MATLAB: Mahalanobis distance for 2 vectors matlab

matlab mahalanobis

Hey,

I tried the method mahal to calculate the mahalanobis distance between 2 vectors of 27 variables(columns) e.g. mahal(X,Y) where X and Y are the 2 vectors but it comes up with an error. After a few minutes of research I got that I can't use it like this but I'm still not sure sure why? can some explain to me why?

Also I have below an example of mahal method :

      mahal([1.55 5 32],[5.76 43 34; 6.7 32 5; 3 3 5; 34 12 6;])
ans =
     11.1706

can someone clarify how matlab calculated the answer in this case?

Best Answer

There appears to be a misconception here. Mahalanobis distance has no meaning between two multiple-element vectors. Ideally it is a distance between a vector (or distances between a set of vectors) and some given distribution defined by means and covariances. See the Wikipedia website

 http://en.wikipedia.org/wiki/Mahalanobis_distance

In Mathworks' 'mahal' function

 d = mahal(Y,X) ,

that distribution is approximated from the X array, which must have more rows than columns to be meaningful. In your case you were trying to use only one row in the second argument and that would not give a meaningful distribution. I suggest you carefully read the documentation at:

 http://www.mathworks.com/help/stats/mahal.html

Related Solutions

MATLAB: Mahalanobis distance in matlab: pdist2() vs. mahal() function

http://stackoverflow.com/questions/19933883/mahalanobis-distance-in-matlab-pdist2-vs-mahal-function/19936086#19936086

An attempt to answer my own question, while adding a new question:

Well, I guess there are two different ways to calculate mahalanobis distance between two clusters of data like you explain above: 1) you compare each data point from your sample set to mu and sigma matrices calculated from your reference distribution (although labeling one cluster sample set and the other reference distribution may be arbitrary), thereby calculating the distance from each point to this so called mahalanobis-centroid of the reference distribution. 2) you compare each datapoint from matrix Y to each datapoint of matrix X, with, X the reference distribution (mu and sigma are calculated from X only)

The values of the distances will be different, but I guess the ordinal order of dissimilarity between clusters is preserved when using either method 1 or 2? I actually wonder when comparing 10 different clusters to a reference matrix X, or to each other, if the order of the dissimilarities would differ using method 1 or method 2? Also, I can't imagine a situation where one method would be wrong and the other method not. Although method 1 seems more intuitive in some situations, like mine.

MATLAB: How to go about finding the standard normal probability based on the z-score

doc normcdf
doc normpdf

When you know what you want but not sure the name, try something like

>> lookfor normal
realmin                        - Smallest positive normalized floating point number.
randn                          - Normally distributed pseudorandom numbers.
sprandn                        - Sparse normally distributed random matrix.
surfnorm                       - Surface normals.
isonormals                     - Isosurface normals.
cde                            - cd elliptic function with normalized complex argument.
sne                            - sn elliptic function with normalized complex argument.
addfreqcsmenu                  - Add a cs menu to switch between linear and normalized frequency
convertfrequnits               - converts between Normalized, Hz, kHz, etc
histfit                        - Histogram with superimposed fitted normal density.
jbtest                         - Jarque-Bera hypothesis test of composite normality.
lhsnorm                        - Generate a latin hypercube sample with a normal distribution
logncdf                        - Lognormal cumulative distribution function (cdf).
lognfit                        - Parameter estimates and confidence intervals for lognormal data.
logninv                        - Inverse of the lognormal cumulative distribution function (cdf).
lognlike                       - Negative log-likelihood for the lognormal distribution.
lognpdf                        - Lognormal probability density function (pdf).
lognrnd                        - Random arrays from the lognormal distribution.
lognstat                       - Mean and variance for the lognormal distribution.
mvncdf                         - Multivariate normal cumulative distribution function (cdf).
mvnpdf                         - Multivariate normal probability density function (pdf).
mvnrnd                         - Random vectors from the multivariate normal distribution.
normcdf                        - Normal cumulative distribution function (cdf).
normfit                        - Parameter estimates and confidence intervals for normal data.
norminv                        - Inverse of the normal cumulative distribution function (cdf).
normlike                       - Negative log-likelihood for the normal distribution.
normpdf                        - Normal probability density function (pdf).
normplot                       - Displays a normal probability plot.
normrnd                        - Random arrays from the normal distribution.
normspec                       - Plots normal density between specification limits.
normstat                       - Mean and variance for the normal distribution.
logn3fit                       - Fit a 3-param lognormal dist'n using cumulative probabilities.
wgtnormfit                     - Fitting example for a weighted normal distribution.
wgtnormfit2                    - Fitting example for a weighted normal distribution (log(sigma) parameterization).
>>

Judicious search terms help but seeing the list of things related to "normal" lets you find the two functions of interest (plus a lot more depending upon which toolboxes are available, maybe) that might be of use/interest...

Best Answer

Related Solutions

MATLAB: Mahalanobis distance in matlab: pdist2() vs. mahal() function

MATLAB: How to go about finding the standard normal probability based on the z-score

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