six steps to pca -凯发k8网页登录

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dimension reduction, but also for making predictive models in machine learning.</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"text\"/></w:ppr><w:r><w:rpr><w:b/></w:rpr><w:t>step 1: centre and standardize</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"text\"/></w:ppr><w:r><w:t>a first step for many multivariate methods begins by removing the influence of location and scale from variables in the raw data. also commonly known as the z-scores of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>x</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>z</w:t></w:r><w:r><w:t> is a transformation of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>x</w:t></w:r><w:r><w:t> such that the columns are centered to have mean 0 and scaled to have standard deviation 1 (unless a column of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>x</w:t></w:r><w:r><w:t> is constant, in which case that column of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>z</w:t></w:r><w:r><w:t> is constant at 0). strictly speaking, z-scores are based on population parameters, whereas the analogous calculation based on sample mean and standard deviation is the student's t-statistic.</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"text\"/></w:ppr><w:r><w:rpr><w:b/></w:rpr><w:t>task</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"text\"/></w:ppr><w:r><w:t>write a function to centre and standardize the input matrix</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>x</w:t></w:r><w:r><w:t>, returning as the output a structure with the following fields:</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"listparagraph\"/><w:numpr><w:numid w:val=\"1\"/></w:numpr></w:ppr><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>z</w:t></w:r><w:r><w:t>: the centred and standardized matrix corresponding to the input</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>x</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"listparagraph\"/><w:numpr><w:numid w:val=\"1\"/></w:numpr></w:ppr><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>mu</w:t></w:r><w:r><w:t>: a vector of the original means of columns of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>x</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"listparagraph\"/><w:numpr><w:numid w:val=\"1\"/></w:numpr></w:ppr><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>sigma</w:t></w:r><w:r><w:t>: a vector of the original standard deviations of columns of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>x</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"text\"/></w:ppr><w:r><w:rpr><w:b/></w:rpr><w:t>tips</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"listparagraph\"/><w:numpr><w:numid w:val=\"1\"/></w:numpr></w:ppr><w:r><w:t>matlab's</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rpr><w:rfonts w:cs=\"monospace\"/></w:rpr><w:t>zscore</w:t></w:r><w:r><w:t> function is part of the stats toolbox which is not available in cody. you'll have to write your own.</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"listparagraph\"/><w:numpr><w:numid w:val=\"1\"/></w:numpr></w:ppr><w:r><w:t>you should take care to avoid division by zero when a column is invariant.</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"text\"/></w:ppr><w:r><w:rpr><w:b/></w:rpr><w:t>following problems in the series</w:t></w:r></w:p><w:p><w:ppr><w:pstyle w:val=\"listparagraph\"/><w:numpr><w:numid w:val=\"1\"/></w:numpr></w:ppr><w:hyperlink w:doclocation=\"http://www.mathworks.co.uk/matlabcentral/cody/problems/2049-six-steps-to-pca-step-2-covariance\"><w:r><w:t>step 2: covariance</w:t></w:r></w:hyperlink></w:p></w:body></w:document>"},{"parturi":"/matlab/output.xml","contenttype":"text/xml","content":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\" ?><embeddedoutputs><metadata><evaluationstate>manual</evaluationstate><layoutstate>code</layoutstate><outputstatus>ready</outputstatus></metadata><outputarray type=\"array\"/><regionarray type=\"array\"/></embeddedoutputs>"}]}

introductionprincipal component analysis (pca) is a classic among the many methods of multivariate data analysis. invented in 1901 by karl pearson the method is mostly used today as a tool in exploratory data analysis and dimension reduction, but also for making predictive models in machine learning.step 1: centre and standardizea first step for many multivariate methods begins by removing the influence of location and scale from variables in the raw data. also commonly known as the z-scores of <tt>x</tt>, <tt>z</tt> is a transformation of <tt>x</tt> such that the columns are centered to have mean 0 and scaled to have standard deviation 1 (unless a column of <tt>x</tt> is constant, in which case that column of <tt>z</tt> is constant at 0). strictly speaking, z-scores are based on population parameters, whereas the analogous calculation based on sample mean and standard deviation is the student's t-statistic.taskwrite a function to centre and standardize the input matrix <tt>x</tt>, returning as the output a structure with the following fields:<ul><li><tt>z</tt>: the centred and standardized matrix corresponding to the input <tt>x</tt></li><li><tt>mu</tt>: a vector of the original means of columns of <tt>x</tt></li><li><tt>sigma</tt>: a vector of the original standard deviations of columns of <tt>x</tt></li></ul>tips<ul><li>matlab's <tt>zscore</tt> function is part of the stats toolbox which is not available in cody. you'll have to write your own.</li><li>you should take care to avoid division by zero when a column is invariant.</li></ul>following problems in the series<ul><li><a href = "http://www.mathworks.co.uk/matlabcentral/cody/problems/2049-six-steps-to-pca-step-2-covariance">step 2: covariance</a></li></ul>

*introduction*
principal component analysis (pca) is a classic among the many methods of multivariate data analysis. invented in 1901 by karl pearson the method is mostly used today as a tool in exploratory data analysis and dimension reduction, but also for making predictive models in machine learning.
*step 1: centre and standardize*
a first step for many multivariate methods begins by removing the influence of location and scale from variables in the raw data. also commonly known as the z-scores of |x|, |z| is a transformation of |x| such that the columns are centered to have mean 0 and scaled to have standard deviation 1 (unless a column of |x| is constant, in which case that column of |z| is constant at 0). strictly speaking, z-scores are based on population parameters, whereas the analogous calculation based on sample mean and standard deviation is the student's t-statistic.
*task*
write a function to centre and standardize the input matrix |x|, returning as the output a structure with the following fields:
* |z|: the centred and standardized matrix corresponding to the input |x|
* |mu|: a vector of the original means of columns of |x|
* |sigma|: a vector of the original standard deviations of columns of |x|
*tips*
* matlab's |zscore| function is part of the stats toolbox which is not available in cody. you'll have to write your own.
* you should take care to avoid division by zero when a column is invariant.
*following problems in the series*
* <http://www.mathworks.co.uk/matlabcentral/cody/problems/2049-six-steps-to-pca-step-2-covariance step 2: covariance>

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last submitted on may 16, 2023

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jean-marie sainthillier on 10 feb 2014

your definition of a constant (or invariant) data with rand is problematic. if you increase the size of your data (n=1000, n=10000...), you can always increase the deviations (so what threshold for sigma ?). i think that with real data, this artifact isn't possible. no ?

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six steps to pca -凯发k8网页登录

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