Questions tagged [mahalanobis]

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Effect of correlation in matching

What is the effect of correlations among observed covariates or between observed and unobserved covariates on the quality of matching, when matching iss done using Propensity score (Euclidian/...
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1answer
23 views

Is there an intuition about the matrix operations in the exponent of the multivariate normal distribution?

In the exponent of the multivariate distribution, there are 2 vectors and a square matrix multiplied together to get a scalar result: $$(\mathbf{x} - \mu)^{\text{T}}\Gamma^{-1}(\mathbf{x} - \mu)$$ ...
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160 views

How to find the variance(s) of a bivariate normal density such that 95% of the mass is within a certain radius from the mean defined by a point A?

I would like to find the variance of a bivariate normal density (BND), centered at the mean M, such that 95% of its mass is within a certain radius, which depends on the position of a point, A. (Note: ...
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2answers
194 views

What are the pros and cons of using mahalanobis distance instead of propensity scores in matching

I learned about this option of using mahalanobis distance instead of PS to do matching from the matchit() function in R. It seems a more nonparametric approach. Could you state its pros and cons and ...
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19 views

Multivariate Statistics and Outlier Detection for Large Time Series of Physically Related Variables

The data: I have somewhat noisy time series measurements for 15 variables, with occasional flat-lining, offsets, outliers, clipping, etc. Some of the data quality issues are consistent enough to ...
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40 views

Mahalanobis distance to detect multivariate outliers [duplicate]

I have to detect outliers on 3 variables. On the internet I found the mahalanobis distance but I understood I can use it only on multivariate normally distributed data, and my data isn't. So, do you ...
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74 views

Covariance Matrix Decomposition - Data Decorrelation

So I recently found out about Mahalanobis distance. Given a r.v $x$ in N-dimensional space, an associated metric is defined by $$M(x) = \sqrt{(x-\mu)^T S^{-1}(x-\mu)}$$ where $\mu$ and $S$ are mean ...
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1answer
37 views

When running a multiple regression, are both dependent and independent variables scanned for outliers?

I want to run a multiple regression analysis using SPSS. I have used the Mahalanobis d square method to find outliers. However my question is, do I add the dependent variable to the list of ...
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1answer
42 views

How to determine an appropriate “closeness” threshold when matching for causal inference?

Say I have a [yes/no] treatment variable (e.g. the customer complained about their order) and I want to estimate the causal impact of this "treatment" on the average customer's future spend. ...
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48 views

Anomaly/Outlier Detection for Arbitrary Shaped Data?

The following plots use the data from Kaggle's House Prices competition. SalePrice is the target variable. I want to find a method to identify outliers (as shown in red in plot 3 & 4) ...
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When to and When not to use time series approaches for anomaly detection?

I am reading several blogs and github repos about doing anomaly detection on IMS bearing data. Here is the time series plot of 4 bearing measurements. In this example blog, the author divides the ...
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1answer
169 views

Anomaly detection using Mahalanobis distance

I am using Mahalanobis distance to identify outliers. I am training using kind of one class classification,by training only on positive samples and trying to predict negative samples using distance ...
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1answer
27 views

Detect outliers / detect classes

Currently I have a dataset that contains several products with different prices and quantities. My goal is to detect if the given product was sold as a package or as a unit and I have used the ...
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28 views

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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1answer
147 views

Mahalanobis Distance for Continuous and Ordinal Covariates

My dataset of home sales includes covariates such as square_feet which are continuous and others like num_bedrooms which are in <...
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29 views

Transforming Covariate Matrix to Mahalanobis Space

I am applying Mahalanobis matching and want to visualize it at a lower dimension with PCA. This post illustrates how the Mahalanobis distance can be seen as the distance between points with shifted ...
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12 views

Covariance of Mahalanobis distances

Assume that $X_1,\ldots,X_n$ iid $N_2(0,\Sigma_x)$ and $Y_1,\ldots,Y_m$ iid $N_2(0,\Sigma_y)$ are independent random vectors and $\Sigma_x \stackrel{rot}{=} \Sigma_y$ (are the same covariance matrices ...
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1answer
90 views

Why does this formula produce $p_{2}$ probabilities for Mahalanobis distances?

At the IBM website it is written that The p1 probabilities are standard probabilities of an observation from a multivariate normal distribution being that far or further from the centroid, ...
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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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1answer
51 views

Discordance between various methods of multivariate outliers detection

Here is a small "toy example" dataset, with 15 individuals described by 6 variables (this is R language): ...
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2answers
620 views

Understanding the R stats mahalanobis() function's Output

An acquaintance recommended I use the Mahalanobis distance on my data instead of Euclidean, Manhattan, etc. I tried using the mahalanobis() function in the R stats package on a data matrix with N ...
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0answers
374 views

Mahalanobis distance between 2 points doesn't work when covariance matrix has values close to 0 [duplicate]

I am working on a project where I am trying to replicate a randomized experiment from an observational study data, using Mahalanobis distance matching to ensure that the control and treated groups are ...
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97 views

How can I use factor analysis to identify variables that contribute most to Mahalanobis distance?

I have 400 samples chemically analysed for 48 elements. Some elements are correlated. My goal is to identify outliers in a multivariate space, samples that are unique in their composition. I compute ...
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934 views

Distribution of the Mahalanobis distance between two samples from a Gaussian distribution

Let $\mathbf{X}=(X_1,\dots,X_p)\sim\mathcal{N}(\mu,\Sigma)$ be a Gaussian random vector. We all know that $$d^2(\mathbf{X},\mu) = (\mathbf{X}-\mu)^T\Sigma^{-1}(\mathbf{X}-\mu) $$ has a $\chi^2_p-$...
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6k views

Mahalanobis Distances Critical Values (Chi-Squared?)

Say I work out the mahalanobis distance 'D' to measure the separation between two objects (which aren't normally distributed). Say I now want to use 'D' against some critical values to decide if it's ...
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the Chi-squared distribution and Mahalanobis

I'm doing some simulations in C++ and OpenGL (2D and 3D) for navigating a robot in unknown environment known as SLAM. I'm using Extended Kalman filter as an optimal estimator. In SLAM problem, once ...