977 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 ...
87 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 ...
43 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 ...
42 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 ...
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 ...
723k 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 ...
26k 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?
8k 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 ...
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?
1k 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 ...
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 ...
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)(...
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'...
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 (...