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

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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} : ...
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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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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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41 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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9 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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11 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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110 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 ...
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35 views

Choosing the right linkage method for hierarchical clustering

I am performing hierarchical clustering on data I've gathered and processed from the reddit data dump on Google BigQuery. My process is the following: Get the latest 1000 posts in /r/politics ...
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22 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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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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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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22 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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299 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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82 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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16 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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76 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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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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26 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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49 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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63 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 ...
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102 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
69 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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60 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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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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31 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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112 views

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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94 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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46 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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72 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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179 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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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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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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39 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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Question on Texture similarity measures

I was wondering whether there is a similarity measure between a discrete image or texture image and a continuous image? I have two images one is discrete (it can be a texture also) and the other is ...
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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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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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105 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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Statistical distances and time series of distributions clustering

I am interested in clustering $N$ time series of $T$ 'values' each. These values are distributions (which can be represented by their cumulative distribution functions (cdf), or their probability ...
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25 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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147 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 ...
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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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25 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 = ...
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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: ...
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243 views

Chosing optimal k and optimal distance-metric for k-means [duplicate]

I have a data-set with roughly 20-dimensions and millions of points which I want to cluster. The goal is to find a set of clusters which: Are as distinct as possible from each other (minimum ...
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123 views

Turn a distance measure into a kernel function

I have read here that an easy way to turn a distance function $d$ into a similarity function $s$ is to compute: $s = e^{-\gamma * d}$. I believe that this is also what is done with the RBF kernel. ...