# -*- coding: utf-8 -*-
from pandas import DataFrame, concat
from collections import namedtuple, OrderedDict
from sklearn.pipeline import Pipeline
from sklearn.utils.validation import check_is_fitted
#interns functions
from ._base import _BaseDA
from ._mpca import MPCA
from ._discrim import DISCRIM
[docs]
class MDA(_BaseDA):
"""
Mixed Discriminant Analysis (MDA)
Performs a linear discrimination analysis (LDA) on mixed predictors. It's a classical linear discriminant analysis carried out on the principal factors of a mixed principal component analysis (MPCA) of explanatory variables.
Discriminat analysis on mixed predictors consists in two steps:
1. Computation of mixed principal component analysis (MPCA) on features.
2. Performns linear discriminant analysis (LDA) on principal components extract in step 1.
Parameters
----------
n_components : int or None, default = 2
Number of components to keep. If ``None``, keep all the components.
priors : str, 1-D array or Series of shape (n_classes,), default = None
The priors statement specifies the class prior probabilities of group membership, possibles values:
- 'equal' to set the prior probabilities equal.
- 'prop' to set the prior probabilities proportional to the sample sizes.
- 1-D array or Series which specify the prior probability for each level of the classification variable.
classes : None, tuple or list, default = None
Name of level in order to return. If None, classes are sorted in unique values in y.
Returns
-------
call_ : NamedTuple
Call informations.
- X : DataFrame of shape (n_samples, n_features)
Training data
- y : Series of shape (n_samples,)
Target values. True values for `X`.
- target : str
Name of target.
- features : list
Names of features seen during ``fit``.
- classes : list
Names of classes.
- priors : Series of shape (n_classes,)
Priors probabilities.
- n_samples : int
Number of samples.
- n_features : int
Number of features.
- n_classes : int
Number of target values.
- max_components : int
Maximum number of components.
- n_components : int
Number of components kept.
cancoef_ : NamedTuple
Canonical coefficients:
- standardized : DataFrame of shape (n_variables, n_components)
The standardized canonical coefficients
- raw : DataFrame of shape (n_variables+1, n_componets)
The raw canonical coefficients
- projection : DataFrame of shape (n_variables+1, n_components)
The projection canonical coefficients.
coef_ : NamedTuple
Linear discriminant coefficients:
- standardized : DataFrame of shape (n_variables, n_classes)
The standardized coefficients.
- raw : DataFrame of shape (n_variables+1, n_classes)
The raw coefficients.
- projection : DataFrame of shape (n_variables+1, n_classes)
The projection coefficients.
ind_ : NamedTuple
Individuals informations:
- scores : DataFrame of shape (n_samples, n_classes)
The scores of individuals.
- projection : DataFrame of shape (n_samples, n_classes)
The projection of individuals.
model_ : str, default = 'mda'
The model fitted.
pipe_ : a sequence of data transformers with two named_steps :
- mpca : mixed principal components analysis (MPCA)
- lda : linear discriminant analysis (LDA)
See also
--------
:class:`~discrimintools.GFA`
General Factor Analysis (GFA)
:class:`~discrimintools.GFALDA`
General Factor Analysis Linear Discriminant Analysis (GFALDA)
:class:`~discrimintools.MPCA`
Mixed Principal Component Analysis (MPCA)
:class:`~discrimintools.summaryGFA`
Printing summaries of General Factor Analysis model.
:class:`~discrimintools.summaryGFALDA`
Printing summaries of General Factor Analysis Linear Discriminant Analysis model.
:class:`~discrimintools.summaryMDA`
Printing summaries of Mixed Discriminant Analysis model.
:class:`~discrimintools.summaryMPCA`
Printing summaries of Mixed Principal Component Analysis model.
References
----------
[1] Abdesselam, R. (2006), « `Mixed principal component analysis`_ ». In M. Nadif & F. X. Jollis (Eds), Actes des XIIIémes Rencontres SFC-2006 (pp. 27-31). Metz, France.
[2] Abdesselam, R. (2010), « `Discriminant Analysis on Mixed Predictors`_ ».
.. _Mixed principal component analysis: https://perso.univ-lyon2.fr/~rabdesse/fr/Publications/IFCS-2006.pdf
.. _Discriminant Analysis on Mixed Predictors: https://perso.univ-lyon2.fr/~rabdesse/fr/Publications/ADMixte.pdf
See also
--------
Examples
--------
>>> from discrimintools.datasets import load_dataset
>>> from discrimintools import MDA
>>> D = load_dataset("heart") # load training data
>>> y, X = D["disease"], D.drop(columns=["disease"]) # split into X and y
>>> clf = MDA(n_components=5)
>>> clf.fit(X,y)
MDA(n_components=5)
```
"""
[docs]
def __init__(
self, n_components = 2, priors = None, classes = False
):
self.n_components = n_components
self.priors = priors
self.classes = classes
def decision_function(self,X) -> DataFrame:
"""
Apply decision function to an input data
Parameters
----------
X : DataFrame of shape (n_samples, n_features)
Input data, where ``n_samples`` is the number of samples and ``n_features`` is the number of features.
Returns
-------
C : DataFrame of shape (n_samples, n_classes)
Decision function values related to each class, per sample.
"""
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
#check if the estimator is fitted by verifying the presence of fitted attributes
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
check_is_fitted(self)
return self.pipe_.decision_function(X)
def fit(self,X,y) -> DataFrame:
"""
Fit the Mixed Discriminant Analysis model
Parameters
----------
X : DataFrame of shape (n_samples, n_features)
Training Data, where ``n_samples`` is the number of samples and ``n_columns`` is the number of features.
y : Series of shape (n_samples,).
Target values. True labels for ``X``.
Returns
-------
self : object
Fitted estimator
"""
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
#mixed discriminant analysis (MDA)
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
self.pipe_ = Pipeline([("mpca",MPCA(n_components=self.n_components)),
("lda",DISCRIM(method='linear',priors=self.priors,classes=self.classes,warn_message=False))]).fit(X, y)
#extract separate fitted models
mpca, clf = self.pipe_["mpca"], self.pipe_["lda"]
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
#canonical discriminant coefficients
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
#total-sample standardized canonical coefficients
std_cancoef = DataFrame(mpca.svd_.V,index=mpca.var_.coord.index,columns=mpca.var_.coord.columns)
#total-sample raw (unstandardized) canonical coefficients
raw_cancoef = concat((std_cancoef.T.dot(-(mpca.call_.center + mpca.call_.xc_center)/mpca.call_.xc_scale).to_frame("Constant").T, std_cancoef.div(mpca.call_.xc_scale,axis=0)),axis=0)
#projection function coefficients
proj_cancoef = mpca.var_.coord.div(mpca.call_.denom,axis=0).div(mpca.svd_.vs[:mpca.call_.n_components],axis=1)
#convert to ordered dictionary
cancoef_ = OrderedDict(standardized=std_cancoef,raw=raw_cancoef,projection=proj_cancoef)
#convert to namedtuple
self.cancoef_ = namedtuple("cancoef",cancoef_.keys())(*cancoef_.values())
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
##classification functions
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
#standardize coefficients
std_coef = concat((clf.coef_.iloc[0,:].to_frame().T,std_cancoef.dot(clf.coef_.iloc[1:,:])),axis=0)
#concatenate
raw_coef = raw_cancoef.dot(clf.coef_.iloc[1:,:])
#add constant to canonical constant
raw_coef.iloc[0,:] = raw_coef.iloc[0,:].to_frame().T.add(clf.coef_.iloc[0,:].to_frame().T,axis=1)
#using projection
proj_coef = concat((clf.coef_.iloc[0,:].to_frame().T,proj_cancoef.dot(clf.coef_.iloc[1:,:])),axis=0)
#convert to ordered dictionary
coef_ = OrderedDict(standardized=std_coef,raw=raw_coef,projection=proj_coef)
#convert to namedtuple
self.coef_ = namedtuple("coef",coef_.keys())(*coef_.values())
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
##Individuals informations
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
#score with unstandardized coefficients
ind_ustd_scores = mpca.call_.Xcod.dot(raw_coef.iloc[1:,:]).add(raw_coef.iloc[0,:].values,axis=1)
#score with unstandardized coefficients
ind_proj_scores = mpca.call_.Xcod.dot(proj_coef.iloc[1:,:]).add(proj_coef.iloc[0,:].values,axis=1)
#convert to ordered dictionary
ind_ = OrderedDict(scores=ind_ustd_scores,projection=ind_proj_scores)
#convert to namedtuple
self.ind_ = namedtuple("ind",ind_.keys())(*ind_.values())
#convert to ordered dictionary
call_ = OrderedDict(Xtot=X,X=X,y=y,target=clf.call_.target,features=list(X.columns),classes=clf.call_.classes,priors=clf.call_.priors,n_samples=clf.call_.n_samples,n_features=clf.call_.n_features,n_classes=clf.call_.n_classes,
max_components = mpca.call_.max_components,n_components=mpca.call_.n_components)
#convert to namedtuple
self.call_ = namedtuple("call",call_.keys())(*call_.values())
#set model name
self.model_ = "mda"
return
def fit_transform(self,X,y) -> DataFrame:
"""
Fit to data, then transform it
Parameters
----------
X : DataFrame of shape (n_samples, n_features)
Training Data, where ``n_samples`` is the number of samples and ``n_features`` is the number of features.
y : Series of shape (n_samples,)
Target values. True labels for ``X``.
Returns
-------
X_new : DataFrame of shape (n_samples, n_classes)
Transformed data, where ``n_samples`` is the number of samples and ``n_classes`` is the number of classes
"""
self.fit(X,y)
return self.ind_.scores
def transform(self,X) -> DataFrame:
"""
Project data to maximize class separation
Parameters
----------
X : DataFrame of shape (n_samples, n_features)
New data, where ``n_samples`` is the number of samples and ``n_features`` is the number of features.
Returns
-------
X_new : DataFrame of shape (n_samples, n_classes)
Transformed data, where ``n_classes`` is the number of classes.
"""
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
#check if the estimator is fitted by verifying the presence of fitted attributes
#---------------------------------------------------------------------------------------------------------------------------------------------------------------------
check_is_fitted(self)
return self.pipe_.transform(X)
