pydiodon.plot_cumulated_quality_per_item

pydiodon.plot_cumulated_quality_per_item(Y, r=2, sort=False, col='blue', title=None, x11=True, plotfile=None, fmt='png')

plots the quality per item

Parameters

Ya 2D \(n \times p\) numpy array

a matrix of principal components

ran integer, the axis for plotting cumulated quality

default value is 2

sortboolean

whether to sort or not the items according to their quality of projection

default value is False

cola string

the color to use for plotting the quality

default value is blue

titlestring

title of the plot

x11boolean

the plot is displayed on the scvreen if x11=True

plotfilestring

name of the file to save the plot

the plot is not saved if plotfile=None

fmtstring

format of the file to save the plot.

accepted values are png, eps, pdf.

Returns

Qual1D \(r\) numpy array

the rowise cumulated quality per axis up to r.

Notes

The quality of the projection of the dataset on a subspace spanned by principal axis is a scalar giving a global estimate of the quality. However, the quality of projection may differ from item to item: some can be well projected on plane (1,2) and some other not. This function computes and plots the quality of projection of each item on subspace \(E_r\) spanned by r first axis.

More precisely, for each row i of the matrix of components Y

• it computes Qual with \(Qual[i,r] = \sum_{j \leq r} Y[i,j]^2 / \sum_{k \leq p} Y[i,k]^2\) for \(1 \leq i \leq n\) and \(1 \leq r \leq p\)

• once an axis r has been selected, it draws the plot of \((i, Q(i,r))\) for \(1 \leq i \leq n\) with i on x axis.

Example

>>> import pydiodon as dio
>>> A, rn, cn = dio.load_dataset("diatoms_sweden")
>>> Y, L, V = dio.pca(A)
>>> Qual = dio.plot_cumulated_quality_per_item(Y)

or, for sorting the items in decreasing quality

>>> Qual = dio.plot_cumulated_quality_per_item(Y, sort=True)

af, revised 22.10.28, 23.01.18