# Questions tagged [mahalanobis-distance]

Question that relates or uses the Mahalanobis distance metric.

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### Instability in Calculating Mahalanobis Distance

I am trying to calculate Mahalanobis distance from a point to a cluster of points. The code below does that. ...
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### What does the $\sum^{-1}$ mean in “$(x-\mu)^T\Sigma^{-1}(x-\mu)$”?

In the following multivariate normal distribution formula the $\sum^{-1}$ seems very unintuitive. Is $(x-\mu)^T\Sigma^{-1}(x-\mu)$ the same as $\Sigma(x-\mu)^2$? If not, what is it and why? ...
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### What is a useful distance metric (euclidean?) if I want to compare different amounts of attributes depending on the instance being compared?

Imagine that I have a data set with 15 examples, and each has 100 attributes. I want to use these 15 examples to classifiy unseen examples based on the similarity/distance between them. The ...
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### Solving for a point where Mahalanobis distances are equal

I am trying to find a general solution for $x$ in the equation $$(x-\mu_1)^T\Sigma_1^{-1}(x-\mu_1)=(x-\mu_2)^T\Sigma_2^{-1}(x-\mu_2)$$ where $x,\mu$ are vectors, and $\Sigma$ is the covariance ...
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### Running race problem(logic)

There are 3 persons named Ram,Shyam and Hari (Yeah,Indian names). In an 100 m race Ram defeats Shyam by 15 m. In another race of 100 m, Hari defeats Shyam by 20 m. If Ram and Hari take part in a 150 m ...
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### Can somebody explain me the intution behind this equation?

Can somebody explain me the name and/or intuition behind this equation? dm(A,B)=max{∥(A−B)x∥:x∈Rn,∥x∥=1} Kindly refer the equation here: Distance/Similarity ...
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### How to calculate the mahalanobis distance of a series of 50 x 2 contours

I have a series of 2d closed curves which are all 50 x 2 on the plane. I wonder how to calculate the mahalanobis distance for these series of contours. For vectors, I can imagine how to calculate ...
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### Story Mathematics [duplicate]

A man usually rides his bike $9$ kilometers per hour, yet the wind slows him to $6.76$ kilometers for $26$ minutes and $5.55$ for $10$; how long until he gets home $11.54$ kilometers away? (This was a ...
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### Calculating Mahalanobis parameters from x data

Roughly speaking, the Mahalanobis distance $d(x) = \sqrt{(x - \mu)^T * \Sigma^{-1} * (x - \mu)}$ is the distance between a multivariate Gaussian distribution ($\mu$, $\Sigma$) and a point. If the ...
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### Encoding the position information in real distance metric

The Euclidean distance doesn't preserve the exact position information. For example, the distance of the points (3,1) and (1,3) would be the same from the origin. Is there any distance metric which ...
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