Factor analysis of mixed data

Resources

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Data

Factor analysis of mixed data is a general purpose method. It supports both numeric and categorical data.

import prince

dataset = prince.datasets.load_beers().head(1000)
dataset.head()

	is_organic	style	alcohol_by_volume	international_bitterness_units	standard_reference_method	final_gravity
name
Lightshine Radler	False	Blonde	4.50	20.0	5.0	1.012
LightSwitch Lager	False	American Light Lager	3.95	7.5	3.0	1.005
Lightwave Belgian Pale	False	Belgian Pale	5.00	25.0	9.0	1.011
Like Weisse	False	Berlinerweisse	3.10	4.5	3.0	1.005
Lil Heaven Session IPA	False	Session	4.55	20.0	2.0	1.007

Fitting

famd = prince.FAMD(
    n_components=2,
    n_iter=3,
    copy=True,
    check_input=True,
    random_state=42,
    engine="sklearn",
    handle_unknown="error"  # same parameter as sklearn.preprocessing.OneHotEncoder
)
famd = famd.fit(dataset)

Eigenvalues

famd.eigenvalues_summary

	eigenvalue	% of variance	% of variance (cumulative)
component
0	3.735	3.70%	3.70%
1	1.662	1.65%	5.34%

Coordinates

famd.row_coordinates(dataset).head()

component	0	1
name
Lightshine Radler	-1.795872	-0.316854
LightSwitch Lager	-3.351119	-0.193896
Lightwave Belgian Pale	-1.429076	-0.083288
Like Weisse	-3.774585	-0.255144
Lil Heaven Session IPA	-2.570021	-0.069867

famd.column_coordinates_

component	0	1
variable
alcohol_by_volume	8.474727e-01	0.024329
international_bitterness_units	6.648504e-01	0.224303
standard_reference_method	3.828369e-01	0.386307
final_gravity	8.401140e-01	0.025106
is_organic	6.361371e-07	0.002685
style	9.994811e-01	0.999218

Visualization

famd.plot(
    dataset,
    x_component=0,
    y_component=1
)

Contributions

(
    famd.row_contributions_
    .sort_values(0, ascending=False)
    .head(5)
    .style.format('{:.3%}')
)

component	0	1
name
Agamemnon	0.536%	0.255%
Hide the Despot	0.536%	0.202%
Game of Thrones: King In the North	0.536%	0.202%
Bakery: Banana Bread	0.536%	0.202%
Entire Wood Aged Stout	0.536%	0.202%

famd.column_contributions_.style.format('{:.0%}')

component	0	1
variable
alcohol_by_volume	23%	1%
international_bitterness_units	18%	13%
standard_reference_method	10%	23%
final_gravity	22%	2%
is_organic	0%	0%
style	27%	60%