# 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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### Normalizing Euclidean distance by the length of the vectors [closed]

Suppose I have 4 vectors, the first 2 vectors are of length 4 and the last 2 vectors are of length 400. all values in the vectors range from 0.5 to 0.6. The Euclidean distance between the last 2 ...
54 views

### Correlation vs Euclidean distance as measures of similarity or closeness between data points with an outlier

I am interested in the comparison of Pearson correlation and Euclidean distance as measures of similarity between data points. Suppose I have 4 data points, w, x, y, z, in a multidimensional space, ...
39 views

### Is "ward.D" a good agglomeration method in R?

I need to do clustering on a large scale file (~12M rows, 18 features + id index). As a first step, i tried different algorythms in Python with a test sample (40k rows) which gave results (clearly ...
71 views

### Word embedding and Euclidean distance

Does a transformation exist that allows to use of the Euclidean distance with the word embeddings? The Cosine distance could be a problem in my case. For example, what if I translate the vector to a ...
70 views

### Best way for measuring dispersion in two dimensional, continuous data

I have a list of coordinates for where different people live over an eight-year period. They are repeat cross-sections of populations served by several county agencies for free workforce training for ...
213 views

### How to choose the Normalization method for a co-occurence matrix?

I have a co-occurrence matrix about hashtags usage (The value in the cell means the number of times two hashtags appear together in a single tweet), it is transformed from a 2-mode matrix. Now I want ...
111 views

### normalizing euclidean distance

I asked a question in SO but was told it is more appropriate here. I'm trying to compute the euclidean distance with vectors of different lengths. ...
1 vote
199 views

### What are the downsides of using euclidean distance for hierarchical clustering of a correlation matrix?

Apologies if this has been answered elsewhere, but I couldn't find any answers discussing this specific question. I am lacking some notion on clustering using euclidean vs correlation distance, when ...
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### Euclidean distance between points in high dimensions

On Wikipedia there's a statement: When a measure such as a Euclidean distance is defined using many coordinates, there is little difference in the distances between different pairs of samples. Is ...
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### How to compare two very large vectors that each represent a probability mass function?

As far as I know, given two vectors that each represent a probability mass function, their difference can be measured using Euclidean distance, Kullback–Leibler divergence, cross entropy and so on. ...
125 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 ...
80 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
1k 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 ...
1 vote
3k 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
58 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
148 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 ...
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### 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 ...
1k 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 ...
537 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 ...
1 vote
130 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. ...
393 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 ...
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### 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 ...
1 vote
169 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 ...
1 vote
171 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 ...
26 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
125 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 ...
139 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 ...
162 views

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### 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 ...
544 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 ...
65 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 ...
51 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 ...
1 vote
220 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 ...
1 vote
531 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
98 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 '...
1 vote
808 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?
5k 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-...
214 views

### Clustering high dimensional data

I was going through this wiki page on clustering in high dimensions and I don't understand the following statement there. Can someone explain to me what this means? The concept of distance becomes ...
3k 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, ...
74 views

### What is the specific normalization chi2 in seqdist?

In the documentation for the seqdist() function it is noted that there is "...a specific normalization for"CHI2" and "EUCLID". See the Details section." (p.60). But in the details section there is no ...
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### Is my variable considered okay to use in k-means clustering with Euclidean distance?

I was wondering if I can use regular kmeans() in R with my variable "number of drug prescriptions" which equals a number between 1-25. From what I've read k-means ...
1 vote
293 views

### Set similarity as weight to ratings

I have a problem deciding which similarity function to use. I want to find the similarity between the users based on their requirements about computer performance metrics normalized to 1. Each user ...
363 views

### What to do when results of hiearchical, k-means elbow, and k-means silhoutte disagree?

I am conducting a cluster analysis involving 60 subjects and 5 continuous variables. After appropriate scaling, I performed hierarchical clustering with Euclidean distance and complete linkage, and ...
1 vote
If we want to calculate the squared distance between 2 vectors, $x$ and $y$, we use the dot product: $$||x-y||^2 = (x-y)(x-y)^T = xx^T - 2xy + yy^T$$ The question is, how to generalize this concept ...