Linked Questions
79 questions linked to/from Bottom to top explanation of the Mahalanobis distance?
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How to normalize by the covariance matrix? [duplicate]
I am trying to understand an image processing research paper [1] that calls for normalizing a distance between an object's center point and the center of a cluster of points by the covariance matrix ...
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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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Interpreting the inverse covariance matrix: $S^{-1}x$ and $x^T S^{-1}x$ [duplicate]
Let $S$ be the covariance matrix of some data set. $S^{-1}$ is the inverse covariance matrix, also called the precision matrix.
Question: In practice, then, what does $S^{-1}x$ mean for a data point $...
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Equivalence between Mahalanobis distance and PCA (mathematical proof) [duplicate]
From this article and this post it emerges the strong connection between Mahalanobis distance and PCA. In particular in the first article I reference it says:
" the squared Mahalanobis distance is ...
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How is the mahalanobis distance like the euclidean distance? [duplicate]
Let's say $\vec{x}$ is an $n$ dimensional observation, $\vec{\mu}$ the $n$ dimensional mean of the sample that $\vec{x}$ is from and $\Sigma$ the $n \times n$ covariance matrix of that sample.
Then ...
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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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Why is the covariance matrix inverted in the definition of the Mahalanobis distance? [duplicate]
I'm on my first course on data science, and I encountered the Mahalanobis distance for the first time. It was mentioned that intuitively, what it does is that it corrects for the fact that some ...
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Making sense of principal component analysis, eigenvectors & eigenvalues
In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.
I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
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How can this counterintiutive result with the Mahalanobis distance be explained?
I encountered a strange issue when performing Mahalanobis distance matching. Let's say I have one treated unit with the following values on two variables: $T:(17, 4)$. I have two control units with ...
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Intuition behind $(X^TX)^{-1}$ in closed form of w in Linear Regression
The closed form of w in Linear regression can be written as
$\hat{w}=(X^TX)^{-1}X^Ty$
How can we intuitively explain the role of $(X^TX)^{-1}$ in this equation?
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What is Mahalanobis distance, & how is it used in pattern recognition?
Can someone explain to me the concept of Mahalanobis distance? For example, what is the Mahalanobis distance between two points x and y, and especially, how is it interpreted for pattern recognition?
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Is Mahalanobis distance equivalent to the Euclidean one on the PCA-rotated data?
I've been led to believe (see here and here) that Mahalanobis distance is the same as the Euclidean distance on the PCA-rotated data. In other words, taking multivariate normal data $X$, the ...
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Prove the relation between Mahalanobis distance and Leverage?
I have seen formulas on Wikipedia. that relate Mahalanobis distance and Leverage:
Mahalanobis distance is closely related to the leverage statistic, $h$, but has a different scale: $$D^2 = (N - 1)(...
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Why doesn't collinearity affect the predictions?
I have read in many places that collinearity doesn't affect the predictions. It only affects the coefficient tests and confidence interval. As a result it cannot be used for causal inference but for ...
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Test whether (x,y) of one set of data points is significantly greater than the (x,y) of another set of data points
What's the most suitable statistical test for testing whether the distribution of the (x,y) coordinates of the blue points is significantly different from the distribution of the (x,y) coordinates of ...
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