Questions tagged [euclidean]
Euclidean distance is the intuitive notion of a 'straight-line' distance between two points in a Euclidean space.
130
questions
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25 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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0answers
11 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 ...
6
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2answers
249 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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0answers
16 views
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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0answers
10 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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0answers
12 views
Is nearest neighbor in low dimensional setting is still the nearest in high-dimensional setting?
I have developed a semi-supervised outlier detection algorithm using K-nearest neighbor approach, where I obtain statistical distributions of Euclidean distances for K-neighbors. I wanted to test it ...
2
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1answer
22 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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0answers
30 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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0answers
35 views
How does one calculate maximum dissimilarity?
I created this test Dataset
data <- data.frame(Gene1 = c(1,2,1,8,9,7), Gene2 = c(5,6,6,3,4,4), Class = c("Male", "Male", "Male", "Female", "Female", "Female"))
...
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0answers
19 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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0answers
40 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
26 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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2answers
197 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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0answers
38 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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147 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?
9
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1answer
1k 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-...
0
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2answers
70 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 ...
1
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1answer
408 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
1answer
39 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 ...
3
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0answers
33 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 ...
0
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0answers
87 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 ...
3
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1answer
144 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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0answers
193 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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0answers
590 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 ...
2
votes
1answer
883 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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0answers
322 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 ...
2
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1answer
186 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 ...
2
votes
1answer
65 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 ...
0
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1answer
126 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
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1answer
518 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 ...
0
votes
1answer
88 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 ...
1
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1answer
284 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 ...
9
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1answer
841 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 ...
0
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1answer
140 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 ...
1
vote
1answer
33 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 ...
2
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0answers
424 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 ...
0
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0answers
288 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 ...
4
votes
2answers
954 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 $...
2
votes
0answers
88 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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0answers
30 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 ...
3
votes
0answers
150 views
Which dimensionality reduction technique preserves the k nearest neighbors (euclidean space)?
I'm looking for a lower dimensional projection of data such that the k nearest neighbors (in Euclidean space) in high dimensions remain the k nearest neighbors in low dimensions. I found that Isomap ...
0
votes
1answer
170 views
Normalized weighted Euclidian Distance
Hi Guys I would like to get an euclidian distance and be able to compare multiple set o data but I am not sure how to normalized it properly
Each data set have values ranging from (-100->100) and ...
1
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0answers
673 views
Distance Matrix for Big Data
I have been struggling to create a distance matrix for some Big Data (800,000x20). I have tried R (dist function), Matlab (pdist function), and cloud computing (to increase RAM).
Ultimately, the ...
0
votes
1answer
882 views
Distance between all the dots in a scatterplot in R [closed]
Is there any possibility in R to get a list of distances between all the points in a Scatterplot? For instance, this Scatterplot:
So, I would like to obtain a list of distances among all the points.
4
votes
1answer
5k views
Explanation for MSE formula for vector comparison with “Euclidean distance”?
I study the loss functions for regression tasks with artificial neural networks. In case of evaluating loss with Mean Squared Error for multidimensional outputs I read the following usual formula ...
0
votes
1answer
302 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 ...
0
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1answer
201 views
Mathematical term for finding the variance of the euclidean distance between two matrices of the same dimension?
Is there any mathematical term for carrying out this procedure. I am finding the euclidean distance between the rows of the matrices by treating them as individual vector. Then I get a single vector A ...
0
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0answers
480 views
Why is only Euclidean distance allowed to be used for Ward's method? [duplicate]
Using scipy, I noticed that I am allowed to use only Euclidean distance for Ward's method.
Is it because Ward's uses Error Sum of Squared?
What if I use Ward's method with cosine similarity?
Cosine ...
1
vote
1answer
43 views
Measuring simmilarity 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 ...
1
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0answers
371 views
Dummy data clustering: OK to apply Euclidian distance hierarchical clustering on Jaccard similarity matrix?
I created dummy variables (binary data) from categorical variables where I want to partition N subjects into multiple classes by some clustering method. I created a Jaccard similarity index matrix for ...
