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

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13 views

Triangular geometry in case of Dynamic Time Warping

I found this paper Using Pivots to Speed-Up k-Medoids Clustering in which authors explain how to use triangular geometry and cosine law to speed up search of new medoids in case of K-medoids. My ...
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0answers
19 views

Appropriate distance measure between two finite state Markov chain models?

I am empirically creating Markov chains similar to this question. I end up with several finite state Markov chain models with the same nodes but varying transition probabilities. I want to calculate a ...
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1answer
17 views

Asymmetric distance measure in k-NN classifier?

What is the problem with an asymmetric distance measure in k-NN classifier? I think it will not cause problem, so long as I compute the distance consistently, say always from ...
4
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1answer
79 views

Get k most diverse objects from dendrogram (hierarchical clustering)

I have a dendrogram which groups similar object in a hierarchical order. The problem I try to solve is based on a dendrogram how to get k most diverse objects. E.g. We start with some random (?) ...
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23 views

Correlation of Distance Matrix

I have a matrix with 15 samples and ~10,000 data points (all z-scores). I calculated a distance matrix with euclidean distances using R. Is it valid to calculate and present a correlation on this ...
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28 views

Distance between independent observations of a categorical variable

I have a random variable $T: \{ \text{blue}, \text{green}, \text{red} \} \rightarrow [0,1]$ and a number of observations of $T$: ...
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9 views

Weights in computing mahalanobis distance

I need to compute distance among 200 observations and 17 variables. Variables are on different scales and not equally important. I computed Mahalanobis distance as Euclidean distance for the principal ...
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22 views

clustering discrete data - how to get “autocorrelative distance” matrix?

I'm trying to cluster discrete (histogram) data with unequal bins. I came across the post: Clustering distributions and calculated the cumulative sums of each data set and interpolated between ...
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30 views

Can I compare Mahalanobis distances from different distributions?

I have a multivariate dataset representing multiple locations, each of which has a set of reference observations and a single test observation. For each location, I would like to measure how anomalous ...
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14 views

Online clustering with distances

I'm pretty new to this field so please excuse me if my question sounds naive. I have a stream of distance tuples in the form of (A, B, d) where ...
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70 views

Multivariate Outlier Detection with Robust Mahalanobis

I am searching some documents and examples related multivariate outlier detection with robust (minimum covariance estimation) mahalanobis distance. I have 6 variables and want to plot them to show ...
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16 views

Multivariate Mahalanobis Distance Vector Normalization

I have a vector including different variables with different scales. For instance ''a'' presents ''dollar value'' in billions.''b'' is a ratio, presents value divided by quantity and it ranges 0 to 1 ...
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2answers
98 views

Clustering based on large Jensen-Shannon Divergence distance matrix

I have a dataset with large number of features and about 15 000 observations. I’m using a probability distribution distance metric related to Jensen-Shannon divergence (JSD) to cluster the ...
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1answer
77 views

Distribution of the Levenshtein distance between two random strings

The Levenshtein or edit distance between two strings is the minimum number of edits (adding a letter, removing a letter or changing a letter) required to transform one into the other. Assume that we ...
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28 views

Definition of normalized Euclidean distance

Recently I have started looking for the definition of normalized Euclidean distance between two real vectors u and v. So far, I have discovered two apparently unrelated definitions: ...
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77 views

Comparing two vectors with the same numbers in different positions [closed]

I have two vectors of the same size representing one score for different sites (x and y coordinates) under distinct situations (each vector is one situation). At each vector the scores only change ...
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0answers
30 views

Testing whether neighbors are more similar to each other than distant points

Suppose you have points x1...xn in a metric space X, each is associated with some measurement y1...yn. I want to test whether points closer to each other in X have similar associated value y. I have ...
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40 views

Extending the Hellinger Distance of discrete probability distributions to multivariate distributions

For two discrete probability distributions P=(p1..pk) and Q=(q1...qk), their Hellinger distance is defined as $$H(P,Q)=\frac{1}{\sqrt{2}}\sqrt{\sum_{i=1}^k(\sqrt{p_i}-\sqrt{q_i})^2}$$ could this be ...
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1answer
43 views

pairwise distances used as features for classification

I have a feature matrix 977x3 features = rand(977,3); where each row is an observation and each column is a feature. I calculate the pairwise distances between ...
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2answers
102 views

Mahalanobis distance measure for clustering

Let's say I have a group of clusters. Would you recommend Mahalanobis distance measure for checking if new arrived data belongs to existing clusters or it is an outlier? Also, would you recommend ...
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62 views

How to measure consistency or simiarity between two data sets?

I am working on a study that elicits priorities (weights) from experts on a set of alternatives using different methods. The snapshot below shows the resulting weights, which sum up to 1 for each ...
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28 views

Kolmogorov-Smirnov and Hellinger distances

I am comparing two distributions with these two methods and sometimes I find no correlation between them! How is it possible? Which one is more believable? I use the D statistic from the KS test and ...
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42 views

t-test as Mahalanobis distance

Our tutor once said that the t-test applies Mahalanobis distance. Could you please explain how it does so?
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17 views

which distance for clustering

I've got 6000 reports that I've cleaned up. I've used 8 different steps to remove words of the reports. For each report, I've got a table of the following form: ...
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1answer
458 views

Gower distance with R functions; “gower.dist” and “daisy”

I have 9 numeric and 5 binary (0-1) variables, with 73 samples in my dataset. I know that the Gower distance is a good metric for datasets with mixed variables. I tried both daisy(cluster) and ...
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1answer
29 views

Test if paired data are more similar than non-paired data

I have a set of ten samples, comprised of five pairs of twins, and I have calculated the pairwise distances between all ten samples. The question I would like to answer with this data is: Are ...
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66 views

Probability that uniformly distributed points in a square region form a cluster

I have a known number of points N uniformly distributed in a square and I want to solve the expected number of clusters of points. I cluster is formed by a growing algorithm. Starting at a point p, ...
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59 views

Gower distance with R

I have 17 numeric and 5 binary (0-1) variables, with 73 samples in my dataset. I know that the Gower distance is a good metric for datasets with mixed variables. When I use daisy function in cluster ...
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32 views

Isolation by distance -data transformation

In population genetics a common analysis is to look for a correlation between genetic distance (e.g. FST) and geographic distance (km) using a scatterplot and linear regression. For this it seems a ...
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27 views

What is variance and co variance related to time series?

I'm trying to understand the Mahalanobis distance method which makes use of a covariance matrix. However i am not clear about the idea of variance and covariance with respect to time series. And also ...
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20 views

r-pnn, normalization and different distance measures for each variable

Since pnn is a NN that uses a Radial kernel to classify data, I think the distance measure is key and, in consequence, the normalization of the data. Am I right? How does pnn package calculate the ...
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3answers
193 views

Why are mixed data a problem for euclidean-based clustering algorithms?

Most classical clustering and dimensionality reduction algorithms (hierarchical clustering, principal component analysis, k-means, self-organizing maps...) are designed specifically for numeric data, ...
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1answer
198 views

How does the Gower distance calculate the difference between binary variables'?

I have 17 numeric and 5 binary (0-1) variables, with 73 samples in my dataset. I need to run a cluster analysis. I know that the Gower distance is a good metric for datasets with mixed variables. ...
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0answers
27 views

Unique matching for quantiles from one half of the density to a subset of the other half?

I am interested in finding the median absolute distance to quantiles. So, for $Q_\alpha$ the $0 \le \alpha \le 1$ quantile, I would like to find $Q_\gamma^*$ such that $Q_\gamma^*$ satisfies ...
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27 views

Want to findout satistical distance unsing another procedure except kullback liebler divergence

i want to find the distance between two pdf(pdf is calculated using kernel density estimator from two random data set of different size ) .Is there any alternative and efficent way to calculate ...
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1answer
60 views

Minimax space-filling design for 2 dimensions in practice

I think I understand the basic idea of a 2d minimax design. Given $n$ data points, choose locations for each point so that the maximum distance between anywhere in the input space and any of the $n$ ...
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86 views

Distance between two independent normal random variable

What is the PDF of $Z=\sqrt{(X-x_0)^2+(Y-y_0)^2}$ when X and y are i.i.d. zero mean normal random variable (i.e., $x\sim N(0,\sigma^2)$ and $x\sim N(0,\sigma^2)$)
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1answer
80 views

Euclidean distance with sparse and high dimension data

I have texts for a bunch of objects. From each text, I removed the stop words, and took each word as an attribute of the object. I then gave each word a rating based on sentiment analysis, so that the ...
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64 views

Average within-cluster distance using divisive clustering

I have to prove that the average within-cluster distance for 10 data points cannot increase when going from 1 cluster to 2 clusters (divisive clustering). Intuitively, it seems obvious that this is ...
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48 views

What is the relationship between naive Bayes and Mahalanobis distance

Recently, I found a code project which uses the Mahalanobis distance to compute Bayes value, but I don't know why you can do that. Second, as I know naive Bayes is based on the Bayes rule, and how ...
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47 views

How to compare the distances or divergence between two groups of datasets

If I have two groups of data sets. Each group has two arrays of empirical data. In the first group each array has, say, 50,000 data points, and in the second group each array has 3,000 data points. ...
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26 views

How to test differences in multiple pairwise distances? With mixed model?

I want to compare two set of variables: X1 = All the pairwise distances between individuals from group A and group ref R X2 = ALL the pairwise distances between individuals from group B and group ...
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33 views

Occupancy octree metrics (Kullback-Leibler)

As I'm currently working on scan matching for outdoor environments I was wondering about the best metric to compare two occupancy octrees (one resulted from the scan matching and one ground truth ...
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23 views

Partial correlations among three distance matrices

I am trying to test the hypothesis that related species should deviate more in niche space the more they overlap in geographic space. In other words, related species either forage similarly and don't ...
2
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1answer
88 views

Metric to compute structural similarity between two directed graphs

I'm working on a small project in which I try to compare directed a-cyclic graphs. Say I have (directed) three graphs: 1) ...
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1answer
23 views

Distribution of distances to an observation from the normal and the median of these distances

Given $x\sim \mathcal{N}(\mu=0, \sigma^2=1)$, the squared distances of the $x$ values to $\mu$ are distributed $\chi^2_1$. I am interested in the distribution of the squared distances to an arbitrary ...
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1answer
313 views

Mahalanobis distance in a hierarchical cluster analysis in SPSS

I am conducting a hierarchical cluster analysis in SPSS on my database with several neuropsychological and psychiatric variables. In my database, some of my variables (that is: two pairs of variables) ...
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1answer
61 views

Order of Matrix Operations in Mahalanobis Calculations

I'm teaching myself to translate equations to code after many years of letting my math skills atrophy, and am trying to do it on my own as much as possible. I've run into a couple of difficult ...
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3answers
177 views

Dynamic Time Warping for irregular time series

I have been reading a lot about Dynamic Time Warping (DTW) lately. I am very surprised that there is no literature at all on the application of DTW to irregular time series, or at least I could not ...
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143 views

R. function hclust, euclidean distances and cosines

My data is a table of cosines and I want to analyze it with hclust, which works on squared Euclidean distances. shall I do: d <- dist(mydata, method = "euclidean") fit <- hclust(d, ...