Linked Questions

1
vote
0answers
969 views

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 ...
0
votes
1answer
56 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 ...
0
votes
0answers
39 views

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 ...
0
votes
0answers
37 views

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 ...
1
vote
0answers
14 views

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 ...
1096
votes
28answers
666k views

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 ...
11
votes
2answers
24k views

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?
8
votes
2answers
7k views

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 ...
10
votes
3answers
2k views

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?
13
votes
2answers
892 views

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 ...
15
votes
1answer
2k views

What are some good interview questions for statistical algorithm developer candidates?

I'm interviewing people for a position of algorithm developer/researcher in a statistics/machine learning/data mining context. I'm looking for questions to ask to determine, specifically, a candidate'...
12
votes
1answer
3k views

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)(...
11
votes
1answer
5k views

Intuitive explanation of logloss

In several kaggle competitions the scoring was based on "logloss". This relates to classification error. Here is a technical answer but I am looking for an intuitive answer. I really liked the ...
5
votes
3answers
5k views

Distances in PCA space [closed]

I'm working on a project involving PCA, and my knowledge up till now with this method is quite good. My work involves finding nearest neighbors (having the least Euclidean distance) to a particular ...
19
votes
1answer
2k views

Geometric understanding of PCA in the subject (dual) space

I am trying to get an intuitive understanding of how principal component analysis (PCA) works in subject (dual) space. Consider 2D dataset with two variables, $x_1$ and $x_2$, and $n$ data points (...

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