stzPCA

(no comment in the source: the name reads as a sentence) initno extension

(no comment in the source: the name reads as a sentence) number of samples

composed example

o1 = new stzPCA([ [1,2] ])
? o1.NumberOfSamples()
#--> 1

composed from the signature, run for this page

no extension

(no comment in the source: the name reads as a sentence) number of features

composed example

o1 = new stzPCA([ [1,2] ])
? o1.NumberOfFeatures()
#--> 2

composed from the signature, run for this page

no extension

THE NAME FORM CARRIES THE SEMANTICS, which is a Softanza law rather than a style: an ACTIVE verb -- Standardize(), Center() -- DOES the thing and returns nothing; the PASSIVE form -- Standardized(), Centered() -- returns the transformed DATA and leaves the object alone; and the Q twin does the thing and returns the object so calls chain. The first version of this class had Standardized() mutating the analysis and returning This, which got both halves wrong at once: a passive name for an active act, and a plain method returning an object where plain methods return data. CENTER each feature on its mean and leave the units alone -- covariance PCA. The features that vary most, in their own units, dominate.QCSXTZZZIBWU

CENTER and then divide each feature by its standard deviation -- correlation PCA. Every feature counts equally, whatever it was measured in.QCSXTZZZIBWU

── and the passive forms, which return the prepared DATA ── The data centered on the column means, original untouched. This is what a covariance PCA actually decomposes, so it is worth being able to look at.

composed example

o1 = new stzPCA([ [1,2] ])
? @@( o1.Centered() )
#--> [ [ 0, 0 ] ]

composed from the signature, run for this page

no extension

The data centered AND divided by the column standard deviations. What a correlation PCA decomposes.no extension

(no comment in the source: the name reads as a sentence) is standardized

composed example

o1 = new stzPCA([ [1,2] ])
? o1.IsStandardized()
#--> 0

composed from the signature, run for this page

no extension

── the variance convention, from the library's one authority ──QCSXTZZZIBWU

(no comment in the source: the name reads as a sentence) use population varianceQCSXTZZZIBWU

(no comment in the source: the name reads as a sentence) uses sample variance

composed example

o1 = new stzPCA([ [1,2] ])
? o1.UsesSampleVariance()
#--> 1

composed from the signature, run for this page

no extension

(no comment in the source: the name reads as a sentence) fitQCSXTZZZIBWU

(no comment in the source: the name reads as a sentence) is fitted

composed example

o1 = new stzPCA([ [1,2] ])
? o1.IsFitted()
#--> 0

composed from the signature, run for this page

no extension

(no comment in the source: the name reads as a sentence) number of componentsno extension

The sign is fixed by convention (the largest loading of each component is made positive) because a direction has no preferred sign -- v and -v are the same axis explaining the same variance -- and without a convention two runs can look like they disagree.also written: Loadingsno extension

The data in component coordinates: row i is sample i, column j its position along component j. Centered by construction, so each column averages zero.no extension

(no comment in the source: the name reads as a sentence) singular valuesno extension

How much variance each component accounts for, in the units of the prepared data. These SUM to TotalVariance() -- the decomposition redistributes the variance and cannot create or destroy any.no extension

(no comment in the source: the name reads as a sentence) total varianceno extension

The same, as fractions of the total. This is the number people quote.no extension

(no comment in the source: the name reads as a sentence) cumulative variance rationo extension

How many components to keep to retain a given fraction of the variance -- the usual way the number of components is chosen.no extension

The centering that was applied, kept because projecting NEW data needs exactly the same one. Data centered on its own mean lands in a different space.no extension

(no comment in the source: the name reads as a sentence) scaleno extension

That identity is checked in the guard, and it is a far stronger statement than any reconstruction number the learned inverses can offer. It says the arithmetic is RIGHT, where they can only say the result looked plausible.no extension

the training rows put through Transform() and back again -- what the analysis retained of the data it was given, which is the picture worth looking at when deciding how many components are enoughno extension

(no comment in the source: the name reads as a sentence) transformno extension

(no comment in the source: the name reads as a sentence) whyno extension