Problem 2043. Six Steps to PCA - Step 1: Centre and Standardize

Solution 370564

Submitted on 15 Dec 2013

Size: 32
Leading solution size is 34.

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1 Comment

1 Comment

Neil Caithness on 17 Dec 2013

Nice solution that looks pretty nifty but it actually produces an unsafe result, just like Matlab's own zscore. It passed on it's first run trough the test suite but fails on some number of repeats. I've now added a second pass with a know random seed.

Test Suite

Test	Status	Code Input and Output
1	Pass	%% m = 100; n = 10; x = rand(m,n); k = false(1,n); k(randi(n,1,3)) = true; x(:,k) = rand; tol = 1.0e-12; out = zscore(x); assert(isstruct(out),'Struct test failed.') assert(isfield(out,'Z'),'Z field test failed.') assert(isfield(out,'Mu'),'Mu field test failed.') assert(isfield(out,'Sigma'),'Sigma field test failed.') assert(isequal(size(x),size(out.Z)),'Z size test failed.') assert(isequal(size(x(1,:)),size(out.Mu)),'Mu size test failed.') assert(isequal(size(x(1,:)),size(out.Sigma)),'Sigma size test failed.') assert(all(abs(mean(out.Z))<tol),'Mean test failed.') assert(all(abs(std(out.Z(:,~k))-1)<tol),'STD test failed.') assert(all(abs(std(out.Z(:,k)))<tol),'STD test for invariant data failed.') assert(isequal(out.Mu,mean(x,1)),'Mean equality test failed.') assert(isequal(out.Sigma,std(x,0,1)),'STD equality test failed.')
2	Fail	%% A second pass known to produce unsafe results with Matlab's zscore m = 100; n = 10; rng(2000,'twister') x = rand(m,n); k = false(1,n); k(randi(n,1,3)) = true; x(:,k) = rand; tol = 1.0e-12; out = zscore(x); assert(isstruct(out),'Struct test failed.') assert(isfield(out,'Z'),'Z field test failed.') assert(isfield(out,'Mu'),'Mu field test failed.') assert(isfield(out,'Sigma'),'Sigma field test failed.') assert(isequal(size(x),size(out.Z)),'Z size test failed.') assert(isequal(size(x(1,:)),size(out.Mu)),'Mu size test failed.') assert(isequal(size(x(1,:)),size(out.Sigma)),'Sigma size test failed.') assert(all(abs(mean(out.Z))<tol),'Mean test failed.') assert(all(abs(std(out.Z(:,~k))-1)<tol),'STD test failed.') assert(all(abs(std(out.Z(:,k)))<tol),'STD test for invariant data failed.') assert(isequal(out.Mu,mean(x,1)),'Mean equality test failed.') assert(isequal(out.Sigma,std(x,0,1)),'STD equality test failed.') Error: Mean test failed.

Test

Status

Code Input and Output

Pass

%% m = 100; n = 10; x = rand(m,n); k = false(1,n); k(randi(n,1,3)) = true; x(:,k) = rand; tol = 1.0e-12; out = zscore(x); assert(isstruct(out),'Struct test failed.') assert(isfield(out,'Z'),'Z field test failed.') assert(isfield(out,'Mu'),'Mu field test failed.') assert(isfield(out,'Sigma'),'Sigma field test failed.') assert(isequal(size(x),size(out.Z)),'Z size test failed.') assert(isequal(size(x(1,:)),size(out.Mu)),'Mu size test failed.') assert(isequal(size(x(1,:)),size(out.Sigma)),'Sigma size test failed.') assert(all(abs(mean(out.Z))<tol),'Mean test failed.') assert(all(abs(std(out.Z(:,~k))-1)<tol),'STD test failed.') assert(all(abs(std(out.Z(:,k)))<tol),'STD test for invariant data failed.') assert(isequal(out.Mu,mean(x,1)),'Mean equality test failed.') assert(isequal(out.Sigma,std(x,0,1)),'STD equality test failed.')

Fail

%% A second pass known to produce unsafe results with Matlab's zscore m = 100; n = 10; rng(2000,'twister') x = rand(m,n); k = false(1,n); k(randi(n,1,3)) = true; x(:,k) = rand; tol = 1.0e-12; out = zscore(x); assert(isstruct(out),'Struct test failed.') assert(isfield(out,'Z'),'Z field test failed.') assert(isfield(out,'Mu'),'Mu field test failed.') assert(isfield(out,'Sigma'),'Sigma field test failed.') assert(isequal(size(x),size(out.Z)),'Z size test failed.') assert(isequal(size(x(1,:)),size(out.Mu)),'Mu size test failed.') assert(isequal(size(x(1,:)),size(out.Sigma)),'Sigma size test failed.') assert(all(abs(mean(out.Z))<tol),'Mean test failed.') assert(all(abs(std(out.Z(:,~k))-1)<tol),'STD test failed.') assert(all(abs(std(out.Z(:,k)))<tol),'STD test for invariant data failed.') assert(isequal(out.Mu,mean(x,1)),'Mean equality test failed.') assert(isequal(out.Sigma,std(x,0,1)),'STD equality test failed.')

Error: Mean test failed.

Problem 2043. Six Steps to PCA - Step 1: Centre and Standardize

Test Suite

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Problem 2043. Six Steps to PCA - Step 1: Centre and Standardize

Test Suite

Suggested Problems

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