# Questions tagged [mahalanobis-distance]

Question that relates or uses the Mahalanobis distance metric.

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### When to use chi square law for confidence intervals with mahalanobis distance?

So right now i'm reading this paper: Distance-based detection of out-of-distribution silent failures for Covid-19 lung lesion segmentation, available here: https://arxiv.org/abs/2208.03217 In brief, ...
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### Minimizing the Mahalanobis distance

Definitions Consider the following optimization problem \begin{equation*}\arg \min_{x\in\mathbb{R}^n} \lVert y-x\rVert_{P}^2\end{equation*} where $y,P$ are given parameters and \begin{equation*} \...
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### Interpretation of Mahalanobis distance: why not two inverses?

In this question, there's an informal answer that gives an intuition to the Mahalanobis distance. From my understanding, the Mahalanobis distance first transforms the vector, using the inverse of the ...
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### Mahalanobis distance on the tangent space of a point in $n$-sphere

Let $\mathbb{S}^n$ be the $n$-sphere and let $\mathbf{s}\in\mathbb{S}^n$ be a point on the it. Also, let $\mathcal{S}=\{\mathbf{s}_i\in\mathbb{S}^n\colon \mathbf{s}_i\neq \mathbf{s}, i=1,\ldots,N\}$ ...
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### What's the distance between triangles?

How can we define distance between, say, two of them? And if we the distance between two of them and the distance of another one to the first, do we know its distance tö rhe second? What ways are ...
568 views

### Multivariate 68–95–99.7 rule for Normal Distributions

For the univariate Normal Distribution, the 68–95–99.7 rule states the percentage of points lying within the intervals defined by the one, two, and three times standard deviation. Or in other words, ...
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### Mahalanobis distance for vectors from different distributions

Given that I want to calculate the distance of a vector x (say from the blue distribution) from the centroid of a different distributions than x's - say centroid of the red vectors: I want to use the ...
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### Averaging over Mahalanobis distance vectors of different clusters

Given vectors from two different clusters (in particular in my example from two different experimental conditions, called "CS" and "US") where the Mahalanobis Distance is ...
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### Mahalanobis distance connection with Euclidean distance

My question is more about the meaning of Mahalanobis distance when compared to L2 distance. As a reminder: Mahalanobis distance is the distance between a point $x$ and a distribution with mean $\mu$ ...
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### Prove that $x^TAx=\begin{Vmatrix} x \end{Vmatrix}^2$

Starting from a multivariate density of $R$, i.e. $f(R,\check{R},\sum)=(2\pi)^{-\frac{M}{2}}|\sum|^{-\frac{1}{2}}e^{-\frac{1}{2}[(R-\check{R})^T\sum^{-1}(R-\check{R})]}$ with $\sum$ covariance matrix ...
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### Can you always apply the log transform over a positive inequality constraint?

I'm having trouble understanding when can you take the log of a constraint in a general way (is this something you can always do for positive inequalities $\geq 1$, or there are limitations?)...it's ...
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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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### Optimization problem with Mahalanobis distance

This question is a follow-up of one of my previous questions: Optimizing a vector equation Let $x$ and $b$ be two vectors of real numbers in k dimensional space. Let $W$ be a k-by-k matrix of real ...
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### PDF of Mahalanobis distance of a multivariate random normal variable

Suppose $x$ is a multivariate normal random variable with mean $\mu$ and covariance matrix $C$. Let $h(x)$ be a the Mahalanobis distance of $x$ given by $h(x)=\sqrt{(x-\mu)^TC^{-1}(x-\mu)}$. Then how ...
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### Composite cost function using angular distance between vectors and distance between points

I am trying to come up with a way to find the transformation parameters between two sets of planes and would like to get a cost function C which incorporates two ...
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### Finding similarity of strings using distance function : Bounding the distance function?

I want to know if 2 binary strings $s$ and $t$ each of $d$ length (dimension) and N = 2 (the alphebet) in this case 0 and 1 are similar to each other or not using the following distance function where ...
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Is there any simple way to calculate the probability of distance in the following form for d-dimensional normal distribution? $P(||\mathbf{x}-\mathbf{\mu}||^2>||\mathbf{x}-\mathbf{a}||^2)$, where \$...