Questions tagged [distance-functions]
Distance functions refer to functions used for quantifying the notion of distance between members of a set, or between objects.
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How can one compute the “average” of a dataset of histograms that minimizes the mean Earth Mover's Distance between all data points and average?
It is my understanding that when the distance metric is euclidean distance, the mean of a dataset minimizes the average distance between all data points and the computed "mean".
In the case ...
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8 views
Relative mean squared error in functions estimation
The questions are actually two:
What is the best way to define a relative error in function estimation?
And what the best to define a relative mean squared error for the estimation of multiple ...
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15 views
Measuring the overlap between two probability distribution [duplicate]
I have many probability distributions, I need to compute the amount of overlap between two probability distributions. I don't know the type of distribution since it really depends on the data itself.
...
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1answer
22 views
Modified distance functions for a cluster analysis
I'm developing some software to allow users to perform various kinds of clustering on some data using a pairwise distance matrix (k-medoids is the main method). I would like to allow the user to tune ...
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44 views
Using KL divergence as a feature selection method
I have a set of features for a binary classification problem. The KL divergence could be considered as how one (probability) distribution differs from another. In a practical sense, I could use this ...
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1answer
24 views
Measure of distance between two survey responses
I've found some survey data where respondents answer 63 question by giving a response for each question between 0-10 (0 for strong disagreement, 10 for strong agreement). So I can view every ...
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1answer
94 views
High Dimensional Swiss Roll? (For Metric Learning/Dimensionality Reduction)
So I've just started a project which includes some metric learning, and came accross this swiss roll in 3D to 2D problem. Ideally, you should 'unroll' the roll.
My question is, can this be extended ...
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13 views
Splitting method for time series
Say I have a website with a lot of pages and traffic. Some of them are more visited, some of them a less. My task is to split pages into two groups for the given time period, so that the total traffic ...
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37 views
How to Show Wasserstein Metric is Sum Invariant?
A paper I'm trying to understand states that that Wasserstein metric obeys certain properties, which I'd like to prove. This metric is defined for two random variables $U, V$ and $p \in (1, \infty)$ ...
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33 views
Measuring the amount of total influence between variables?
I have a group of people with a series of yes/no questuins about preferences in various topics. The thing is they could see each other answers and change theirs hence might be influenced by a common ...
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1answer
56 views
Do $k$-means, dbscan, and hierarchical clustering all rely on (pseudo)metrics?
I seems to me that the clustering methods $k$-means, dbscan, and hierarchical clustering all work on distance measures $d$ that are (pseudo)metrics, i.e., fulfill the following requirements:
$$ d(x,x)=...
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486 views
Is Jaccard similarity/distance suitable for non-binary, quantitative data?
I have a dataset with each row a country and 10 columns with numerical features like GDP,Electrcity consumption, GNI etc. I am trying to use distance metrics to find similarity between the countries ...
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Creating a covariance matrix from a distance matrix—normalizing matrix with infinity
I'm trying to simulate spatially autocorrelated data by creating a covariance matrix from a distance matrix and using said covariance matrix as the $\Sigma$ parameter of a multivariate normal.
I have ...
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1answer
308 views
What's an intuitive way to understand how KL divergence differs from other similarity metrics?
The general intuition I have seen for KL divergence is that it computes the difference in expected length sampling from distribution $P$ with an optimal code for $P$ versus sampling from distribution $...
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15 views
How to calculate similarity between two sets of items rated on a single dimension?
(I'm just making up variables for this example.)
Let's say I have 100 words rated on their pleasantness.
I also have 100 images rated on their pleasantness.
I then had participants rate the fit ...
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1answer
57 views
Is there a distance metric between ordered vectors?
I am looking for a distance metric between vectors whose elements are ordered,
i.e so the vectors:
[1,5,0,0,0,0,1], [1,0,4,0,0,1,0]
will be considered closer than
[1,5,0,0,0,0,1], [1,0,0,1,5,0,0]
for ...
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57 views
Metric to measure distance between two percentage values [duplicate]
I would like to find a function that measure how much two percentage values differ from each other. Now, a norm $\|\cdot \|$ does not quite fit this criterion as a jump from 1% to 30% is, for many ...
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1answer
26 views
Ordering list of items by two criteria
I have a list of items with two scores: scoreA and scoreB. To be more specific they represent the average of a list of accuracy scores and their maximum. Both of the scores range from 0 to 100%. I'm ...
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81 views
Jaccard/binary (dis)similarity calculation to multidimensional scaling analysis
I have n N x n dataset of features (n) and subjects (N) in which I am attempting to cluster into a lower-dimensional space via multi-dimensional scaling.
I'm confused about which MDS setup I need to ...
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21 views
Distance metric for probability distribution
I'm looking for a distance metric that would be good for what I think is a probability distribution:
I have a fixed number of samples
I have a fixed number of features
Each sample can have, at most,...
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0answers
10 views
How to define a weight function for response time?
I have a repeated measurement over time and the variable of interest is user compliance. However, since users use different questionnaire length, the duration of response time is also important. I ...
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0answers
9 views
Distance in Square between Randomly Selected [duplicate]
I am trying to find the expected Euclidean distance between independent, randomly-selected variables in the unit square and I have some technical questions. For co text, I know if we were selecting ...
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72 views
What is the difference between np.linalg.norm(x-y,axis=1) and np.linalg.norm(x-y)?
I'm creating a K-Medoids algorithm from scratch in Python using numpy, and I'm in the process of using a distance function to determine the cluster center. I want the center to be the point in the ...
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20 views
distance between two lists
I am using the normalized manhattan distance (L1-norm) between two lists as a metric to measure how much change has happened. Let's call this changeIdx .This ...
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0answers
25 views
Similarity between clusters/groups?
I have a dataset consisting of multiple groups in a high dimensional space. An example is shown below:
What would be the best way to calculate similarities between groups. Say how similar is group A ...
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233 views
How to calculate Mahalanobis distance in very high dimensions with both continuous and categorical variables?
The objective is outlier detection via a distance measure.
Does mahalanobis distance suffer from curse of dimensionality just like Eucledian distance for
very high dimensions? (say around 5000 ...
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46 views
Hierarchical clustering: distance/linkage combination that allows starting in the middle of the dendrogram
I want to use hierarchical clustering to classify some ecological data (species abundances on different places), so I would like to use a Manhattan type distance that doesn't account for double ...
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Finding the relative 'importance' of different vector components when defining distance of two vectors in a space [duplicate]
I have a multi-dimensional space with $d$ dimensions wherein $i$ vectors ($v_1 ... v_i$) with $d$ components live. I want to find a function $s(v_a, v_b)$ which takes in two of these vectors and ...
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1answer
51 views
Metric for distance of sinewaves
I have time-series data consisting of the sum of 2 sinewaves and my goal
is to predict their frequencies and their amplitudes.
I would like to know what are the best distance metrics/loss functions I ...
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1answer
44 views
How to unsupervised-cluster of binary vectors?
I have a set of binary vectors of roughly 500 dimensions. For EDA purposes mainly, I'd like to cluster them, maybe hierarchically.
What could be the right distance metric for my problem?
Is the ...
2
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0answers
31 views
Determine outliers for robust Mahalanobis distance
I want to apply a robust mahal distance and found an implementation in scikit: https://scikit-learn.org/stable/auto_examples/covariance/plot_mahalanobis_distances.html
but there is the number of ...
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89 views
Distance measure for two probability distribution of unequal sample size
Context: I have 100 stores and these stores are divided into 10 business markets. I want to select 3 markets where each market is a good representation of the 100 stores i.e. the population.
There ...
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34 views
How to transform $P[k_1\leq (x_i-\mu - \sigma\cdot Z)^2 \leq k_2]$ to $P[k_1\leq \frac{(x_i-\mu)^2}{\sigma^2}+e \leq k_2]$?
Taste estimation
As an example consider an experiment conducted to determine the optimal concentration of salt in popcorn. The concentration of salt in sample $i$ is denoted by ${x_i}$.
The subject ...
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1answer
47 views
Understanding PAM - why is it greedy?
I've been studying k-medoids for a while but i can't understand the first step or BUILD step: in particular i can't get how the initial medoids would be "greedy". I'm not much confident with the ...
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82 views
How to measure the difference between two random forest models?
Suppose that I have training data defined as a set of N records (or samples) defined by its attributes (or descriptors, features, as you prefer), and I trained two random forest models with two parts ...
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1answer
86 views
Mahalanobis distance - understanding the formula [duplicate]
I've read quite a few explanations on this topic, liking this one the most:
https://mccormickml.com/2014/07/22/mahalanobis-distance/
But there is still one thing I don't understand.
I understand ...
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46 views
Type of logarithm in Jenson-Shannon and Bhattacharyya distance
Both Jenson-Shannon and Bhattacharyya distance can be used to measure the similarity of two probability distributions.
Bhattacharyya distance between two distributions $p$ and $q$ is defined as $D_B(...
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1answer
22 views
Dissimilarity or distance metrics between pairs of values
I have cubes (objects) in which their volume was manually calculated (let's call this method the "manual method". Assume that the volume measures obtained by this method are considered the "true" ...
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1answer
387 views
Am I right that Calinski-Harabasz index (Pseudo-F) can not be calculated from a distance matrix other than euclidean?
Part:
I wonder if one could calculate the Calinski-Harabasz index when only having a distance matrix (and a cluster solution, of course). As you need the within and between sum of squares to come up ...
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Does Mahalanabis Distance have something to do with Min-Max normalisation? [duplicate]
Does Mahalanabis Distance have something to do with Min-Max normalisation?
I know that it has something to do with Z-score normalisation, but when I tried Mahalanabis Distance on the Min-max ...
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1answer
618 views
Is Hierarchical clustering a special case of knn(specific n=1)?
I'm working on time series in the scope of similarity detection at the moment. What seems to be a well researched approach is dynamic time warping in combination with k-1NN as classification ...
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1answer
60 views
Non-metrics give “pathological” solutions: what does this mean?
In this set of slides on DTW, slide 25 says that we generally prefer metrics over measures because,
"Non-Metrics can sometimes give pathological solutions when clustering or classifying data etc."
...
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0answers
166 views
Which distance metric to use to cluster categorical sequences (clickstreams or clickpaths)?
For my research, I want to cluster website visitors based on their clickstreams to understand different information behavior patterns (i.e., customer/visitor journeys). The data can be characterized ...
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31 views
Proxy for Mahalanobis distance when n < p? [duplicate]
I'm working on a ranking problem where I want to measure the distance between a collection of query points (as a group) and each target point in my database. Each query point is part of the set of ...
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1answer
25 views
Finding the effect of nodes on a density heatmap
Let's say I have a geo-tagged dataset of all payment transactions for businesses in a city. I know whether each payment is made by cash or card, and have made a heatmap of where in the city the ...
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348 views
Relationship between KL divergence, JS divergence, and MMD?
What kind of relationship is there between the KL (Kullback-Leibler) divergence, JS (Jensen-Shannon) divergence, and MMD (maximum mean discrepancy)?
I know that they all share a global minimum at $P=...
3
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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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48 views
Distance between two distributions
I am analyzing time-series data, and I would like to detect a significant change in data distribution. I already know about Bhattacharyya distance, but that requires histograms of equal-sized bins. ...
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1answer
1k views
Calculation of relative distance
I have 100 term triplets as shown in the below mentioned figure. Each triplet contains 3 objects namely x, y and z. I want to rank the triplets according to the following two properties.
y should be ...
3
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1answer
231 views
The violation of triangle inequality in KNN
If the 0<p<1 in the distance metrics, then the triangle inequality is violated.
The question as follows
Does the violation of this inequality affect the ...
