Process columns of matrix with principal component analysis
[Y,PS] = processpca(X,maxfrac)
[Y,PS] = processpca(X,FP)
Y = processpca('apply',X,PS)
X = processpca('reverse',Y,PS)
name = processpca('name')
fp = processpca('pdefaults')
names = processpca('pdesc')
processpca('pcheck',fp);
processpca
processes matrices using principal component analysis so that
each row is uncorrelated, the rows are in the order of the amount they contribute to total
variation, and rows whose contribution to total variation are less than
maxfrac
are removed.
[Y,PS] = processpca(X,maxfrac)
takes X
and an
optional parameter,
X 

maxfrac  Maximum fraction of variance for removed rows (default is 0) 
and returns
Y 

PS  Process settings that allow consistent processing of values 
[Y,PS] = processpca(X,FP)
takes parameters as a struct:
FP.maxfrac
.
Y = processpca('apply',X,PS)
returns Y
, given
X
and settings PS
.
X = processpca('reverse',Y,PS)
returns X
, given
Y
and settings PS
.
name = processpca('name')
returns the name of this process
method.
fp = processpca('pdefaults')
returns default process parameter
structure.
names = processpca('pdesc')
returns the process parameter
descriptions.
processpca('pcheck',fp);
throws an error if any parameter is
illegal.
Here is how to format a matrix with an independent row, a correlated row, and a completely redundant row so that its rows are uncorrelated and the redundant row is dropped.
x1_independent = rand(1,5) x1_correlated = rand(1,5) + x1_independent; x1_redundant = x1_independent + x1_correlated x1 = [x1_independent; x1_correlated; x1_redundant] [y1,ps] = processpca(x1)
Next, apply the same processing settings to new values.
x2_independent = rand(1,5) x2_correlated = rand(1,5) + x1_independent; x2_redundant = x1_independent + x1_correlated x2 = [x2_independent; x2_correlated; x2_redundant]; y2 = processpca('apply',x2,ps)
Reverse the processing of y1
to get x1
again.
x1_again = processpca('reverse',y1,ps)
Values in rows whose elements are not all the same value are set to
y = 2*(xminx)/(maxxminx)  1;
Values in rows with all the same value are set to 0.