Part 1 of the video about the logistic regressor as classificator.

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Readme.md

from sklearn import datasets
iris = datasets.load_iris()
print(iris.DESCR)

.. _iris_dataset:

Iris plants dataset
--------------------

**Data Set Characteristics:**

:Number of Instances: 150 (50 in each of three classes)
:Number of Attributes: 4 numeric, predictive attributes and the class
:Attribute Information:
    - sepal length in cm
    - sepal width in cm
    - petal length in cm
    - petal width in cm
    - class:
            - Iris-Setosa
            - Iris-Versicolour
            - Iris-Virginica

:Summary Statistics:

============== ==== ==== ======= ===== ====================
                Min  Max   Mean    SD   Class Correlation
============== ==== ==== ======= ===== ====================
sepal length:   4.3  7.9   5.84   0.83    0.7826
sepal width:    2.0  4.4   3.05   0.43   -0.4194
petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)
petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)
============== ==== ==== ======= ===== ====================

:Missing Attribute Values: None
:Class Distribution: 33.3% for each of 3 classes.
:Creator: R.A. Fisher
:Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
:Date: July, 1988

The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken
from Fisher's paper. Note that it's the same as in R, but not as in the UCI
Machine Learning Repository, which has two wrong data points.

This is perhaps the best known database to be found in the
pattern recognition literature.  Fisher's paper is a classic in the field and
is referenced frequently to this day.  (See Duda & Hart, for example.)  The
data set contains 3 classes of 50 instances each, where each class refers to a
type of iris plant.  One class is linearly separable from the other 2; the
latter are NOT linearly separable from each other.

|details-start|
**References**
|details-split|

- Fisher, R.A. "The use of multiple measurements in taxonomic problems"
  Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to
  Mathematical Statistics" (John Wiley, NY, 1950).
- Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.
  (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.
- Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System
  Structure and Classification Rule for Recognition in Partially Exposed
  Environments".  IEEE Transactions on Pattern Analysis and Machine
  Intelligence, Vol. PAMI-2, No. 1, 67-71.
- Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule".  IEEE Transactions
  on Information Theory, May 1972, 431-433.
- See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al"s AUTOCLASS II
  conceptual clustering system finds 3 classes in the data.
- Many, many more ...

|details-end|

import matplotlib.pyplot as plt
import numpy as np

sl = iris.data[:,0:1]
sw = iris.data[:,1:2]
plt.plot(sl,sw, '.k')
plt.show()

iris.target

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])

Decision boundaries

import numpy as np 
import matplotlib.pyplot as plt
t = np.linspace(-10,10, 100)
sig = 1/(1+np.exp(-t-4))
plt.plot(t,sig, '.b', label=r"$\sigma$")
plt.legend(loc='upper left', fontsize =20)
plt.show()

Iris-Setosa Classifier based on petal width

X = iris.data[:,3:4]
y = (iris.target == 0).astype(int)

from sklearn.linear_model import LogisticRegression
mylr = LogisticRegression(solver='lbfgs', random_state=42)
mylr.fit(X,y)

LogisticRegression(random_state=42)

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LogisticRegression?Documentation for LogisticRegressioniFitted

LogisticRegression(random_state=42)

Xnew = np.linspace(-1,3,100).reshape(-1,1)
yPred = mylr.predict_proba(Xnew)
#plt.plot(Xnew,yPred[:,0], label='No Iris')
plt.plot(Xnew,yPred[:,1], label='Yes Iris')
plt.legend()
plt.plot(X,y,'og')
plt.show()

Iris-Setosa petal length

X = iris.data[:,2:3]
y = (iris.target == 0).astype(int)
from sklearn.linear_model import LogisticRegression
mylr = LogisticRegression(solver='lbfgs', random_state=42)
mylr.fit(X,y)

LogisticRegression(random_state=42)

LogisticRegression?Documentation for LogisticRegressioniFitted

LogisticRegression(random_state=42)

Xnew = np.linspace(0,8,100).reshape(-1,1)
yPred = mylr.predict_proba(Xnew)
#plt.plot(Xnew,yPred[:,0], label='No Iris')
plt.plot(Xnew,yPred[:,1], label='Yes Iris')
plt.legend()
plt.plot(X,y,'og')
plt.axis([1.5, 5, -0.1, 1.1])
plt.show()

Iris-Setosa Sepal-Length

X = iris.data[:,0:1]
y = (iris.target == 0).astype(int)
from sklearn.linear_model import LogisticRegression
mylr = LogisticRegression(solver='lbfgs', random_state=42)
mylr.fit(X,y)

LogisticRegression(random_state=42)

LogisticRegression?Documentation for LogisticRegressioniFitted

LogisticRegression(random_state=42)

Xnew = np.linspace(0,8,100).reshape(-1,1)
yPred = mylr.predict_proba(Xnew)
#plt.plot(Xnew,yPred[:,0], label='No Iris')
plt.plot(Xnew,yPred[:,1], label='Yes Iris')
plt.legend()
plt.plot(X,y,'og')
plt.axis([3.5, 7, -0.1, 1.1])
plt.show()

Multiple features classifier

import matplotlib.pyplot as plt
sl = iris.data[:,0:1]
sw = iris.data[:,1:2]
tg = iris.target
plt.plot(sl[tg==0,0], sw[tg==0,0],'.g' ,label='Set')
plt.plot(sl[tg==1,0], sw[tg==1,0],'.r', label='Ver')
plt.plot(sl[tg==2,0], sw[tg==2,0],'.b', label='Vir')
plt.legend()
plt.show()

from sklearn.linear_model import LogisticRegression
X = iris.data[:,0:2]
y = (iris.target==2).astype(int)

mylrvir = LogisticRegression(
    random_state=22,
    tol=1e-5,
    C=100,
    max_iter=100,
    solver='newton-cg'
)
mylrvir.fit(X,y)

LogisticRegression(C=100, random_state=22, solver='newton-cg', tol=1e-05)

LogisticRegression?Documentation for LogisticRegressioniFitted

LogisticRegression(C=100, random_state=22, solver='newton-cg', tol=1e-05)

import numpy as np
x0, x1 = np.meshgrid(
    np.linspace(3,8,100).reshape(-1,1),
    np.linspace(0,6,100).reshape(-1,1)
)
Xnew = np.c_[x0.ravel(), x1.ravel()]
yPred = mylrvir.predict_proba(Xnew)

plt.figure(figsize=(10,4))
plt.plot(X[y==0,0], X[y==0,1],'bs',label='No Virg')
plt.plot(X[y==1,0], X[y==1,1],'g^',label='Virginica')
zz=yPred[:,1].reshape(x0.shape)
contour=plt.contour(x0,x1,zz)
plt.clabel(contour, inline=1,fontsize=15)
plt.xlabel("Sepal Length")
plt.ylabel("Sepal Width")
plt.legend()
plt.show()

fig, ax =plt.subplots(subplot_kw={"projection": "3d"})
surf = ax.plot_surface(x0,x1,zz, cmap='jet')
ax.scatter(iris.data[:,0:1], iris.data[:,1:2], y, 'or')

<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x16c24cda0>

Multiple features and muticlass classifier

X = iris.data[:,0:2]
y = iris.target
lrmc = LogisticRegression(
    multi_class='multinomial',
    solver='lbfgs',
    C=100,
    random_state=22
)
lrmc.fit(X,y)

LogisticRegression(C=100, multi_class='multinomial', random_state=22)

LogisticRegression?Documentation for LogisticRegressioniFitted

LogisticRegression(C=100, multi_class='multinomial', random_state=22)

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])

import numpy as np
x0, x1 = np.meshgrid(
    np.linspace(3,8,100).reshape(-1,1),
    np.linspace(0,6,100).reshape(-1,1)
)
Xnew = np.c_[x0.ravel(), x1.ravel()]
yPred = lrmc.predict_proba(Xnew)

plt.figure(figsize=(10,4))
plt.plot(X[y==0,0], X[y==0,1],'.b',label='Setosa')
plt.plot(X[y==1,0], X[y==1,1],'+g',label='Versi')
plt.plot(X[y==2,0], X[y==2,1],'*m',label='Virgi')
zz=yPred[:,1].reshape(x0.shape)
contour=plt.contour(x0,x1,zz)
plt.clabel(contour, inline=1,fontsize=15)
plt.xlabel("Sepal Length")
plt.ylabel("Sepal Width")
plt.legend()
plt.show()

yPred = lrmc.predict(Xnew)
plt.figure(figsize=(10,6))
plt.plot(X[y==0,0], X[y==0,1],'bs',label='Setosa')
plt.plot(X[y==1,0], X[y==1,1],'g^',label='Versi')
plt.plot(X[y==2,0], X[y==2,1],'*m',label='Virgi')
zz=yPred.reshape(x0.shape)
contour=plt.contourf(x0,x1,zz, cmap='jet', alpha=0.3)
plt.clabel(contour, inline=1,fontsize=15)
plt.xlabel("Sepal Length")
plt.ylabel("Sepal Width")
plt.legend()
plt.show()

fig, ax =plt.subplots(subplot_kw={"projection": "3d"})
surf = ax.plot_surface(x0,x1,zz, cmap='jet')
#ax.scatter(iris.data[:,0:1], iris.data[:,1:2], y, 'or')