# 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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34 views

### Comparison of two test metrics

I'm trying to compare two test metrics (Metric A and Metric B) to determine which one better predicts a delta value, which represents a Euclidean difference. I am unsure how to determining which ...
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1 vote
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### Are there strategies for measuring accuracy of Euclidean distance-based similarity without ground truthing?

I have subjects with about 200 features each. These feature vectors are stored in a vector database, where similarity searching with Euclidean distance is used to find subjects that are similar to a ...
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### Using one distance metric on another distance matrix

In general, is it correct to use one distance metric on another distance matrix? For example, is it valid to use Euclidean metric on Jaccard distance matrix as input data in algorithms? or any other ...
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### What is the standard threshold value that is best for accuracy when employing Euclidean distance as a metric for gauging textual similarity?

I'm using Euclidean distance as a metric to compare two sentences for similarity while clustering them using my custom incremental KMeans algorithm. The current threshold value I'm using is 0.7 which ...
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### Distance metric for dummy and continous variables

I'm trying to apply the KNN regression model to the data I have at my disposal which contains one dummy variable and two continuous variables (which I have normalized). I was wondering if it is okay ...
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### Panel data clustering - how to assess the distance between individuals when the data are multivariate and longitudinal?

I have an (unbalanced) panel dataset with 20 countries, 57 years, and 8 variables, and I would like to cluster the countries according to their dynamic trend in these variables (whether using kmeans ...
281 views

### 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 ...
561 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, ...
61 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 ...
329 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 ...
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210 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 ...
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### 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 ...
177 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. ...
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1 vote
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### 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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### 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 ...
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### 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
2k 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 ...
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1 vote
5k 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
67 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 ...
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1 vote
187 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 ...
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### 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 ...
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### 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 ...
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1 vote
150 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. ...
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### 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
185 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 ...
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1 vote
203 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 ...
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### 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
158 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 ...
159 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 ...
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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 ...
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### 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 ...
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### 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 ...
53 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 ...
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1 vote
240 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 ...
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1 vote
548 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
101 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 '...
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1 vote
956 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?
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### 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-...
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### 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 ...
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, ...