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

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Comparing the degree of similarity between groups

I have three groups A, B and C and I want to prove that similarity between group B and group A is significantly higher than between group B and group C. How to prove it? Simple example: I have ...
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4 views

Mahalanobis vs Bhattacharayya distance

I am currently trying to study class separability in a binary classification problem. I found Bhattacharayya distance to be a good (and canonical) separability measure, but it appears that Mahalanobis ...
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1answer
18 views

Does vector normalization alter distance relationships?

Simple question, but one I'm struggling to visualize. Does L2 normalization affect the Euclidean distance computation between pairs of vectors? I can't imagine it would, because it's just the length ...
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1answer
16 views

Distance Metrics for Comparing Theoretical Sampling Distributions

I have a sampling probability density function (denoted $f(x|M,N)$ that becomes hard to calculate for large degrees of freedom (i.e. as $M$ and $N$ get big). If I have another pdf (say $f^{*}(x|M,N)$ ...
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35 views

Any distance measures that are more useful for binary data clustering?

I was taking a look at Clustering a binary matrix but it didn't seem to answer my question. I used a basic euclidean distance measure which definitely works but I am exploring alternative distance ...
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40 views

how to find similarity based on only one column value

I am not sure if it is possible and that is why I am asking the question here. I have a data looks like below ...
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2answers
36 views

Is it legit to run clustering on MDS result of a distance matrix?

I am new to the topic of clustering and face the following problem: I have multiple binary datasets with 10k to 40k entries and 135 features each: $$ \begin{matrix} \newcommand{\feat}{\text{feat}} \...
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3answers
51 views

Maximize response for input params clusters from a blackbox function

I have a blackbox function which takes finite number of integers V1, V2, Vn parameters and based on time series variable produce a scalar response. I would like to ...
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20 views

How to calculate normalized euclidean distance on two vectors?

Let's say I have the following two vectors: x = [(10-1).*rand(7,1) + 1; randi(10,1,1)]; y = [(10-1).*rand(7,1) + 1; randi(10,1,1)]; The first seven elements are ...
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46 views

How to cluster my data with binary variables?

I have a dataset like df and I want to cluster the data in R. These variables are binary showing that a person uses a programming language or not. I have these questions: 1- How can I visualize my ...
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38 views

Link between the $L_1$ distance between CDFs and PDFs?

Let $F:(-\infty,\infty)\rightarrow[0,1]$ and $G:(-\infty,\infty)\rightarrow[0,1]$ be two CDFs with PDFs $f$ and $g$, respectively. Is there a connection/inequality between: $$d_1 = \int_{-\infty}^{\...
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How badly does it affect if we compare two machine learning algorithms one using Cosine Sim and other using Cosine Distance?

I am working on a research project such that I need to compare several distance based classifiers - say TF-IDF based KNN and Kmeans for clustering. Suppose I use Cosine Similarity for one and Cosine ...
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15 views

Mahalanobis Function with test and train data

I am new to R programming. I was given a task at work with minimal explaination. I have a huge Data set. Can someone explain the use of Test data and train data? How to use that along with a ...
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0answers
22 views

Permanova for microbial ecology using adonis (R): should I include block?

I know this is a very basic question, but I have been quite unsuccessful in finding a good solution to the following issue. First the data. My spreadsheet is too big, so here is a fictional example: ...
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0answers
15 views

Cosine distance between two vectors containing positive as well as negative elements

I have two vectors whose elements $\in \mathbb{R}$. Everywhere I have seen the usual definition of cosine similarity and the distance = 1 - similarity. However, on ...
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0answers
18 views

estimate NND in the cluster with missing data [closed]

Would very appreciate any comments on the following problem: Imagine one has N sets of elements (points on the plane), coordinates (x,y) of 30% of the points in each set are known. So if we have 30 ...
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58 views

Euclidean distance between the unbiased covariance estimator and the true covariance

Let X be a n*p matrix whose p columns are sampled from a centred normal multivariate distribution with true covariance matrix $\Sigma$ and let $\Sigma_{n}$ be its unbiased sample covariance estimator ...
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1answer
56 views

Does it make sense to cluster based on Euclidean distances between rows of a cosine matrix?

I calculated the Cosine distances for binary data and got the relations between different variables. I need to cluster them. I tried passing the cosine matrix directly to the (clustering) function ...
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38 views

How to calculate the distance in KNN for mixed data types?

when the data is from different types (numerical and categorical) of course euclidean distance alone or hamming distance alone can't help. so i have 2 approaches: standardize all the data with ...
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1answer
35 views

How Gower's dissimilarity handle missing values in numeric columns?

I would like to ask a question about Gower dissimilarity, I was wondering how Gower measure handle missing values in numeric columns, especially that Gower standardized each column based on the range ...
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0answers
21 views

Nearest neighbor symmetric matrix

I have a k nearest neighbors (kNN) distance matrix for $n$ samples $S_n$, which is a sparse, almost-symmetric matrix with the property $x_{ij} ∈ \{0, x_{ji}\}~∀~i, j ∈ \{1,...,n\}$. A matrix entry $x_{...
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41 views
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18 views

Is it possible to scale categorical variable before calculating a distance matrix?

My ultimate goal is to find similar customers by comparing characteristics of non-customers to existing customers. The characteristics are mostly non-numeric. My hope was to scale(data) and then ...
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1answer
104 views

MDS: Is Kruskal's Stress-1 affected by scale of the data, or the number of points?

In Multidimensional Scaling, Kruskal's Stress-1 is a commonly used measure of fit. It is defined as: $\sqrt{\frac{\sum (d_{ij}-\delta_{ij})^{2}}{\sum d_{ij}^{2}}}$ where $d_{ij}$ represents the ...
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27 views

Difference between languages (spoken)?

I'm trying to perform a hierarchical clustering, to aggregate some "zones" or neighborhoods of a city, based on the language that is used most in that zone In order to do so, I have at hand a dataset ...
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21 views

What family of GLM when response is Bray-Curtis dissimilarity? Should I use “adonis” instead?

I have some questions about testing for effects of different experimental levels on community similarity. I'll explain my planned experimental design before I ask the questions: I have two methods ...
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8 views

Combine several measures to one using mahalanobis or euclidean distance

I have 7 financial variables (ratios and simple interval variables), which I want to combine in one measure. I will further use it the regression analysis.The aggregate measure has to account for the ...
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10 views

Hierarchical classification distance based measures

I have sentences that have been assigned a class. The class belongs to a hierarchy. A sentence has one class each. I've performed flat classification experiments and returned some predicted classes on ...
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33 views

Is there a multi-Gaussian version of the Mahalanobis distance ?

Let's say we are in an $N$-dimensional space and that we have a large set of data. The distribution of this $N$-dimensional point cloud can be modeled by a multivariate Gaussian mixture model (...
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20 views

A distance measure for intervals in [0,1] [closed]

We are carrying out an experiment about automatic generation of fuzzy synsets and, as a result of the experiment, we have a lot of closed intervals in [0,1] which we need to compare (between them and ...
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6 views

How to determine a formula for an index of adherence

I hope you will be patient with the inarticulate question of a non-mathematician. It's hard to get an answer when you don't even know how to ask the question. Here the contest: Let's say that I have ...
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19 views

python: how to use cholesky decomposition for whiting the feature matrix before k-means

I would like to use scipy.linalg.cholesky before scipy.cluster.vq.kmeans2 so the clustering will be on the "Mahalanobis" ...
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1answer
41 views

Evaluating two sets of random samples

Let $p$ be a probability distribution that can be computed tractably for any given point. I use two MCMC methods to generate samples from the distributions. For each MCMC method, I run 1000 Markov ...
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28 views

Why leverage measure the distance of the ith observation from the center of the x space? [duplicate]

I know the definition of leverage points in regression, that is $h_{ii}=x_{i}'(X'X)^{-1}x_{i}. $ In many places and text books, they always say that leverage is a standardized measure of the distance ...
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66 views

Calculate real-world disparity from disparity map

I am trying to estimate the distance moved by a car using stereo images captured from cameras mounted on a car. For this, I have planned on getting the depth to an object at time t0 and then get the ...
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55 views

Distance between random variables [closed]

I have found plenty of ways to compute the distance between random variables. However, I did not find any taking something else than the random variables as input. Do you know whether or not there is ...
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22 views

Compute probability from distance-score

I compute Euclidian distances between a point I want to analyze and a set of points I have. I want to sort my points by descreasing "similarity". I used to compute a "score" by inverting the distance ...
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1answer
80 views

distance measure of two discrete probability histograms (distance between two vectors)

I have multiple sets of discrete probability histograms(vectors) and I want to measure the distance between each histogram. I have done some research but I am in doubt. Literature suggest I could ...
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30 views

Selecting correct settings for the order of Minkowski distance

I am looking to compute the distance between vectors of word frequencies (and I am new to this). I am trying out the Minkowski distance as implemented in Scipy. The documentation asks me to specify a "...
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17 views

Does maximal Bhattacharyya coefficient imply mimimal total variation distance?

Some context: I`m working on numerical optimization (linear programming), on probability distributions denoted P,Q. We want to find the minimal total variation distance and maximal Bhattacharyya ...
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1answer
51 views

Get distance matrix directly condensed

I am developing a content-recommender Python system and most of my items (~8 millions) are static so I have thought about pre-computing the top 150 similar items for each item. This way, when a user ...
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1answer
63 views

Finding optimal correspondences between objects given two square distance matrices

I would like to find the optimal correspondences between two systems of objects based on the distances between objects WITHIN the two systems. So, the input to the algorithm would be two square ...
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20 views

Hamming distance of Bernoulli RV

Assume you draw $k$ data points out of $n$ data points. Each data point is composed of $m$ Bernoulli random variables. You may assume that the data points are i.i.d and likewise their coordinates, but ...
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1answer
37 views

Distribution-free test for two-sample multivariate distributions

Suppose that $X_1, \cdots, X_n$ and $Y_1, \cdots, Y_n$ are samples of $R^d$ vectors with distributions $X$ and $Y$ respectively. In addition, assume that there is one-to-one mapping between the first ...
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1answer
16 views

How to deal with non-independent data when comparing populations across a range of distances

I am trying to figure out how to carry out an analysis but am having trouble finding any information. I am interested in finding out whether values of sensitivity across populations are more similar ...
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36 views

Kolmogorov-Smirnov test between two distributions - R

I've two distributions computed on the same grid (that is, for each point of the grid I know the value of each CDF at that point). I want to check whether the two distributions are the same. I can't ...
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34 views

Distance Estimation from Signal Level?

So, I want to learn about machine learning and apply it to my project. I have set of data which includes position of a car and unknown emitter signal level. I have to estimate the distance based on ...
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22 views

Metric from a positive definite matrix

I'm trying to prove that the Mahalanobis distance is an actual distance, more in general Given B symmetric and positive definite matrix set d(x,y)=(x-y)'B(x-y) ( ...
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35 views

Elbow method implementation for hierarchical clustering

I've got a dataset that I need to divide intro clusters using hierarchical clustering algorithm. I've decided to try to employ an Elbow Method as a way of determining optimal no. of clusters k. ...
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Kullback-Leibler and Battacharyya divergences between Hidden Markov Models with discrete emissions

Im trying to figure out how to compute KL or Battacharyya divergences between two HMMs models. I found papers which are about HMMs with normaly distributed emissions, but nothing for discrete ...