DiCA - divay dataset#
[1]:
#disable warnings
from warnings import simplefilter, filterwarnings
simplefilter(action='ignore', category=FutureWarning)
filterwarnings("ignore")
divay data#
[2]:
#vins dataset
from discrimintools.datasets import load_divay
D = load_divay()
D.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 12 entries, 0 to 11
Data columns (total 6 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Region 12 non-null object
1 Woody 12 non-null object
2 Fruity 12 non-null object
3 Sweet 12 non-null object
4 Alcohol 12 non-null object
5 Hedonic 12 non-null object
dtypes: object(6)
memory usage: 704.0+ bytes
[3]:
#display
print(D)
Region Woody Fruity Sweet Alcohol Hedonic
0 Loire Woody_A Fruity_C Sweet_B Alcohol_A Hedonic_A
1 Loire Woody_B Fruity_C Sweet_C Alcohol_B Hedonic_C
2 Loire Woody_A Fruity_B Sweet_B Alcohol_A Hedonic_B
3 Loire Woody_A Fruity_C Sweet_C Alcohol_B Hedonic_D
4 Rhone Woody_A Fruity_B Sweet_A Alcohol_C Hedonic_C
5 Rhone Woody_B Fruity_A Sweet_A Alcohol_C Hedonic_B
6 Rhone Woody_C Fruity_B Sweet_B Alcohol_B Hedonic_A
7 Rhone Woody_B Fruity_C Sweet_C Alcohol_C Hedonic_D
8 Beaujolais Woody_C Fruity_A Sweet_C Alcohol_A Hedonic_A
9 Beaujolais Woody_B Fruity_A Sweet_C Alcohol_A Hedonic_B
10 Beaujolais Woody_C Fruity_B Sweet_B Alcohol_B Hedonic_D
11 Beaujolais Woody_C Fruity_A Sweet_A Alcohol_A Hedonic_C
[4]:
#split into X and y
y, X = D["Region"], D.drop(columns=["Region"])
Instanciation & training#
[5]:
#instanciation and training
from discrimintools import DiCA
clf = DiCA(n_components=2)
`fit function#
[6]:
#fit function
clf.fit(X,y)
[6]:
DiCA()In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
Parameters
| n_components | 2 | |
| classes | None |
decision_function function#
[7]:
#decision_function function
print(clf.decision_function(X))
Beaujolais Loire Rhone
0 -2.046775 -1.129275 -2.076775
1 -1.716775 -1.129275 -1.506775
2 -1.593228 -1.125728 -1.623228
3 -2.163228 -1.125728 -1.953228
4 -2.330710 -2.093210 -1.200710
5 -1.976415 -2.638915 -1.296415
6 -1.241993 -1.404493 -1.361993
7 -1.984479 -1.546979 -1.174479
8 -1.171483 -2.203983 -2.221483
9 -1.109922 -1.692422 -1.709922
10 -1.241993 -1.404493 -1.361993
11 -1.183472 -2.415972 -1.913472
eval_predict function#
[8]:
#eval_predict function
evl = clf.eval_predict(X,y,verbose=True)
Observation Profile:
Read Used
Number of Observations 12 12
Number of Observations Classified into Region:
prediction Beaujolais Loire Rhone Total
Region
Beaujolais 4 0 0 4
Loire 0 4 0 4
Rhone 1 0 3 4
Total 5 4 3 12
Percent Classified into Region:
prediction Beaujolais Loire Rhone Total
Region
Beaujolais 100.000000 0.000000 0.000000 100.0
Loire 0.000000 100.000000 0.000000 100.0
Rhone 25.000000 0.000000 75.000000 100.0
Total 41.666667 33.333333 25.000000 100.0
Priors 0.333333 0.333333 0.333333 NaN
Error Count Estimates for Region:
Beaujolais Loire Rhone Total
Rate 0.000000 0.000000 0.250000 0.083333
Priors 0.333333 0.333333 0.333333 NaN
Classification Report for Region:
precision recall f1-score support
Beaujolais 0.800000 1.000000 0.888889 4.000000
Loire 1.000000 1.000000 1.000000 4.000000
Rhone 1.000000 0.750000 0.857143 4.000000
accuracy 0.916667 0.916667 0.916667 0.916667
macro avg 0.933333 0.916667 0.915344 12.000000
weighted avg 0.933333 0.916667 0.915344 12.000000
fit_transform function#
[9]:
#fit_transform function
print(clf.fit_transform(X,y))
Can1 Can2
0 -0.819841 -0.423303
1 -0.499227 -0.045801
2 -0.427087 -0.248651
3 -0.891982 -0.220453
4 -0.068806 1.046165
5 0.655588 0.927798
6 0.110547 -0.097673
7 -0.286823 0.635976
8 0.743569 -0.726531
9 0.411929 -0.433513
10 0.110547 -0.097673
11 0.961586 -0.316342
pred_table function#
[10]:
#pred_table function
print(clf.pred_table(X,y))
prediction Beaujolais Loire Rhone
Region
Beaujolais 4 0 0
Loire 0 4 0
Rhone 1 0 3
predict function#
[11]:
#predict function
print(clf.predict(X))
0 Loire
1 Loire
2 Loire
3 Loire
4 Rhone
5 Rhone
6 Beaujolais
7 Rhone
8 Beaujolais
9 Beaujolais
10 Beaujolais
11 Beaujolais
Name: prediction, dtype: object
predict_log_proba function#
[12]:
#predict_log_prob function
print(clf.predict_log_proba(X))
Beaujolais Loire Rhone
0 -1.498165 -0.580665 -1.528165
1 -1.394551 -0.807051 -1.184551
2 -1.271569 -0.804069 -1.301569
3 -1.620542 -0.583042 -1.410542
4 -1.679660 -1.442160 -0.549660
5 -1.249741 -1.912241 -0.569741
6 -1.006839 -1.169339 -1.126839
7 -1.567936 -1.130436 -0.757936
8 -0.534183 -1.566683 -1.584183
9 -0.745413 -1.327913 -1.345413
10 -1.006839 -1.169339 -1.126839
11 -0.572939 -1.805439 -1.302939
predic_proba function#
[13]:
#predict_proba function
print(clf.predict_proba(X))
Beaujolais Loire Rhone
0 0.223540 0.559526 0.216933
1 0.247944 0.446172 0.305884
2 0.280391 0.447504 0.272104
3 0.197791 0.558198 0.244011
4 0.186437 0.236417 0.577146
5 0.286579 0.147749 0.565672
6 0.365372 0.310572 0.324056
7 0.208475 0.322892 0.468633
8 0.586148 0.208736 0.205115
9 0.474538 0.265030 0.260432
10 0.365372 0.310572 0.324056
11 0.563866 0.164402 0.271732
score function#
[14]:
#score function
print("Accurary = {}%".format(round(100*clf.score(X,y))))
Accurary = 92%
transform function#
[15]:
#transform function
print(clf.transform(X))
Can1 Can2
0 -0.819841 -0.423303
1 -0.499227 -0.045801
2 -0.427087 -0.248651
3 -0.891982 -0.220453
4 -0.068806 1.046165
5 0.655588 0.927798
6 0.110547 -0.097673
7 -0.286823 0.635976
8 0.743569 -0.726531
9 0.411929 -0.433513
10 0.110547 -0.097673
11 0.961586 -0.316342
Canonical coefficients#
[16]:
#canonical coefficients
cancoef = clf.cancoef_
for i, k in enumerate(cancoef._fields):
print("\n{} coefficients".format(k))
print(cancoef[i].round(3))
standardized coefficients
Can1 Can2
Woody_A -1.862 -0.094
Woody_B 0.102 0.779
Woody_C 1.760 -0.686
Fruity_A 1.760 -0.686
Fruity_B 0.102 0.779
Fruity_C -1.862 -0.094
Sweet_A 1.009 1.427
Sweet_B -0.655 -0.291
Sweet_C -0.081 -0.624
Alcohol_A 0.279 -1.638
Alcohol_B -0.655 -0.291
Alcohol_C 0.407 3.118
Hedonic_A -0.000 -0.000
Hedonic_B -0.000 -0.000
Hedonic_C -0.000 -0.000
Hedonic_D -0.000 -0.000
projection coefficients
Can1 Can2
Woody_A -0.372 -0.019
Woody_B 0.020 0.156
Woody_C 0.352 -0.137
Fruity_A 0.352 -0.137
Fruity_B 0.020 0.156
Fruity_C -0.372 -0.019
Sweet_A 0.202 0.285
Sweet_B -0.131 -0.058
Sweet_C -0.016 -0.125
Alcohol_A 0.056 -0.328
Alcohol_B -0.131 -0.058
Alcohol_C 0.081 0.624
Hedonic_A -0.000 -0.000
Hedonic_B -0.000 -0.000
Hedonic_C -0.000 -0.000
Hedonic_D -0.000 -0.000
summary#
[17]:
#summary
from discrimintools import summaryDiCA
summaryDiCA(clf, detailed=True)
Discriminant Correspondence Analysis - Results
Class Level Information:
Frequency Proportion Prior Probability
Beaujolais 4 0.3333 0.3333
Loire 4 0.3333 0.3333
Rhone 4 0.3333 0.3333
Importance of components:
Eigenvalue Difference Proportion (%) Cumulative (%)
Can1 0.2519 0.0504 55.5635 55.5635
Can2 0.2014 NaN 44.4365 100.0000
Canonical correlation:
Eigenvalue Total SS Eta Sq. Canonical Correlation
Can1 0.2519 4.0879 0.7394 0.8599
Can2 0.2014 3.4864 0.6934 0.8327
Classification (projection) coefficients:
Can1 Can2
Woody_A -0.3724 -0.0188
Woody_B 0.0204 0.1559
Woody_C 0.3520 -0.1371
Fruity_A 0.3520 -0.1371
Fruity_B 0.0204 0.1559
Fruity_C -0.3724 -0.0188
Sweet_A 0.2017 0.2855
Sweet_B -0.1309 -0.0582
Sweet_C -0.0163 -0.1247
Alcohol_A 0.0558 -0.3276
Alcohol_B -0.1309 -0.0582
Alcohol_C 0.0815 0.6236
Hedonic_A -0.0000 -0.0000
Hedonic_B -0.0000 -0.0000
Hedonic_C -0.0000 -0.0000
Hedonic_D -0.0000 -0.0000
Classification Summary for Calibration Data:
Observation Profile:
Read Used
Number of Observations 12 12
Number of Observations Classified into Region:
prediction Beaujolais Loire Rhone Total
Region
Beaujolais 4 0 0 4
Loire 0 4 0 4
Rhone 1 0 3 4
Total 5 4 3 12
Percent Classified into Region:
prediction Beaujolais Loire Rhone Total
Region
Beaujolais 100.0000 0.0000 0.0000 100.0
Loire 0.0000 100.0000 0.0000 100.0
Rhone 25.0000 0.0000 75.0000 100.0
Total 41.6667 33.3333 25.0000 100.0
Priors 0.3333 0.3333 0.3333 NaN
Error Count Estimates for Region:
Beaujolais Loire Rhone Total
Rate 0.0000 0.0000 0.2500 0.0833
Priors 0.3333 0.3333 0.3333 NaN
Classification Report for Region:
precision recall f1-score support
Beaujolais 0.8000 1.0000 0.8889 4.0000
Loire 1.0000 1.0000 1.0000 4.0000
Rhone 1.0000 0.7500 0.8571 4.0000
accuracy 0.9167 0.9167 0.9167 0.9167
macro avg 0.9333 0.9167 0.9153 12.0000
weighted avg 0.9333 0.9167 0.9153 12.0000
Evaluation of prediction on testing dataset#
[18]:
#test data
XTest = load_divay("test")
print(XTest.info())
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1 entries, 0 to 0
Data columns (total 5 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Woody 1 non-null object
1 Fruity 1 non-null object
2 Sweet 1 non-null object
3 Alcohol 1 non-null object
4 Hedonic 1 non-null object
dtypes: object(5)
memory usage: 168.0+ bytes
None
[19]:
#display test data
print(XTest)
Woody Fruity Sweet Alcohol Hedonic
0 Woody_A Fruity_C Sweet_B Alcohol_B Hedonic_A
Coordinates of new individuals#
[20]:
#coordinates of new individuals
print(clf.transform(XTest))
Can1 Can2
0 -1.006603 -0.153958
Prediction on new individuals#
[21]:
#predict on supplementary
print(clf.predict(XTest))
0 Loire
Name: prediction, dtype: object
Correspondence Analysis#
Eigenvalues#
[22]:
#eigenvalues
print(clf.eig_)
Eigenvalue Difference Proportion (%) Cumulative (%)
Can1 0.251888 0.050442 55.56351 55.56351
Can2 0.201445 NaN 44.43649 100.00000
Classes#
[23]:
#classes
classes = clf.classes_
classes._fields
[23]:
('infos', 'coord', 'eucl', 'gen')
Classes level informations#
[24]:
#classes level information
print(classes.infos)
Frequency Proportion Prior Probability
Beaujolais 4 0.333333 0.333333
Loire 4 0.333333 0.333333
Rhone 4 0.333333 0.333333
Classes coordinates#
[25]:
#classes coordinates
print(classes.coord)
Can1 Can2
Beaujolais 0.556908 -0.393515
Loire -0.659534 -0.234552
Rhone 0.102626 0.628067
Classes squared euclidean distance#
[26]:
#classes squared euclidean distance
print(classes.eucl)
Beaujolais Loire Rhone
Beaujolais 0.000 1.505 1.250
Loire 1.505 0.000 1.325
Rhone 1.250 1.325 0.000
Classes generalized squared distance#
[27]:
#classes generalized squared distance
print(classes.gen)
Beaujolais Loire Rhone
Beaujolais 2.197225 3.702225 3.447225
Loire 3.702225 2.197225 3.522225
Rhone 3.447225 3.522225 2.197225
Variables#
[28]:
#variables
var = clf.var_
var._fields
[28]:
('coord', 'eta2')
Variables coordinates#
[29]:
#variables coordinates
print(var.coord)
Can1 Can2
Woody_A -9.344663e-01 -4.210386e-02
Woody_B 5.112059e-02 3.498381e-01
Woody_C 8.833457e-01 -3.077342e-01
Fruity_A 8.833457e-01 -3.077342e-01
Fruity_B 5.112059e-02 3.498381e-01
Fruity_C -9.344663e-01 -4.210386e-02
Sweet_A 5.061994e-01 6.406472e-01
Sweet_B -3.285290e-01 -1.306473e-01
Sweet_C -4.089647e-02 -2.798705e-01
Alcohol_A 1.401338e-01 -7.350936e-01
Alcohol_B -3.285290e-01 -1.306473e-01
Alcohol_C 2.044823e-01 1.399352e+00
Hedonic_A -2.543383e-32 -6.351547e-32
Hedonic_B -2.543383e-32 -6.351547e-32
Hedonic_C -2.543383e-32 -6.351547e-32
Hedonic_D -2.543383e-32 -6.351547e-32
Variables squared correlation ratio#
[30]:
#variables squared correlation ratio
print(var.eta2)
Can1 Can2
Woody 0.529840 0.195969
Fruity 0.856351 0.047788
Sweet 0.273208 0.352479
Alcohol 0.128115 0.931320
Hedonic 0.139224 0.208958
Individuals#
[31]:
#individuals
ind = clf.ind_
ind._fields
[31]:
('coord', 'eucl', 'gen')
Individuals coordinates#
[32]:
#individuals coordinates
print(ind.coord)
Can1 Can2
0 -0.819841 -0.423303
1 -0.499227 -0.045801
2 -0.427087 -0.248651
3 -0.891982 -0.220453
4 -0.068806 1.046165
5 0.655588 0.927798
6 0.110547 -0.097673
7 -0.286823 0.635976
8 0.743569 -0.726531
9 0.411929 -0.433513
10 0.110547 -0.097673
11 0.961586 -0.316342
Individuals squared euclidean distance#
[33]:
#individuals squared euclidean distance
print(ind.eucl)
Beaujolais Loire Rhone
0 1.896325 0.061325 1.956325
1 1.236325 0.061325 0.816325
2 0.989231 0.054231 1.049231
3 2.129231 0.054231 1.709231
4 2.464195 1.989195 0.204195
5 1.755606 3.080606 0.395606
6 0.286761 0.611761 0.526761
7 1.771733 0.896733 0.151733
8 0.145742 2.210742 2.245742
9 0.022619 1.187619 1.222619
10 0.286761 0.611761 0.526761
11 0.169720 2.634720 1.629720
Individuals generalized squared distance#
[34]:
#individuals generalized squared dsistance
print(ind.gen)
Beaujolais Loire Rhone
0 4.093550 2.258550 4.153550
1 3.433550 2.258550 3.013550
2 3.186455 2.251455 3.246455
3 4.326455 2.251455 3.906455
4 4.661420 4.186420 2.401420
5 3.952831 5.277831 2.592831
6 2.483985 2.808985 2.723985
7 3.968958 3.093958 2.348958
8 2.342967 4.407967 4.442967
9 2.219843 3.384843 3.419843
10 2.483985 2.808985 2.723985
11 2.366945 4.831945 3.826945
Discriminat analysis#
Canonical coefficients#
[35]:
#canonical coefficients
cancoef = clf.cancoef_
cancoef._fields
[35]:
('standardized', 'projection')
Standardized canonical coefficients#
[36]:
#standardized canonical coefficients
print(cancoef.standardized)
Can1 Can2
Woody_A -1.861916e+00 -9.380873e-02
Woody_B 1.018573e-01 7.794502e-01
Woody_C 1.760058e+00 -6.856415e-01
Fruity_A 1.760058e+00 -6.856415e-01
Fruity_B 1.018573e-01 7.794502e-01
Fruity_C -1.861916e+00 -9.380873e-02
Sweet_A 1.008598e+00 1.427382e+00
Sweet_B -6.545910e-01 -2.910863e-01
Sweet_C -8.148584e-02 -6.235602e-01
Alcohol_A 2.792152e-01 -1.637811e+00
Alcohol_B -6.545910e-01 -2.910863e-01
Alcohol_C 4.074292e-01 3.117801e+00
Hedonic_A -5.067666e-32 -1.415145e-31
Hedonic_B -5.067666e-32 -1.415145e-31
Hedonic_C -5.067666e-32 -1.415145e-31
Hedonic_D -5.067666e-32 -1.415145e-31
Projection canonical coefficients#
[37]:
#projection canonical coefficients
print(cancoef.projection)
Can1 Can2
Woody_A -3.723831e-01 -1.876175e-02
Woody_B 2.037146e-02 1.558900e-01
Woody_C 3.520117e-01 -1.371283e-01
Fruity_A 3.520117e-01 -1.371283e-01
Fruity_B 2.037146e-02 1.558900e-01
Fruity_C -3.723831e-01 -1.876175e-02
Sweet_A 2.017195e-01 2.854764e-01
Sweet_B -1.309182e-01 -5.821726e-02
Sweet_C -1.629717e-02 -1.247120e-01
Alcohol_A 5.584305e-02 -3.275623e-01
Alcohol_B -1.309182e-01 -5.821726e-02
Alcohol_C 8.148584e-02 6.235602e-01
Hedonic_A -1.013533e-32 -2.830289e-32
Hedonic_B -1.013533e-32 -2.830289e-32
Hedonic_C -1.013533e-32 -2.830289e-32
Hedonic_D -1.013533e-32 -2.830289e-32
plotting#
[38]:
from discrimintools import fviz_dica
Graph of individuals#
[39]:
#graph of individuals
p = fviz_dica(clf,element="ind",repel=True)
p.show()
we add supplementary individuals
[40]:
#with supplementary individuals
from discrimintools import add_scatter
p = add_scatter(p,clf.transform(XTest),color="blue",repel=True)
print(p.show())
None
Graph of variables/categories#
[41]:
#graph of variables/categories
p = fviz_dica(clf,element="var",repel=True)
p.show()
7 [0.80808934 0.18000401]
10 [0.17267555 0.31122708]
12 [-0.38605933 -0.84780643]
13 [-0.93712423 0.78493652]
14 [ 0.04563277 -0.59299836]
15 [ 0.58311963 -0.64587052]
1 [-0.82428 0.52043105]
4 [-0.71021836 -0.06343767]
2 [ 0.24321259 -0.12849718]
3 [0.11850763 0.87743293]
Biplot of individuals and variables/categories#
[42]:
#biplot of individuals and variables/categories
p = fviz_dica(clf,element="var",repel=False)
p.show()
Graph of qualitative variables#
[43]:
#graph of qualitative variables
p = fviz_dica(clf,element="quali_var",repel=True)
p.show()
Distance between barycenter#
[44]:
#Distance between barycenter
p = fviz_dica(clf,element="ind",repel=True)
p.show()
