PLSLDA - breast dataset

#disable warnings
from warnings import simplefilter, filterwarnings
simplefilter(action='ignore', category=FutureWarning)
filterwarnings("ignore")

breast dataset

#alcools dataset
from discrimintools.datasets import load_dataset
D = load_dataset("breast")
D.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 699 entries, 0 to 698
Data columns (total 4 columns):
 #   Column     Non-Null Count  Dtype
---  ------     --------------  -----
 0   ucellsize  699 non-null    int64
 1   normnucl   699 non-null    int64
 2   mitoses    699 non-null    int64
 3   Class      699 non-null    object
dtypes: int64(3), object(1)
memory usage: 22.0+ KB

#split into X and y
y, X = D["Class"], D.drop(columns=["Class"])

Instanciation and training

#instanciation and training
from discrimintools import PLSLDA
clf = PLSLDA()
clf.fit(X,y)

PLSLDA()

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Canonical coefficients

#canonical coefficients
cancoef = clf.cancoef_
cancoef._fields

('standardized', 'raw')

Standardized canonical coefficients

#standardized canonical coefficients
print(cancoef.standardized)

               Can1      Can2
ucellsize  0.702554 -0.605737
normnucl   0.611795  0.025466
mitoses    0.363490  0.803929

Raw canonical coefficients

#raw canonical coefficients
print(cancoef.raw)

               Can1      Can2
Constant  -1.632918 -0.146717
ucellsize  0.230235 -0.198507
normnucl   0.200350  0.008340
mitoses    0.211938  0.468742

Coefficients

#coefficients
coef = clf.coef_
coef._fields

('standardized', 'raw')

Standardized coefficients

#standardized coefficients
print(coef.standardized)

           negative  positive
Constant  -1.022831 -3.231980
ucellsize -1.302482  2.475256
normnucl  -0.813468  1.545927
mitoses   -0.025749  0.048934

Raw coefficients

#raw coefficients
print(coef.raw)

           negative  positive
Constant   1.102686 -7.271345
ucellsize -0.426839  0.811171
normnucl  -0.266394  0.506258
mitoses   -0.015013  0.028531

Summary

#summary
from discrimintools import summaryPLSLDA
summaryPLSLDA(clf,detailed=True)

                     Partial Least Squares Linear Discriminant Analysis - Results

Class Level Information:
          Frequency  Proportion  Prior Probability
negative        458      0.6552             0.6552
positive        241      0.3448             0.3448

Importance of PLS components:
      Proportion (%)  Cumulative (%)
Can1         69.1520         69.1520
Can2         20.1981         89.3501

Raw Canonical and Classification Functions Coefficients:
             Can1    Can2  negative  positive
Constant  -1.6329 -0.1467    1.1027   -7.2713
ucellsize  0.2302 -0.1985   -0.4268    0.8112
normnucl   0.2003  0.0083   -0.2664    0.5063
mitoses    0.2119  0.4687   -0.0150    0.0285

Multivariate Analysis of Variance (MANOVA) Summary:
          Statistic     Value  p-value
0     Wilks' Lambda    0.3042      NaN
1  Bartlett -- C(2)  828.2718      0.0
2   Rao -- F(2,696)  795.9566      0.0

LDA Classification functions & Statistical Evaluation:
          negative  positive  Wilks' Lambda  Partial R-Square    F Value  \
Constant   -1.0228   -3.2320            NaN               NaN        NaN
Can1       -1.3538    2.5728         0.9666            0.3147  1515.4447
Can2        0.5801   -1.1024         0.3376            0.9010    76.4684

          Num DF  Den DF  Pr>F
Constant     NaN     NaN   NaN
Can1         1.0   696.0   0.0
Can2         1.0   696.0   0.0

Classification Summary for Calibration Data:

Observation Profile:
                        Read  Used
Number of Observations   699   699

Number of Observations Classified into Class:
prediction  negative  positive  Total
Class
negative         447        11    458
positive          55       186    241
Total            502       197    699

Percent Classified into Class:
prediction  negative  positive  Total
Class
negative     97.5983    2.4017  100.0
positive     22.8216   77.1784  100.0
Total        71.8169   28.1831  100.0
Priors        0.6552    0.3448    NaN

Error Count Estimates for Class:
        negative  positive   Total
Rate      0.0240    0.2282  0.0944
Priors    0.6552    0.3448     NaN

Classification Report for Class:
              precision  recall  f1-score   support
negative         0.8904  0.9760    0.9312  458.0000
positive         0.9442  0.7718    0.8493  241.0000
accuracy         0.9056  0.9056    0.9056    0.9056
macro avg        0.9173  0.8739    0.8903  699.0000
weighted avg     0.9090  0.9056    0.9030  699.0000

Plotting

#plotting
from discrimintools import fviz_plsr

Graph of individuals

#graph of individuals
p = fviz_plsr(clf,element="ind",repel=False)
p.show()

Graph of variables

#graph of variables
p = fviz_plsr(clf,element="var",repel=True)
p.show()

Distance between barycenter

#distance between barycenter
p = fviz_plsr(clf,element="dist",repel=False,y_lim=(-0.2,0.15))
p.show()