen economists use $\int f(x)g(x) dx$ as some kind of similarity measure. For example, Jaffe (1986) uses sum of product of two ...
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30 views
Distance of a vector to a sample of a distribution?
Is there a better measure than Euclidean distance for my problem?
I have two functions e() and f(x). x is a vector of continuous values. The process e() outputs a variable z. Subsequently, a variable ...
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24 views
Is there a metric to identify whether samples are uniformly distributed when number of samples is small?
Suppose I have a small number of samples drawn from an unknown distribution $\{X_1,X_2,...,X_n\}$, where $0\le X_i \le L$, and $3\le n \le10$. I want to identify a metric to understand how far these ...
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63 views
Finding a sub-population from dataset matching another target dataset
Let's say one has a finite collection of i.i.d. samples from an unknown source distribution $S=\{x_{i} | i \in [1,n_{S}], x_{i} \sim p_{X_{S}}(x)\}$. Where each $x$ is multidimensional and has ...
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1answer
49 views
Distance matrix time series analysis? (Ecology/diversity)
I am trying to analyze a time series of ecological data. Each time point in the series is a matrix of animals-by-foods (that they were observed to eat). For each of these time points, I compute the ...
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1answer
29 views
two times square in distance calculation on one example?
I read a book on Kernels, See the following example. Why the authors take square two times here? what is the logic?
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26 views
Best approximation of the Mahalanobis distance by standardized Euclidean distance
I am looking for the best way to approximate the Mahalanobis distance by the standardized Euclidean distance, which would reduce the number of the required multiplications. The easiest way is the ...
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44 views
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 $\gamma(x,y)$ that minimizes ...
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21 views
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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0answers
10 views
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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24 views
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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16 views
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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44 views
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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1answer
73 views
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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1answer
174 views
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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0answers
21 views
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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1answer
43 views
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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13 views
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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0answers
48 views
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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25 views
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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52 views
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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1answer
57 views
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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0answers
32 views
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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0answers
40 views
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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1answer
67 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 ...
3
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1answer
55 views
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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23 views
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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1answer
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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48 views
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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0answers
30 views
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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38 views
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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1answer
67 views
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 ...
2
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1answer
72 views
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 ...
