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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14 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 ...
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77 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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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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13 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 ...
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18 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 ...
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15 views

Hierarchical agglomerative cluster analysis

I have recently compiled a simple script to make cluster dendrogram using euclidean distance as the distance metric and Ward's method as the linkage. I am try to calculate Wishart's Objective ...
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1answer
59 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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17 views

Best way to compare time series data similiarity

I have two time series'. One represents ground truth heart rate in a a subject (top in blue), and the other a prediction of heart rate using a novel method (bottom in orange). It looks like this: ...
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1answer
137 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 $...
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52 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, $c =\sqrt{X_1^2+X_2^2+...X_k^2}$?
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83 views

Cosine similarity for Categorical datasets?

Can I use Cosine similarity measure for estimating similarity/relationship between D1 and D2 (two categorical datasets)
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111 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 ...
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47 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, ...
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108 views

Performance of model decreases when calculating Euclidean distance between vectors with TF.IDF weigths compared to TF weights

My problem in short: I use Jaccard similarity, cosine similarity and euclidean distance to compute a similarity between documents. The documents consists of either the words,hashtags or combination of ...
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295 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 $...
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Is a normalized cosine similarity a bregman divergence?

A Bregman divergence is defined as $D(p,q) = F(p) - F(q) - < \nabla F(q), p-q>$ with F a strictly convex function of the Legendre type. Squared Euclidian distance is a Bregman divergence, with $...
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17 views

How best to compare Euclidean distance error and latency across two different scales?

I have two sets of data from two different behavioural tasks, in which participants make judgements as to where an object should be within a circle. In one task, the circle has a diameter of 6 metres, ...
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61 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 ...
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84 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 ...
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22 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 ...
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44 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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1answer
28 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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283 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 ...
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42 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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321 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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2k 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-...
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90 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 ...
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1answer
809 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, ...
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1answer
51 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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34 views

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 ...
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134 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 ...
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1answer
186 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 ...
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215 views

How to improve Pairwise Euclidean Distance for Similarity Measure

I am trying to identify the most similar stations between two DataFrames like below: ...
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912 views

Dot Product and Distance Matrix

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 ...
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1answer
1k 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 ...
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425 views

Clustering: choosing correlation-based over euclidean distance (fviz_dist)

I'm trying to cluster some business data. You can imagine the data as describing customers (age, no. of purchases, satisfaction after the first purchase, etc.). I work with normalised data. I also ...
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1answer
388 views

$L_2$ norm of product of two vectors

Let's assume we have two matrices $A^{d\times 1}$ and $B^{1 \times e}$, and we define their product as $C^{d\times e}$. Assuming $A,B$ are real valued with all entries in $[-1,1]$. I can intuitively ...
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1answer
82 views

Distance metric with characteristics of cosine and Manhattan

I'm working on a project where I want to find similarities between groups of events. So far I have expressed groups of events as vectors of event counts and computing similarities between them. I'm ...
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1answer
287 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, ...
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1answer
680 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 ...
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1answer
141 views

Similarity between 2 profiles (observations). Is it possible to generate a % similarity?

I have multiple profiles for 10 different people. Each person has been measured for 5 different continuous variables of different magnitudes. So my dataframe is 10x5 where each row represents a person ...
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1answer
394 views

Does it make sense to cluster asymmetric binary data with Ward's method?

I'm working with 104x42 data set where all variables are (asymmetric) binary (0-1). I've read that Ward's linkage method doesn't work theoretically properly with binary data beaucause it requests ...
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1k views

My neural network can't even learn Euclidean distance

So I'm trying to teach myself neural networks (for regression applications, not classifying pictures of cats). My first experiments were training a network to implement an FIR filter and a Discrete ...
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1answer
194 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 ...
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1answer
37 views

Hierarchical Cluster Analysis of 100 objects with 114 variables each

I'm intending to make a cluster analysis of 100 objects. I've read a couple of books and determined that a Hierarchical agglomerative procedure with Ward's linkage method should be used in my case. As ...
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576 views

Obtain within-group Gram matrix out of distance matrix

Gram matrix Let $\bf X$ be a n x p dataset with columns (variables) centered. Then p x p $\bf X'X$ is the total scatter matrix ...
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386 views

Common methods to calculate total distance from data with categorical, continuous and counting variables

I have a data set with categorical, continuous and counting variables. I want to be able to use a method that will give me a distance for each pairwise data point. From my understanding, each type ...
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2answers
1k views

Is the maximum bound of Euclidean distance between two probability distributions equal to $\sqrt{2}$?

I used Euclidean distance to compute the distance between two probability distribution. The example of computation shown in the Figure below. As my understanding, the maximum distance occur while $...
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96 views

Recovering a distance matrix from nonnegative sparse correlation matrix?

After doing extensive literature research in all sorts of science I am completely puzzled. I am trying to find out what the state-of-the-art techniques would be to recover a (let's say euclidean) ...
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34 views

Shrinking the mean: distance loss function and risk function

I'm reading some slides about the shrinkage of the mean and I cannot understand some results. Assume an n-dimensional vector $\mathbf{x} \sim N(\mu, I_n)$. We are interested in obtaining an estimate ...