PCA

Type or paste the variables' data, row by row: i.e. rows are variables, columns are individuals/observations. data only, no names.

Optional. Type or paste the categories/species of each observation. For color-coding the plot.

    


Results

#variables (rows):
#observations per variable (columns):

Variables' statistics:

Covariance matrix: symmetric


Data centered at origin and scaled by SD, i.e. standardized:

Their statistics: should be 0 and 1

Their Covariance matrix K (=correlation matrix):

Their eigenvalues λi, eigenvectors ei:          Magnitudes |ei|
of a square symmetric matrix: all eigenvectors are orthogonal, all eigenvalues are [non-negative?] real.
DAMN: the math.js eigs() gives normed eigenvectors.... OK for PCs etc. that follows.
λ1 e1 |e1|
λ2 e2 |e2|
λ3 e3 |e3|
λ4 e4 |e4|
λ5 e5 |e5|

Loadings/weights: each PC row's α's i.e. NORMED
eigenvalues λi, eigenvectors ei          Magnitudes |ei| (=1)
λ1 e1 |e1|
λ2 e2 |e2|
λ3 e3 |e3|
λ4 e4 |e4|
λ5 e5 |e5|

standardized Covariance matrix times each normed eigenvector equals normed eigenvalue times normed eigenvector: Keiiei
eigenvectors are only stretched by matrix (not any rotation)

Sum of eigenvalues = sum of its matrix K's diagonal (its trace)
Product of eigenvalues = det(matrix K)

Primary components Scores of standardized data:
PC1
PC2
PC3
PC4
PC5
Their statistics:

Total VARiation:
Screes:

PC1+PC2 % of total VARiation:


X min: X max: Y min: Y max:



Fisher's iris data