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

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Distance between Vectors with Confidence Intervals

I have a machine learning application where I extract numerical features $a_{i1}, a_{i2}, \dots, a_{ik}$ for each object $a_i$ to study. Objects are then compared using standard euclidean distance. ...
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9 views

Robust Sparse K Means clusters and valid index

I used the robust sparse k-means for clustering my dataset and I would like to calculate some distance-based statistics for evaluating my results. Should I compute them on the dissimilarity matrix ...
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7 views

Find the set of K elements between n that maximize the total distance [migrated]

Given a set $Q$ of $n$ points, we want to find the subset $S_{max}\subset Q$ of $k$ elements that maximize the total distance between them. $S_{max} = \max_S\sum_{\mbox{$\begin{array}{c} i,j\in S\\ ...
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14 views

How to compare closeness of points with 4 variables

I have data for the percentage of people of different races and ethnicities for each state the US as of 2013. I also have this same data on a national level from 1900-2060, using Census predictions. ...
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1answer
31 views

Using a distance matrix *with errors* to find the coordinates of points

(I asked this same question in stackoverflow, without getting any answer, but maybe this is a more appropriate forum.) I would like to find the coordinates of a set of points in 3D from a distance ...
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17 views

show the distance between two groups with same variables using mahalanobis distance

There are two groups in my database, the first group is called unhealthy group and the other group is healthy group. each group has 4 variables (Same variables) but different values for similar ...
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9 views

Statistical distance in R with samples of different lengths

I have it really hard to find R functions that estimate various statistical distances (e.g. the Hellinger distance between two samples that have different lengths. I have gone through the R package ...
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4answers
313 views

How I can convert distance (Euclidean) to similarity score

I am using $k$ means clustering to cluster speaker voices. When I compare an utterance with clustered speaker data I get (Euclidean distance-based) average distortion. This distance can be in range of ...
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2answers
53 views

K-means: Why minimizing WCSS is maximizing Distance between clusters?

From a conceptual and algorithmic standpoint, I understand how K-means works. However, from a mathematical standpoint, I don't understand why minimizing the WCSS (within-cluster sums of squares) will ...
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20 views

Distance between blocks in a file

I am working on my research and it's computer related. I need to calculate how blocks in a file are close to each other (the distance between the blocks). For example, if we have the following three ...
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1answer
19 views

learning ranked instance similarity by machine learning

Here there are many vectors with rank. a = c(1, 2, 3, 5, 10,...) b = c(4,2,3,2,8,...) ... please note, here it's the rank of value but not the value itself in these vectors. There are a few ...
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8 views

What is the best practice to deal with NA values when calculating a dissimilarity matrix?

I need to calculate a matrix of distances between sites where different variables were measured. I will use it in a cluster analysis. The following is a sample of the matrix I am dealing with: ...
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42 views

Comparing Euclidean distances

I have 3 sets of values for X, Y & Z eg X = 7,8,7,8,6,9,8 Y = 8,7,7,6,7,8,8 Z = 8,8,8,7,8,9,9 I want compare the euclidean distance between these sets (X ...
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8 views

distances for partial rankings

I would like to know how I can compute the "Kendall distance" and the "Footrule distance" for partial rankings. I know only the general definitions for these distance that are exploitable only on full ...
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25 views

assumptions to compute mahalanobis distance

Which are the assumptions to compute the Mahalanobis distance between two groups? Do all the variables of the two groups be normal distributed?
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1answer
47 views

Doubt with a distance based Redundancy analysis

I conducted a distance based redundancy analysis (dbRDA) to explore the relevance of some environmental variables in explaining the patterns of the distribution (i.e., spatial and temporal) of two ...
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1answer
38 views

Distances in PCA space

I'm working on a project involving PCA, and my knowledge up till now with this method is quite good. My work involves finding nearest neighbors (having the least Euclidean distance) to a particular ...
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1answer
147 views

Efficient way to compute distances between centroids from distance matrix

Let us have square symmetric matrix of squared euclidean distances $\bf D$ between $n$ points and vector lengthed $n$ indicating cluster or group membership ($k$ clusters) of the points; a cluster may ...
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3answers
129 views

Is it feasible to use k-Nearest Neighbours to identify text language?

I have seen various language identification libraries that claim to use naive Bayes classifier for text language identification, like CLD2 and language detector, but not any library that uses other ...
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1answer
51 views

k means with binary variables

Is it OK to use kmeans with binary variables? I mean Euclidean distance? I guess the binary variables will be the ones that get the most power to determine the ...
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1answer
55 views

Cholesky factorization and forward substitution less accurate than inversion?

I recently asked this question asking for an efficient way to compute the Mahalanobis distance (without calculating the inverse). The accepted solution was to use the Cholesky factorization and ...
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1answer
259 views

Efficient/fast Mahalanobis distance computation

Suppose I have $n$ data points $x_1,\dots,x_n$, each of which is $p$-dimensional. Let $\Sigma$ be the (non-singular) population covariance of these samples. With respect to $\Sigma$, what is the most ...
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16 views

calculating distance among unordered set partitions for k-mean clustering?

I have a dataset for which I construct unordered set partitions for each data point, e.g. {{1,2,3}{4,6}{5}} for one and {{1,3}{2,4,5}{6}} for the next. I would like to perform k-means clustering on ...
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1answer
29 views

FAMES 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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40 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
23 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 ...
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1answer
96 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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46 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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30 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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16 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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46 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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16 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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119 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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29 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
187 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
98 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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1answer
265 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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167 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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33 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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69 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
49 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
132 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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156 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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38 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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53 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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21 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
1k 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
43 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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77 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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104 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 ...