Distance functions refer to functions used for quantifying the notion of distance between members of a set, or between objects.

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What is the best way to cluster the gower similarity matrix?

I have a dataset that contains the gower similarity of each observation from each other. So the dataset looks like this: ...
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21 views

R - Weighted Euclidean distance function [closed]

Does a Weighted Euclidean distance function already exists in R ?
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53 views

Properties of Levenshtein, N-Gram, cosine and Jaccard distance coefficients - in sentence matching

Let's say I have two strings: string A: 'I went to the cafeteria and bought a sandwich.' string B: 'I heard the cafeteria is serving roast-beef sandwiches today'. ...
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5 views

Distance Measure for Local Regression when Input components have Different Units

So the problem I am trying to tackle is one where a given input vector consists of vector components with widely different units. An example is an input vector having a speed component, an angular ...
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20 views

Hamming distance with weights [closed]

I wonder if there is already existing variation of Hamming distance that takes into account not only two vector to calculate the distance but also their weights that reflect the significance or the ...
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1answer
156 views

Similarity function with given properties

I would like to find a similarity function $f$ between two values (each value is continuous and is bounded by $[0,1]$) that would have the following properties: $$ f(1, 1) = 0.5 $$ $$ f(0.5, 0.5) =...
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9 views

Understanding minimum loss projection

I am trying to understand the paper: pseudo-metric online learning algorithm(Link). It intends to learn a matrix threshold pair by projecting it into space $C_t$ $C_t = ${$(A,b) \in R^{n^2 +1} : l(A,...
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1answer
16 views

Mahalanobis Distance and feature scaling

I've been using Mahalanobis distance to look for outliers. This link: https://www.cs.princeton.edu/courses/archive/fall08/cos436/Duda/PR_Mahal/M_metric.htm says that feature scaling is addressed in ...
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2answers
90 views

Lower-bound for total-variation between two sub-gaussian random variables

Problem setup Let $X$ and $Y$ random variables on the real line with following properties: $X$ and $Y$ are $\sigma^2$ sub-gaussian $E[X] = 0$ and $E[Y] = \Delta$. Question Whats the lower ...
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1answer
49 views

ABC with Lotka-Volterra (or any dynamical system)

I have set out to implement a simple ABC rejection sampling algorithm in order to approximate the posterior distribution of parameters for Lotka-Volterra system and I have a few questions: 1) What ...
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1answer
18 views

How to build a distance function given a cluster of points?

Given a non-elliptical cluster of points in a n-dimensional space I would like to get a distance function from the centroid of this cluster such that its "equipotential" surfaces has the same shape as ...
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15 views

Hellinger Distance between discrete distributions of different supports?

In this dissertation here: link, it mentions that Hellinger distance is defined for probability distributions of different supports. I am attempting to write a function to calculate this in Python, ...
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1answer
54 views

How to soften or mitigate vector similarity measure?

I would like to evaluate a similarity between two objects X and Y by comparing a neighbourhood in which they're located. I construct two sets of nine concentric and equidistant circles with centers ...
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13 views

Hypothesis Testing With Distance Measurements - Variance Calculation

I am looking at an existing method that is making decisions based on hypothesis testing using a distance measurement. The test looks like a Z- or T-test, where the computed distance and its variance ...
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1answer
185 views

Estimate Epsilon in DBSCAN with k-nearest neighbor algorithm

Following DBSCAN paper (quote below), I'm trying to develop a simple heuristic to determine the parameter Epsilon with K-nearest neighbors (k-NN) algorithm. For a given k we define a function k-...
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23 views

Computing 'histogram' similarity when the elements can be positively or negatively weighted

The 'histograms' I want to compare may have positive or negative bin-values. I use the quotes because I am not sure histogram is the correct name. The elements that are being sample have associated ...
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25 views

Normalizing factor for distance metric as dimensionality (marginally) increases

The expectation of a squared Euclidian distance from a $d$-dimensional distribution with covariance matrix $\mathbf{I}$ should be $d$, because the expectation of the squared variables making up the ...
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109 views

How to calculate the distance between clusters using log-likelihood in two step clustering? [closed]

Log-Likelihood Distance (TwoStep clustering algorithms) How to calculate the distance between clusters(i.e record and cluster) using log-likelihood in two step clustering using the below mentioned ...
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26 views

Finding a subset of points in a set that is closest to a known empirical distribution

I am given two samples (sets) of points: $A$ and $B$, in a $p$-dimensional space. I am interested in finding a subset of points in $A$, denoted by $S_A$, that appears closest to the distribution of ...
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1answer
422 views

Find K-nearest neighbour with custom distance metric

I am working on finding similar items. Each item has a representation as a vector of features. Instead of using one kind of distance metric for each feature like "Ć«uclidean" distance. I want a mixture ...
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104 views

Multivariate time series Euclidean distance

I would like to know how to use Euclidean distance to find similarity between two multivariate time series. Suppose, I have two $N$-variate time series $u$ and $v$, with $u_i(t)$ denoting the $i$-th ...
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21 views

R: Multiple distance functions in clustering

I want to consider different matrices for different variables, e.g., Euclidean for numerical, Hamming for categorical, earth distance for lat-long etc., in clustering, say k-mean clustering. Is it ...
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1answer
81 views

Real data example of Mahalanobis distance - proper data values given

Here is my real data example (these are real data check below pictures to see. I am comparing real documents (words represented as TF-IDF values). I equalize list sizes with missing words added as 0 ...
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$L_1$ distance between two Gaussian processes

In Brown's famous paper (1996), the $L_1$ norm between two Gaussian processes defined on time domain $[0,1]$ $$dY_t = f(t)dt + \sigma(t)dB_t\quad\text{and}\quad dZ_t = g(t)dt + \sigma(t)dB_t$$ is ...
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15 views

How to find similar documents with mixed features

I am working on finding a similar documents problem. I have 3 sets of features ...
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28 views

Multivariate DTW

I am not able to find any resources in case of DTW for multivariate signals. For example, I would like to find DTW similarity between two objects where each object contains following signals: ...
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50 views

Ensemble LDA on different feature spaces?

I'm working on a classification problem where I'd like to do the following: I have a space of features that live in $R^m$, and another set of features that are related that live in $R^n$. I want to ...
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73 views

Does chi-square distance between two vectors (not histograms) have any meaning

I have used the chi-square distance with the KNN for a classification task and I get a good results. My feature vectors each have size 10000. The feature vectors are not histograms. I know that chi-...
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122 views

Why the chi-square distance gives a better in high dimensional space

I am a beginner in machine learning. I did a classification program using KNN using two similarity distances: Euclidean distance and chi-square distance.The size of each feature vector is 10000. I ...
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1answer
72 views

Distance metric invariant to dimensionality?

I'm working on a classification/prediction problem where I have to predict a location of an object. The problem that I have is that for every location, I have a unique and different number of feature ...
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62 views

Name of an $f$-divergence

The term divergence means a function $D$, which, given two probability distributions $P,Q$, assigns a non-negative real number $D(P,Q)$ such that $D(P,Q) = 0$ iff $P(x)=Q(x) \forall x$. The relative ...
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2answers
56 views

In clustering, how does Normalized Euclidean Distance represent the number of standard deviations from a cluster?

In clustering, one has to choose a distance metric. I've seen Normalized Euclidean Distance used for two reasons: 1) Because it scales by the variance. 2) Because it quantifies the distance in ...
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1answer
32 views

Clustering experiments based on event distance matricies

I'm running a bunch of experiments with randomly picked "knobs", and I'm recording various event types and times they occurred during the event. I'm particularly interested in getting a good variety ...
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Measuring salient changes in 2 Dimensional clusters using using existing functions in Matlab

I have a series of frames where I want to analyse changes in spatial distributions of points. I have a list of x,y values or 2D coordinates measuring changes in particle distribution. As shown in ...
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Similarity measure between groups

Imagine there is a group of people numbered 1-100, each of which have a few numerical attributes e.g. height, weight, age. There is a small sub-group (A) which ...
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1answer
95 views

Estimating equation for power divergences

The inference based on minimizing the power divergence $$D_{\lambda}(g\|f) = \frac{1}{\lambda - 1} \log \int g^{\lambda} f^{1-\lambda} dx$$ is known to be robust against outliers for $\lambda <1$. ...
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52 views

Gower Distance, Ordinal Variable, R, Error?

I am trying to implement the CritCF function from http://www.sciencedirect.com/science/article/pii/S0031320310004905 for feature selection in clustering. I need to compute the distance from cluster ...
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Is there a distance metric that measures the ratio between the two rows of data?

I have about one hundred groups of chemical testing results data. Within each group there are between 1 and 200 chemical testing results. Each set of results contains testing data for 5 chemicals. ...
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1answer
79 views

Do I have to normalise the data for PERMANOVA?

Why do I have to normalise my dataset to do a PERMANOVA? What is the difference between Euclidean distance and Bray-Curtis similarity? Which is the most suitable for CPUE (abundance) data?
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1answer
208 views

How does the Proxy::dist package for r compute cross-distance matrix between two matrices?

I am trying to understand how a cross-distance matrix between two matrices is computed. Can anyone help? Maybe a simple example would help, two matrices having nrow observations of ncol variables (...
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47 views

How to compute Voronoi tesselation based on manhattan distance in R [closed]

I am trying to compute a Voronoi tesselation in 2D with the Manhattan distance in R. Ideally this would be a function that takes a set of two-dimensional points ...
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25 views

How to create a (perceptual) distance function from human-generated examples?

My goal is to create a perceptually balanced distance metric to compute the similarity between two scatter plots (inspired by the work on Graph-Theoretic Scagnostics). My plan is to run a user study ...
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26 views

Bhattacharyya Distance for Age/Gender Groups?

I'm calculating distances for groups based on Age/Gender Compositions (to rank their similarity in demographic composition.) I'm working with the following: Men 18-34, Men 35-49, Men 50-64, Men 65+, ...
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37 views

Clustering before or after ordination

Can someone explain the implications of performing clustering either before or after performing NMDS? I have some ecological data and I am performing a clustering analysis to identify communities of ...
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108 views

Distribution of “sample” mahalanobis distances

Let $x_1,\dots,x_n$ be i.i.d. observations from $N_p(0,\Sigma)$. Let $\hat S=\frac1n\sum_{i=1}^n x_ix_i^T$ be the sample covariance of the samples. Recall that the Mahalanobis distance is defined: $...
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26 views

Classifying with a distance/error metric

I have a bunch of data of the form (x0, x1, x2) -> y (everything is categorical data), and I want a decision/classification rule for predicting y a metric on y's space (there is no "natural" metric) ...
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1answer
191 views

A similarity measure with binary data: does this one have a name?

There are many binary similarity measures (e.g. Jaccard, Sorensen, etc), each of them is sensitive to different properties of the compared sets. I would like to use the metric $S=\frac{N_{A\bigcap B}}{...
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Looking for a robust, distribution-free/nonparametric distance between multivariate samples

There are many distance functions for distributions out there, but I'm having a hard time wading through them all to find one that is "distribution-free", or "nonparametric", by which I mean only ...
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27 views

Finding vectors with an extreme component

I'm looking for a function that measures if a vector component dominates all the rest. Let $$ \mathbf{v} = [v_1, v_2, \ldots, v_n] $$ and assume that it is L2 normalized, $|\mathbf{v}|_2 = \sqrt{\...
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Is there a distance algorithm similar to Jaccard distance that handles scalar data?

we have the characteristics and (scalar) values of those characteristics for three (or more) people: ...