Problem 2049. Six Steps to PCA - Step 2: Covariance

Created by Neil Caithness

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Previous problems in this series<ul><li><a href = "http://www.mathworks.co.uk/matlabcentral/cody/problems/2043-six-steps-to-pca-step-1-centre-and-standardize">Step 1: Centre and Standardize</a></li></ul>Step 2: CovarianceFor the second step we want the covariance matrix of the centred and standardized data that we calculated in Step 1. We could conveniently use Matlab's <tt>cov</tt> function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.TaskBuild on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data matrix.Add the following field to those already produced by your <tt>zscore</tt> function.<ul><li><tt>Cov</tt>: a square matrix of covariances</li></ul>Tips<ul><li>It's not as complicated as it sounds. Write one new line of code.</li><li>Don't just call Matlab's own <tt>cov</tt> function.</li><li>Keep to the structure of the code template with <tt>zscore</tt> as a local function.</li></ul>

*Previous problems in this series*

* <http://www.mathworks.co.uk/matlabcentral/cody/problems/2043-six-steps-to-pca-step-1-centre-and-standardize Step 1: Centre and Standardize>

*Step 2: Covariance*

For the second step we want the covariance matrix of the centred and standardized data that we calculated in Step 1. We could conveniently use Matlab's |cov| function, but this repeats much of what we've already done, for instance centering by removing the mean. It also has to deal with a wider range of possible inputs, whereas we have a very well specified starting point.

*Task*

Build on the code produced for Step 1 by writing a function to calculate the covariance matrix of the centred and standardized data matrix.

Add the following field to those already produced by your |zscore| function.

* |Cov|: a square matrix of covariances

*Tips*

* It's not as complicated as it sounds. Write one new line of code.
* Don't just call Matlab's own |cov| function.
* Keep to the structure of the code template with |zscore| as a local function.

Solve

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Last Solution submitted on May 16, 2023

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Jean-Marie Sainthillier on 10 Feb 2014

Where are the other steps Neil ?

Rafael S.T. Vieira on 2 Sep 2020

The problem wants the covariance matrix of the z-score obtained at the previous step if someone else found the problem description unclear.

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Problem 2049. Six Steps to PCA - Step 2: Covariance

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