# 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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### 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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### What is a good dissimilarity on rooted ordered labeled trees with probabilities on the leaves?

Consider a rooted ordered labeled tree that is "binary" in that there are at most two children of any vertex and whose leaves are decorated with probabilities (the sum of the leaf ...
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1 vote
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### How to define a distance metric between nodes of an Origin-Destination matrix?

I have an Origin-Destination matrix expressing (weekly) flows of people between every couple of nodes (cities). The number of people traveling from city $i$ to city $j$ in a specific week is $OD_{ij}$....
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### Help calculating the Bhattacharya Coefficient for measuring tracking efficiency

I'm working with OpenCV which has some tracking algorithms (BOOSTING, MIL, KCF, MEDIANFLOW, TLD, ...). I've read many papers where they use the Bhattacharya Coefficient to measure the efficiency of ...
1 vote
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### 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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### 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 ...
1 vote
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### 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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### 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 ...
• 327
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### 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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### 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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### 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 ...
1 vote
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### 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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### 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 ...
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### Determine outliers for robust Mahalanobis distance

I want to apply a robust mahal distance and found an implementation in scikit. but there is the number of outliers already given in advance. For me, who wants to find out the number of outliers, this ...
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### 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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1 vote
### 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 ...