Questions tagged [euclidean]

Euclidean distance is the intuitive notion of a 'straight-line' distance between two points in a Euclidean space.

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2 votes
1 answer
302 views

Should we apply PCA before calculating similarities in high-dimensional space if my observations have length 1?

I have high-dimensional space (around 20 features) and I want to calculate similarity based on the angle of observation, not the magnitude. I have a nice function that can compute euclidean distance ...
1 vote
1 answer
149 views

Euclidean distance between points in PCA space along different principal component dimensions

I've picked up this project half way through, and I'm working through the last guy's code, so please bear with me. So the original data consists of 500+ points in 150 dimensions, and I want to ...
0 votes
0 answers
14 views

Is cosine similarity enough to measure word embedding similarity?

Is cosine similarity a good metric to measure word embedding similarity? Suppose that we have two vectors of word embedding in same direction but with different length( first one with len=1 and second ...
0 votes
1 answer
31 views

In R perform k means clustering with k=3 and euclidean distance a 100 different times [closed]

I would like to perform k mean clustering with k=3 and the Euclidean distance a 100 different time. But it only gives me 2 iterations, how do i do a loop so it give me 100. Thanks
1 vote
1 answer
320 views

Does DTW return smaller distance measure than Euclidean Distance?

QUESTION 1: When computing the distance between two time series, shouldn't the DTW distance measure return a smaller distance than the Euclidean distance (assuming DTW internally uses the Euclidean ...
2 votes
1 answer
252 views

Cosine similarity for Categorical datasets?

Can I use Cosine similarity measure for estimating similarity/relationship between D1 and D2 (two categorical datasets)
2 votes
1 answer
148 views

Applying Dynamic Time Warping (DTW) instead of Euclidean Distance for Clustering Synchronized Time series data

I am trying to cluster members based on hourly login data. As this is mostly synchronized, I first applied Euclidean and it failed to cluster them into groups with sensible patterns. I tried DTW ...
1 vote
1 answer
236 views

Intuitive explanation of Ward's method

I got this explanation of the Ward's method of hierarchical clustering from Malhotra et. al (2017), and I don't really get what it means: Ward’s procedure is a variance method which attempts to ...
1 vote
0 answers
30 views

Similarity between datasets A and B where B is a subset of A

I have two datasets A and B, and for each entry in both datasets I have a mixture of ordered and unordered categorical variables such as gender, age (integral value) and date. It is believed that ...
1 vote
0 answers
57 views

What are the moments of the Beckmann distribution?

Let $U=(u_1, u_2)$ and $V=(v_1, v_2)$ be two randomly distributed points on the Euclidean plane assuming bivariate normal distributions $U \sim N(\mu_u, \Sigma_u)$ and $V \sim N(\mu_v, \Sigma_v)$ with ...
2 votes
0 answers
100 views

About the calculation of covariance matrix in mahalanobis distance: How $W^TW$ is equal to the covariance matrix? [closed]

I was reading about deep metric learning (from here) and came across the mahalanobis distance. I understood why we can not use euclidean distance if the distribution is not isotropic (the covariance ...
0 votes
0 answers
572 views

Analysis or Comparison of Euclidean Distance matrix

Related: Average distance in distance matrix I'm looking for some way to compare euclidean distance matrices. The matrices I need to compare will have constant number of rows but varying number of ...
2 votes
1 answer
293 views

Cosine similarity seems to perform better with higher dimensions than Euclidean distance? Should this be the case?

I've generated 100 random vectors (data points) in n∈[1,...,50] dimensions. I then compared distances between each pair of vectors and calculated the mean value. I've done this for all dimensions ...
2 votes
2 answers
235 views

How to define distance for vector of angles?

I have a vector of angles and I am looking for a method to compute the distance of my vector with any other vector of angles? I am looking for something similar to Euclidean distance but I know that ...
0 votes
2 answers
1k views

How k-means computes cluster centroids differently for each distance metric?

K-means computes cluster centroids differently for each distance metric. I don't know why the way of computing the centroid is dependent of the distance measure. I don't know how we compute the ...
17 votes
4 answers
44k 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: http://en....
4 votes
1 answer
2k views

Is one-hot encoding and standardization of data equivalent to Gower's distance?

For clustering and other techniques for mixed data (numerical and categorical), Gower's distance is usually more preferred than Euclidean distance because the former computes distance differently for ...
0 votes
0 answers
539 views

Euclidean distances in spaces of different dimensions

A modest attempt to illustrate my question: Setup Consider a survey where you have to choose if you like to do an activity or not. You do this for a number of activities $A_1,...,A_8$. In addition, ...
1 vote
0 answers
63 views

Euclidean Norm normalized Normal Distribution

Let $X$ be a multivariate normal $\mathcal{N}(\mu, \Sigma^2)$ and let $X$ be anistropic, that is I am considering $\Sigma$ to be a diagonal matrix but the elements on the diagonal might be different. ...
0 votes
0 answers
17 views

Significance test for comparing two mean Euclidean distances?

First time poster here, so please let me know if more details are needed! In short, I'm analyzing a dataset that has scores from 98 siblings from 64 families. So some families contributed only one ...
14 votes
3 answers
38k views

Which distance to use? e.g., manhattan, euclidean, Bray-Curtis, etc

I am not a community ecologist, but these days I am working on community ecology data. What I couldn't understand, apart from the mathematics of these distances, is the criteria for each distance to ...
21 votes
5 answers
21k 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 ...
1 vote
0 answers
124 views

What is the effect of the limitations of Euclidean distances in high dimensions to multiple regression?

This is eye-opening, and the effect on KNN, for example, is easy to predict, but should the limitations of Euclidean distance in high dimension be a reason for concern in the very common application ...
3 votes
1 answer
535 views

Distances between random points in a hypercube and statistics of exponents

TL;DR: Why is $\text{avg}\left(|a-b|^k\right)=\frac{2}{(k+1)(k+2)}$? I.e. for $k=2$, as for finding average Euclidian distances, the result is $\frac{1}{6}$? I've been reading a book about "Corobs," ...
0 votes
1 answer
65 views

Is Euclidean distance the same as distance-from-correlation as $d(x, y) = \sqrt{2m[1 - r(x, y)]}$

I found in a couple of documents (e.g. this) that the Euclidean distance $d(x, y) = \sqrt{\sum_{i = 1}^{n}{(x_i - y_i)^2}}$ can be obtained from correlation coeffcient if $x$ and $y$ are standardised ...
0 votes
1 answer
18 views

How can I cluster plant biomass and grain weight for different plant varieties using Ward's method based clustering?

I have plant biomass and grain weight data for different plant varieties which I now need to cluster. Do I need to define the number of clusters if using Ward's method and Squared Euclidean distance ...
1 vote
0 answers
65 views

How to find the average distance between randomly distributed points in a rectangle?

Assume there are n points randomly distributed in a rectangle (x being the height y being the width) shown below in the figure. I would like to calculate the average distance between 2 random red ...
0 votes
1 answer
284 views

What is the difference between these distances in self organized maps

I am building an anomaly model and am confused between these distances below. What is the difference between these distances in self organized maps. som.iris$distances dist(som.iris$codes[[1]]) As ...
3 votes
1 answer
2k views

Difference between Euclidean, Pearson, Geodesic and Mahalanobis distance metrics

Given a set of samples $X$. We are tasked to find an appropriate distance metric for $X$ from the given options which are Euclidean Pearson Geodesic and Mahalanobis distance metrics. To solve this, ...
1 vote
1 answer
157 views

Measuring similarity of observations (non numeric)

I have a dataset of format : day,measurement1,measurement2 1,a,b 1,a,c 1,f,s 2,a,b 2,a,c 2,f,g 3,a,d 3,a,q 3,f,s In this example day1 is more similar with day2 ...
2 votes
1 answer
99 views

Non-Euclidean analogue to MSE loss

The most basic machine learning model called OLS uses the RSS (squared loss) or its average, mean squared error (MSE), for its loss function, which is aligned with Euclidean geometry. What is the ...
5 votes
2 answers
3k views

Z-Normalized Euclidean Distance Derivation

I am going through this paper: http://www.cs.ucr.edu/~eamonn/PID4481997_extend_Matrix%20Profile_I.pdf And on Page 4, it is claimed that the squared z-normalized euclidean distance between two ...
2 votes
1 answer
153 views

Probability of one point being closer to fixed $x \in \mathbf{R}^2$ than another

Let $x, x^{(0)}, x^{(1)} \in \mathbb{R}^2$, $r_1, r_2 \sim U[-1, 1]$. Point $x$ is fixed, $x = (0.32, 0)$, and $x^{(0)} = (0, r_1)$, $x^{(1)} = (1,r_2)$. What is the probability that the fixed point $...
0 votes
1 answer
73 views

Generate Uniform Random Variates with Constant Norm [duplicate]

How can one generate $k$ uniform random variates centered at zero, $X_1, X_2, ..., X_k$, given a constant Euclidean norm, $c =\sqrt{X_1^2+X_2^2+...X_k^2}$?
90 votes
7 answers
38k views

Euclidean distance is usually not good for sparse data (and more general case)?

I have seen somewhere that classical distances (like Euclidean distance) become weakly discriminant when we have multidimensional and sparse data. Why? Do you have an example of two sparse data ...
0 votes
0 answers
437 views

PCoA/MDS on sqrt transformed Bray-Curtis dissmilarity using cmdscale

I would like to use PCoA to visualize beta diversity of a large community. I chose Bray-Curtis as distance measure to calculate the dissimilarity matrix and would like to apply a square root ...
0 votes
0 answers
149 views

Euclidean distance from zero

I am trying to create my own weights for relative work task importance, or weight. For every task, I have a value of importance, ...
87 votes
6 answers
149k views

Why does k-means clustering algorithm use only Euclidean distance metric?

Is there a specific purpose in terms of efficiency or functionality why the k-means algorithm does not use for example cosine (dis)similarity as a distance metric, but can only use the Euclidean norm? ...
3 votes
0 answers
3k views

Appropriateness of Hierarchical Cluster Analysis with Bray-Curtis Dissimilarity Matrix

I am looking at a zooplankton community assemblages using hierarchical cluster analysis, indicator species analysis, and non-metric multidimensional scaling based on Bray-Curtis dissimilarities. My ...
7 votes
2 answers
456 views

Variance and asymptotic normality of $\frac{1}{n-1}\sum_{i=1}^{n-1}(x_{i+1}-x_i)^2$, where $X \sim \mathcal{N}(0,1)$

Consider a length $n$ vector $\mathbf{x}$ containing $n$ i.i.d. observations $\{x_i\}_{i=1}^n$ of a standard normal random variable $X$. Let $\mathbf{z}$ be a length $n-1$ vector whose entries are $...
0 votes
0 answers
40 views

Plotting Vector Embeddings

I am currently working on a project that requires some form of data on the paper. Even though I was able to get some coding done and communicate results, I need some graphs. What I want to do is ...
0 votes
0 answers
50 views

Manhattan vs Euclidian Distance Measure [duplicate]

In which case we should pickup Manhattan distance and when we should use euclidian distance measure. To my understanding both are used for continues numeric data(not like cosine or others who works ...
13 votes
1 answer
4k views

Why is Kullback-Leilbler divergence a better metric for measuring distance between two probability distributions than squared error? [duplicate]

I know that KL-divergence is a metric that is more suitable when we want to measure the distance between numbers which a probability form. However, I am still confused what is the benefit of using KL-...
1 vote
1 answer
130 views

How to find the list of nearest vectors if ony a vector is given?

I know there are many ways to compute similarity of two different non-zero vectors but is it possible to get a list of nearest vectors whose values are continous given a single continous vector. Lets ...
15 votes
1 answer
35k views

Cosine Distance as Similarity Measure in KMeans [duplicate]

I am currently solving a problem where I have to use Cosine distance as the similarity measure for k-means clustering. However, the standard k-means clustering package (from Sklearn package) uses ...
1 vote
2 answers
458 views

How Rapidminer handle same distance for KNN Algorithm

Actually I already asked in rapidminer forum, but no one has given an answer yet.. https://community.rapidminer.com/discussion/55963/how-k-nn-algorithms-work-with-same-distance-in-rapidminer#latest ...
1 vote
1 answer
677 views

Comparing distance of two matrices with different sizes using eqdist.etest function in R

I want to compute a test statistic based on the Euclidean norm of two data matrices with same number of columns (i.e variables) but very different number of rows (i.e observations). I am using the ...
1 vote
0 answers
71 views

the accuracy of covariance between two high-dimensional vectors

Question Is the covariance between high-dimensional vectors less accruate than covariance between two vectors in low-dimensional vecotrs? I am asking this questio to check if there is a need for '...
0 votes
0 answers
615 views

Difference between standardizing variables and using Mahalanobis distance

I am wondering how and/or why the Mahalanobis distance is different from using the Euclidean distance on standardized variables?
0 votes
1 answer
1k 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?